Financial Math Study Guide Notes #2

Financial Math NotesConsumer CreditIdentify the costs, benefits, and sources of various types of credit.Revolving Credit: a form of credit where the person borrowing money can continuously borrow money up until a certain limit that is initially agreed upon. The costs involved with revolving credit are usually interest that builds up over time and certain fees that need to be paid, such as annual fees or fees for late payments. A poor repayment rate can also result in a poor credit score. Revolving credit is mostly found in credit cards and other credit lines. The benefits of revolving credit involve a high flexibility, as money can be easily accessible and borrowed without the need for an approval process that could take a long time. Revolving credit can be paid back slowly without needing to pay it completely in full, giving it great flexibility in payments. Revolving credit also can have perks such as points or cash back (usually for credit cards) as well as building up a good credit score. This form of credit is generally safe from fraud, and does not need any collateral to obtain.Open-End Credit: a form of credit where the borrower can access a certain limit of credit but must pay it back by an agreed upon date (usually monthly). Some examples of open credit are charge cards and collection accounts. The costs of open-end credit are the required paying-back in full of the borrowed amount by the date, which creates a time limit, which can cause debt to accumulate and credit scores to plummet. The benefits of open-end credit is that if paid back in time, it usually does not give any interest to the borrower, which can help save money compared to other methods with interest. It is also very flexible, as if the borrower is able to consistently pay back their balances, they can borrow money fast and efficiently. Installment Credit: a form of credit where a borrower receives all the money upfront, and is required to pay the money back in regular installments over a period of time. (usually months) Installment credit is found very commonly in loans and mortgages, which require money to be paid back over a long period of time. Installment credit has the costs of having lower flexibility due to the limited amount of funds provided at the start, as well as the possibility of going into heavy debt if payments are not paid back in time. The benefits of installment credit are the low and fixed interest rates, which allow borrowers to plan out how much money they need to pay for each payment. This method also allows for credit scores to build up over time if payments are made. Calculate sales tax and computer total price with sales tax.Sales tax is usually calculated by multiplying the final purchase price with the percentage of tax that is being charged. A formula for this can be (Purchase Price * Sales Tax Rate/100) where the sales tax rate is not already converted into a percentage. The second part of the prompt is asking for a computer total price, so I am guessing that it is asking to calculate the price of a computer with sales tax. To calculate this, first find the price of the computer, and use the equation listed above with the sales tax rate to determine the sales tax. Finally, add the sales tax and computer price to find the total price with tax. Compute total purchase price with interest/finance charges addedThe total purchase price of an item or object includes the selling price of the item, as well as interest or finance charges. To find this price, first add the selling price of the item. To calculate the interest, multiply the price by tax rate/100, and add it to the total price. Finance charges are charges usually involved with service or payment for labor. This is not subject to taxes, so adding it to the previous selling price and interest will determine the total purchase price.Compute the costs involved in owning and buying an item such as an automobile, appliances, home, or furniture.Everything purchased comes with its initial purchase price. This price is subject to taxes, which should be calculated with the interest formula (rate/100) with the purchase price. There are also miscellaneous fees, such as maintenance of quality and repairs, insurance, and deprecation over time. Homes usually have payment plans for utilities such as electricity, water, etc. Appliances can involve electricity bills and fees to install. Automobiles can have prices for fuel and registration. All of these can be subject to finance charges if paid for on a loan or credit. Compute finance charges for single payment loans.When loans are taken out for single payment, there are a variety of factors that lead to charges above the borrowed amount. There is always interest, which is extra money paid on top of the principal in exchange for the loan and time to pay it off over a longer period of time. The term of the loan can determine finance charges, as short term loans usually have a higher interest rate compared to a long term one. There are also prices in fees, such as for processing that need to be financed on top of the principal.6. Calculate installment loan costs such as amount financed, installment price, finance charge, and installment payment.The amount financed is the principal of the loan, or how much it originally was worth/needed to be paid back. The installment price is the total amount of money that the borrower will pay over the length of the loan, including extra finance charges. Finance charges are extra fees such as interest and one time fees that are included in the loan. The installment payment is the fixed amount of money a borrower will pay to the loaner in intervals agreed upon. Installment loans usually will cost more than the amount financed, and will usually be the installment price due to interest and fees. The total amount of money paid above the amount financed can be calculated by the formula Total=Amount Financed - installment price. The installment payment can be determined by finding the total installment price needed, and dividing it by the intervals of the terms of the loan to find the (usually) monthly payment. Find the estimated annual percentage rate (APR) using a table.On an APR table, we need to find the principal loan value, terms of the loan, and the amount of monthly payments. A column on the left usually notes monthly payments, which you would need to find the value for the loan you are working on. For rows, you would need to look for the row that is closest to the amount of the loan you are, or looking for the monthly payment that matches yours the closest. When found, find the intersection where the row and column crosses, then look at the top for the APR. Compare costs of leasing and buying.The main difference between leasing and buying is that buying gives you ownership of the item, while leasing only loans you that item for a specified period of time. To elaborate, buying something means financing the full price for the item, including taxes and interest for an item. After this purchase, you are liable for all damages and deprecation amounts over time. In contrast, a lease, you are paying for the rental and deprecation of the item you are using. However, the item won't be under your ownership, and will likely have to be returned at the end of the agreed upon term. Major damages will be paid for by the leaser instead of the customer. Find the finance charge and new balance using the average daily balance method.The average daily balance method utilizes a method to find the total amount of interest charges by multiplying the credit balance daily with the credit's finance charge, or APR. In this method, you can add up all the daily balances for a period of time, and divide it by the amount of days in that time. This will give you the average of the balance you have, which can be used to predict and find interest charges for credit.Read amortization tables to determine payment, interest and balance.You can determine interest by using the remaining loan balance of an amortization table by the interest rate, and then dividing by 12 again if you want the interest for the month. The principal payment amount per month can be found by subtracting the interest from the monthly payment for the principal per month. The balance can be found by subtracting the principal from the remaining loan balance, helping to find the updated balance. Compute Annual and monthly Percentage Rate for credit cards or loan.The monthly percentage rates for credit cards and loans can be found by dividing the interest rate per year by 12, which will find the monthly percentage rate as a part of the entire interest rate. Similarly, the annual percentage rate is just the interest rate multiplied by the principal. To find the rates from an amount, divide the interest payment from the principal, and by 12 to find monthly rates. Find the monthly mortgage payment.Monthly mortgage payments can be found with the total amount owed, period of payment, and interest. First, convert the period to months (*12 if years, etc) and divide the loan amount by this number. Then, multiply the new amount by the interest rate (rate/100) and add it to the total/months value again. This will determine the monthly mortgage payment, but can change if taxes are involved. Find the total interest on a mortgage and the PITI.The total interest on a mortgage can be determined by multiplying the monthly mortgage payment by the total amount of months, then subtracting the principal of the loan. PITI stands for principal, interest, taxes, and insurance; it makes up the monthly mortgage payment. The PITI can be found by adding up the total payments for the principal, taxes, interest, and insurance. Prepare a partial amortization schedule of a mortgage.The first step of preparing a partial amortization schedule of a mortgage is to find the details of the mortgage. This included the principal, interest rates, term length, frequency of payments, and the length of the schedule that you are planning. The formula to calculate monthly payments is P*(r(1+r)^n/(1+r)^n-1), where P is principal, r is the monthly rate, and n is the total number of monthly payments. With this info, the schedule can be created. For every payment period counted, find the interest paid by multiplying the remaining balance by the monthly interest rate (r), calculating the total principal paid by subtracting the interest paid from the monthly payment(M), and updating the remaining balance by subtracting the principal paid from the previous remaining balance. By doing this for every payment period until the length of the schedule is met, you can determine the remaining balance. The columns should go: Payment #, Payment Amount, Interest Paid, Principal Paid, and Remaining Balance. Compare the total interest paid on a 15-year and 30-year fixed rate mortgage.On both loans, the 30 year fixed rate mortgage will result in a lot higher of a payment than the 15 year one. The 30 year loan will usually have a slightly higher interest rate, which can result in a significant increase in price over time. Since 30 years is double of 15, you will be paying interest for double the amount of time, likely resulting in more than double the interest payment. However, the 30 year loan will usually result in a lower monthly payment, which can be appealing to many. Define and compare the interest only, fixed rate, and adjustable-rate loans.Interest-only loans typically require the borrowers to pay only the interest on the loan for a period of time in the start, not paying any money towards the principal. This has benefits of allowing usually less loan payments in the period of interest-only payments, but also has consequences, such as being forced to pay a significantly higher amount in the future per payment. The term for this loan can also usually be longer than other loans, such as 30 years. A fixed rate loan is a type of loan where the interest rate always remains the same throughout the entire period of the loan. This allows for stability and prediction of future loan payments, as all payments will cost the same regardless of the duration of the loan. This loan also allows more of the money paid to go towards the principal, allowing for a slow but steady decrease of payments over time. Adjustable-rate loans are loans where the interest rates can change based on certain benchmarks or events. The monthly payments of this loan can change over the period of the loan, which can be good or bad depending on certain factors. Usual benefits of this loan include a lower rate for the beginning of the loan period which is fixed, giving a little bit of stability and safety in the beginning. However, later in the loan the interest rates can change according to the market, which can make it cost more or less per month. In summary, interest-only loans are better for people who can make more money later, fixed-rate loans are better for those in the long term, and adjustable rate loans are best for those borrow short term. Data Analysis and ReportingUsing a data set, determine mean, median, and mode.The mean is the "average" value of a data set. This can be found by adding up all the values of the data in the set, and dividing it by the total number of values. (ex. 1, 2, 3, mean is (1+2+3)/3=2) The median is the middle point of a data set. This can be found by either ordering all numbers in increasing order and selecting the middle value with an odd number of values, or finding the mean (average) of the two middle values of an even number of values. The mode of a data set is the value that appears most frequently. To find the mode, find the value that shows up in the set the most, and that is the mode. Distinguish between a simple average and a weighted average and calculate each.A simple average is just calculated like the mean, adding up the total value of all data values in the set and dividing it by the total number of values. (ex. 5, 7, and 9: (5+7+9)/3=7) All numbers in the set will be equally weighted, which means that simply finding the mean will suffice. A weighted average gives more "importance" or weight to some values of the data set, which will hold more significance in the calculations than others. This will need to be accounted for when calculating the weighted average of a data set. You will need to multiply the values by their weights, and divide by the sum of the weights. (ex. 4, 6, and 8 with respective weights 1, 2, and 3; ((41)+(62)+(8*3))/(1+2+3)=40/6.Identify and construct various types of graphs and charts.A bar graph is a graph that uses bars, whether horizontal or vertical to display data, typically used to represent high/total values of information. In this graph, the x-axis is the independent variable, and the y-axis is the dependent variable, or vice versa for a horizontal one. A line graph draws lines from data points on a graph, which connects them and compares them over time, typically tracking changes. A pie chart shows or demonstrates percentages or proportions of a whole, showing a total amount being divided into segments of a circle. A histogram shows the distribution of data and frequencies in ranges rather than categories, such as a bar graph. These are only some examples of graphs, and there are many more. Compile and arrange facts in organized manner for a table, chart, or figure.Data and facts can be organized into a table, chart, or figure depending on the situation. Firstly, we need to find the type and purpose of the data. For example, if the data is used for the total number of sales, we need to gather the data of sales over time, and we also learn the purpose of the data is to record the sales. Next, we need to compile the data, which means we need to find accurate information and numbers to be put in our chart or table. Third, we need to organize the data, which can commonly be used in a table with descriptions of the rows and columns. Finally, we need to determine the type of graph we need to plot the data. A bar graph is useful for comparing values, while line graphs are good for showing changes over time. There are many examples of graphs we can use that are not listed here. Explain or prepare written summary of findings expressed in tables, charts, graphs and figures.When building a graph or chart, we would need to deeply understand it and be able to summarize it in front of the audience we are trying to reach. The introduction of the data should be a description of what the data entails, such as its purpose of being analyzed. (ex. sales) We would need to explain where the data came from (best choice is a proven accurate source) and be able to introduce the data, describing what type of graph was used to show the data and what it shows. If we want to think deeper, we can go into further details, such as what the data means, (why is it important?) what it could show us about the future, trends in the data that could be important, and a conclusion/explanation of the key points that can be gained from the data. These skills allow for a strong data presentation and summary to be viewed by others. Make predictions and decisions based on data and communicate their reasoning.By analyzing data very carefully, we can make predictions and decisions based on the results. For example, if we notice certain trends in the data, such as a growth in an industry, we can predict that the industry might grow at a similar rate in the future. Continuing on, it can lead us to make a decision such as pursuing that industry to maximize the chances of participating in a growing industry. In order to reason this, we need to use our data to show that our predictions are accurate. One major factor we need to recognize are "risks" or certain factors that could cause our predictions to be wrong. If we can clearly convey our understanding of our data and why it is reasonable by using statistical data and proving the weakness of risks, we can clearly demonstrate our understanding of the data, which can help make accurate predictions and potentially smart decisions down the line. Explain the usage of statistics, probability, and systems of measurement in business.Statistics are used in business to calculate data and potential predictions for future results. For example, by using statistical data after analyzing consumer spending habits and interests, businesses can semi-accurately predict products or goods that will appeal or cause customers to gain an interest, which can boost sales. Probability helps to assess certain factors, such as odds of success or risk. For example, determining the probability of something succeeding using data can help make smarter decisions, as investing in a higher probability of success is much more favorable than a lower one. We can also predict certain outcomes, such as potential customer demand and supply to make decisions on spending. By using systems of measurement, we can analyze certain factors that require units, such as costs of goods, performance of workers, time needed, production total, etc. This can allow for businesses to more efficiently predict certain variables that can be fixed/changed beforehand to maximize the odds of success. Interest RatesFigure rates, interest, and proceeds of bank discounts.An equation for bank discounts can be expressed by D = F * R * T, where D is the discount, F is the original (face) value, R is the rates, and T is time. The proceeds of a bank discount can be determined as the value the borrower receives after discounts, which can be calculated through subtracting the discount from the face value. The interest of bank discounts can be referred to as D, or just the discount amount. The rate of the discount can either be given already, or can be found by multiplying sides to get R=D/FT. Calculate simple interest using the simple interest formula.The simple interest formula is simply Prt=A, or principal times interest rate times time (years) is equal to the amount of interest. In this equation, we can find the amount of interest given the other variables, or use another method of changing both sides to solve for another variable. For example, with a problem of $4000 principal, 6% interest, and a term of 3 months, we can find the total interest by multiplying 40000.063/12 to get 60, which is the total amount of interest over the term period. Calculate any single variable – principal, interest rate, amount of interest, or time – given the other three.The formula for simple interest is Principal * interest rate * time = amount of interest. If we are missing the amount of interest, we can simply multiply the other three by each other in order to obtain the amount of interest gained over a period of time. If we are missing one of the others, there is a more complex equation needed in order to solve for the missing variable. For example, if we are missing principal, we can divide the amount of interest by (time *interest rate) in order to find the principal. Likewise, if we are missing interest rate we can divide the amount of interest by principal times time, and we if we missing time we can divide the amount of interest by principal times interest rate. Explain the process of discounting a promissory note and calculate the proceeds of a discounted promissory note.A promissory note is a written promise from a borrower to be paid at a future date with interest. In order to calculate discounts for promissory notes, we can use the equation F-(1-r*t), where F is the original/face value, r is the rate, and t is the time of the loan. Through this method, we can multiply the rate by time and subtract the amount by one, giving us a decimal 0<x<1. This number can be multiplied by the original value to find the process, or the total discounted amount. Define maturity value and find the maturity value of a loan.The maturity value of a loan is the total amount or value of currency that must be paid at the end of the term of a loan. This amount can be found by adding the total amount of interest needed at the end of a loan to the principal amount of money that the loan was owed. For example, if a loan was worth 450, then adding the two numbers would give a $5450 maturity value. Convert months to a fractional or decimal part of a year.In a year, there is a total of 12 months. In order to comparatively transform or convert this number into fractions or decimals, we would need to find the exact value of 1/12 for 1 month as an example. The term n/12 would suffice for any number of n months, as for example n=6 would mean 6 months equals half a year, which is a true statement. The decimal form of 1/12 is 0.083333 repeating, giving us a formula of 0.08333333n for months compared to years. For example, 12 months would be 12(0.08333333) which would equal one, which is a true statement as 12 months is equivalent to one year. Find the future value and compound interest by compounding manually.The general formula for compound interest is V = P(1+r/n)^(nt), where V is the final value, P is the principal/original value, r is the interest rate, n is the amount of times interest is compounded a year, and t is the total time in years. Through this method, we can manually compound interest by putting in the given principal, rate, compound number, and time values. If we are missing one, we are usually given the final value, and can use methods such as moving numbers or logarithms to calculate the missing value. Find the interest compounded daily using a table.Interest compounded daily can be given by the equation V=P(1+r/365)^365t, where V is final value, P is principal. r is interest rate, and t is time. A table would give us the compound interest for multiple rates and periods. Using this, we could simply multiply the principal value by the number given in the table that matches the values of r and t that we have. Mark-ups and DiscountsIdentify the various types of discounts.Some types of discounts include cash discounts, trade discounts, student discounts, employee discounts, etc. A cash discount is the reduction of price of a product when something is paid in cash or paid early, such as "2/10, n/30". A trade discount is a discount made to promote bulk buying in exchange for a discount, such as manufacturers selling a large quantity of goods to retailers for a lower price per unit. A student discount is a special discount given to students, which can be used by stores to attract a younger customer base. An employee discount is usually a perk given to employees of a store or company, where they can get discounts on store products. There are just some types of discounts, as there are many more.Calculate chain, trade, and cash discounts and net selling price of each kind of discount.Chain discounts are a series of consecutive discounts, which are applied to a product in a chain, one after another. Chain discounts can be calculated by multiplying/applying the discount rates to the items in succession, but not together. For example, a $100 item with chain discount 20%, 10%, and 5% can be calculated with the equation 1000.80.9*0.95. A trade discount is a simpler discount, which is a reduction or lowering of prices given to buyers who buy in bulk or repeatedly. This discount simply takes off a percentage of the whole price, requiring a single step equation. A cash discount is made to promote early payments, giving discounts when doing so. A way to write this would be "2/10, n/30", meaning a 2 percent discount if paid fully within 10 days, otherwise the payments would be due in 30 days. In terms of hierarchy, trade discounts usually come first, then chain discounts, and finally cash discounts. Determine price of product after coupons and/or rebates.Coupons and rebates can be applied directly to the purchase of a product in order to create incentives for the customer to purchase goods. A coupon is a type of voucher that gives the customer a discount on an item, such as a 20% off coupon. These are usually applied immediately to the price, offering a discount at the time of purchase. On the contrary, rebates are usually discounts that occur after purchases, where customers can receive something such as a check, gift card, or cash after submitting proof of purchase. For example, a store could have a rebate offer to give a 20$ refund to a customer after a purchase. This can be calculated after finding the original price after coupons (if it applies) and then subtracting the rebate from the total price. Define and calculate markup and markdown.Markups are the amount of money added to the price it takes to create a product in order to create a selling price. This is usually the case in order for businesses to make profit from the products they sell, otherwise they would not make profit and become unable to run. The markup amount can be calculated by subtracting the amount it takes to produce the product from its selling price. (ex. 100 production, 120 selling would be 20 markup) A markdown is a reduction or lowering of the initial price of a product, which can be used to clear store inventory or create sales. This can be calculated by subtracting the new selling price from the original selling price. Determine the rate of the markup or markdown.The markup percentage can be found by dividing the selling price by the production price, where the extra digits above 1 show the markup percent. For example, for a 20 selling price, we could use the equation 30/20 to get 1.5, where the markup percentage would be 50%. The markdown percentage can be found by dividing the new selling price from the original selling price, where (1-x) with x as the answer from the previous equation gives the markdown percentage. For example, if an initial selling price was 5035 was enacted, we can use the equation 35/50 to get 0.7. We then subtract the quotient from 1 (1-0.7) to get a 30% markdown. Find the cost, markup or selling price when any two of the three are known.The general equation to find any of the amounts is "selling price = cost * (1+markup/100). If we wanted to find the selling price, we could just multiply the cost by (1markup/100). To find the cost, we need to divide the selling price by (1+markup/100). To find the markup, we could divide the selling price by cost, then subtract one and multiply by 100 to find the markup. For example, if the selling price of 80 were given, we could set up the equation as 100 = 80(1+markup/100). Dividing both sides by 80 gives us 1.25=1+markup/100. Subtracting 1 gives us 0.25=markup/100. Finally, multiplying both sides by 100 gives us markup = 25, meaning there was a 25% markup on price. Find the amount of markdown, the reduced price and the percent of markdown of an item.Similarly to markup, markdown can be found with the equation "markdown percentage = (markdown amount / original selling price)*100. The exact markdown amount can be found by subtracting the original price from the new price. The reduced price of the product can be found the same way as the total markdown amount, just using the new price instead. For example, if given a price of 200140, we could immediately find the markdown amount as 140. To find the percentage of markdown, we could simply divide 140/200 to get 0.7, where using 1-0.7 gives us a 30% markdown. Calculate markup based on cost.To find markup based on cost, we use the formula markup amount = cost price * markup percentage. Markup based on cost means the markup is applied to the cost and not the selling price, which means everything should be applied to the cost. For example, with a cost of 80$ and a markup of 35%, we could multiply 80 and 35/100 (percentage) to get the markup amount, which is 28, being the markup amount. We could add the 80 and 28 to get 98, the new selling price of the product. Calculate markup based on selling price.For markup based on the selling price, we need to find the markup in relation to the selling price. This formula can be written as "markup amount = selling price * markup percentage". In this equation, the selling price and markup amount (or any of the 2) need to be known to find the third. For example, if given a 40 markup, to find the percentage we could use the division equation 40/200 * 100 to get 20%, which would be the rate of markup, which when applied to the original equation gives us a new $240 selling price. Convert markups from cost to selling price or from selling price to costs.To convert cost markups to the selling price, we can use the previous markup based on the cost equation to find the cost markup. For example, the previous equation gave us 24 markup amount. In doing the steps above, we can convert the markups into a selling price, which is 100 and 25% markup based on the selling price, we can divide 100/(1+0.25) to get 80, which is the cost. PayrollCalculate pay based on piecework, salary, commissions, and graduated commissions.The first type of pay is piecework pay. With this method, an employee would be paid based on effort, more specifically the "pieces" of work they make or produce. For example, a company that manufactures mechanical parts can pay a certain amount per part produced. A salary is another method of payment which is fixed and paid at set intervals. This is a very common form of payment, which is agreed upon when hiring. This can change in terms of hours, as a hourly salary would pay money per hour, while a yearly salary would pay you that much regardless of how many hours you work. A commission is a payment given to employees based on the amount of money/sales they make for a certain period of time. Typically, a commission rate would be applied to a total amount of sales. (ex. a 10% commission applied to all sales an employee makes) The final method of payment is graduated commissions, which is a type of commission that changes when certain thresholds for sales are made. For example, a form of graduated commissions can be 5% for sales under 10,000, 7% for sales 10,001 - 20,000, 9% for sales 20,001 - 30,000, etc. The total amount of pay an employee could be the added totals of piecework, salary, and commissions if any apply.Calculate gross pay based on an hourly wage with an overtime policy.To calculate gross pay based on hourly wage with overtime, you would need to apply the overtime rate to the hours worked above the usual hours. For example, a typical schedule would be 40 hours a week with normal pay, and normally either 1.5 times or double pay on any hours above. To find the gross pay, we would first multiply the salary by the regular hours (40 and under) and if applicable, multiply the overtime hours by the overtime rate and regular salary. Adding it all up gives the gross pay.Calculate an employee’s net earnings per paycheck.The amount of money an individual makes during a job is their gross pay, but there are actually deductions and taxes that take place, which means the person will take home a lesser amount, which is the net pay. To calculate net pay, we need to apply the deductions to the gross pay. Firstly, if there are deductions before taxes, we just subtract them from the gross pay. Then, we remove the amount from taxes, which are usually a small percentage of the gross profit. Finally, we take off any deductions after taxes. The left over money is the net pay the employee takes home. Prepare an individual payroll or earnings record.To prepare an individual's payroll or earnings, we need to document all their earnings, deductions, and finally net pay. This would typically have a person's name, id, period of payment, the date on which they were paid, and usually a type of pay (piecework, commission, salary, etc). Then, we would need to add up all their total earnings on the left of the record, making up a gross pay. Then, we calculate all their deductions (pre-tax, taxes, post-tax) on the right side. Finally, we subtract the total deductions from the gross pay to find the net pay. Find federal tax withholding per paycheck using IRS tax tables and IRS percentage method.The IRS taxes tables is a method to find federal tax withholdings using a table with certain filters. These filters include filing status, method of payment, and amount of income. For example, we need to find their status, (single, married, etc) payment method, (biweekly, monthly, etc) and total income for a period. Then, we can use the table to find taxable income. The IRS percentage method can be used for larger incomes or incomes unapplicable in tables. This method uses the exact same filters as the previous method, but applies a flat tax rate to the income instead of changing rates per threshold of money.Calculate Social Security Tax and Medicare tax per paycheck.Social Security and Medicare taxes are common taxes that individuals have to pay, which are a certain percentage of their income. For example, Social Security tax in 2024 was 6.2% of gross income all the way up until 160,200, while Medicare was 1.45% of the total gross income, with no limit. There is another version of the Medicare tax, being 0.9% of income over 200,000 for singles and over 250,000 for married couples. To find the tax, just multiply the rate by the gross income. Find an employer’s total deposit for withholding tax, social security tax, and Medicare tax per pay period and quarterly.Per pay period, an employer would have to deposit a specific amount of money based on certain factors. These factors include a withheld federal income tax from the employee, as well as Social Security and Medicare taxes from both the employer and employee (5 total). For example, with an employee's gross pay of 3,000 (10% from IRS table) would be withheld for federal income, but also 186 (6.2% of gross) for social security and 43.5 (1.45% of gross)for Medicare. The employer would have to match the second two, giving a total of (300+186+186+43.5+43.5) to make 759 for the payment period. For quarterly, we would find the amount of pay periods in the year divided by 4 (quarters). For example, if an employee is paid monthly, they have 12 pay periods, meaning 3 of those periods would make a quarter. Calculate federal and state unemployment taxes.Federal taxes are taxes given by the state applied to gross income of individuals. Federal tax only applies to 6% of the first 420 per person who makes above 5,000 - 23,000 as an example).Compute business expenses related to employees: benefits, disability insurance, travel, and employee training.There are many benefits that can be applied to employees, such as health insurance and plans for retirement by taking money from the employee's paychecks. Health insurance can be calculated based on a rate (typically amount per month) while the retirement plans usually consists of a rate of an employee's yearly salary per year. Disability insurance is a form of insurance given to employees. This makes up for some of the lost income if employees are unable to work due to a disability, such as an injury. This insurance can be calculated by multiplying the rate by the time by the number of employees. Travel expenses for business purposes can include a variety of different expenses, such as for transportation, food, or areas of residence/lodging. This can be calculated by adding up all the expenses and multiplying (if applicable) by the number of employees. Employee training can have costs for events to improve the skills and work ethic of employees. This can be calculated by adding the total costs. InvestmentsDefine investment terms such as risk, yields, P/E ratio, and rate of return. ind info here from MBA Research Modules: FI:097.A risk on an investment is the chance or possibility that an investment will not give what is expected, and most of the time actually causes a loss of currency or money put into the investment. For example, if an investment goes down 5%, that technically means that you just lost 5% of whatever money you put in there. Yield is how much the investment pays, which can be whenever the value of the investment goes up, or when money is paid regularly in dividends or interest. The P/E ratio is also called the "Price-to-Earning Ratio", and it can be calculated to find the value of stock in relativity to the earnings or money made by a company or investment. The ratio for this can be calculated by dividing the price per share by the earnings made from a share. The rate of return measures how much an investment goes up or down over time, represented as a rate. A positive rate means a profit, while a negative rate means a loss. This can be calculated with (ending worth - starting worth)/starting worth * 100, but also usually includes all income gained from the investment. (interest)Explain the effect compounding has in an investment and lending environment.The standard equation for compound interest is P(1+r/n)^nt, where P is the principal amount, r is the rate, n is the number of times compounded yearly, and t is time. Compounding interest allows earnings to be reinvested into the principal amount, therefore making more money if compounded more. On the contrary, compounding interest can be bad on lending, as that means you will need to pay more interest than a less compounded loan. It also gives a time crunch, as the longer the loan lasts the more the debt will grow over time, making it very bad for borrowers. In summary, compounding is good for investments, but bad for loans.Compare investment decisions and make mathematical comparisons of investment alternatives. ind info here from MBA Research Modules: QS-043,QS-046.Using the compound interest formula when given enough information allows us to find the ending value, interest amount, and other factors. This allows us to compare two different investment decisions by calculating the ending value, amount of money made in a period of time, or total growth (rate of return) over time. This same theory allows us to compare investment alternatives, where we can compare two investments with different terms (rate, time, compound) to find which one is better and gives more money in the same period. Calculate the net present value of an investment such as certificate of deposit, savings account, stocks, and mutual funds. ind info here from MBA Research Modules: FI:238.The net present value of an investment can be defined as how much money can be made in an investment (how profitable it is). The general formula for this involves summation, being sigma(cash flow at a time t/ (1+interest rate)^t) - the initial amount. For a certificate of deposit, it usually has a fixed interest amount over a period of time. For example, if we do 3 years, the formula can be interest amount/(1+i)^n, when we can continue this until n=3, then add initial value/ (1+i)^3 and subtract the initial amount. For a savings account, we can use the compound interest formula used before. Stocks uses the exact formula for CoD, but it uses given dividends instead of interest amount. Mutual funds combine interest and dividends, therefore using the same equation, but for the last term multiplies the initial amount by (1+i)^last n, but still using the same terms otherwise. (still divide by (1+i)^ last n)Determine stock yield, earnings per share, and price-earnings ratio. ind info here from MBA Research Modules: FI:097.In an investment, there are many factors that can contribute to the amount of money made/earned. A stock yield is the exact amount a person makes in an investment over a period of time. Yield is just the amount of money made, not considering how much the value of an investment changes over time. To find stock yield, simply divide the dividend (earnings) per share by the price per share. This would give you a fraction, which would give you how much percent money you would have made. Earnings per share can be calculated by subtracting the ending amount by the initial amount, which would give us the total amount the share has grown, which in turn is how much earnings were made through that stock. The price-earnings ratio is typically used in relation to a company. This ratio is the ratio of stock prices to the company's earnings, which can help us find a decently accurate valuation of a company. Compute the anticipated rate of return on specific investments and savings accounts using various factors such as simple or compound interest, dividends, fees, etc.The rate of return can be calculated using the (final value - original value)/ original value formula, giving us a rate of how much percent money is made/lost. Simple or compound interest can change the results, as it will change depending on how often compounds are made. We can account for this by using the formulas Prt or P(1+r/n)^nt to find the rate of return. For dividends, we need to account for the extra money made per share. This can be calculated by adding the dividends to the rate (add the dividend rate, found by dividing dividen per share / # of shares). Fees take away money from the rate of return (if positive), so we need to subtract it from the final amount made or if at the same rate of money being paid, find the rate and subtract it from the current rate. TaxesDefine tax terms such as standard deduction, itemized deductions, exemptions, and various types of taxes such as income tax, sales tax, and property tax. ind info here from MBA Research Modules: FI:074.A standard deduction is a specific amount of money that can be removed from the income tax of an individual. This amount is set, for example the 2024 standard deduction being $14,600 per individual. Itemized deductions is another method of deduction that can be chosen instead of standard deduction. For this method, specific expenses can be removed from tax, such as state taxes or medical expenses instead of a large sum without specificity. An exemption allows a specific amount of money to be subtracted from the total income, which in turn will lower the amount of money that can be taxed. Income tax is a tax that is based around an individual's earnings, or income. Usually this tax will rise as the income an individual makes, making it a set percentage. Sales tax is a tax that is put on the sale of goods, which is then given to the state to use. Property tax is based on the value of property owned by individuals, such as buildings or vehicles. 2. Define and calculate property taxes based on local percentages/guidelines.Property tax can be calculated by multiplying the tax rate by the value of the property. For example, if a property is worth 2,000. Calculating property tax can include a variety of special cases, as cities or states vary on assessment value and tax rates. Deductions or exemptions can also take place, which changes the amount of tax to be paid. Calculate sales tax on purchase. ind info here from MBA Research Modules: SE:475.To find the sales tax on a purchase, simply multiply the sales tax rate by the total price of the item sold. For example, for a product worth 300 sales tax. There are special cases, as sales tax can change in percentage per city, or some items might be exempt from sales tax. Complete a 1040 EZ Federal Income Tax Form with a W2 form. ind info here from MBA Research Modules: FI:074.The form 1040 EZ Federal Income Tax was created as a simplified version of the US tax return. A W-2 form is given by employers to record wages paid and taxes withheld in relation to the employee. On the form, there are a variety of things that need to be filled out. First, fill out your total taxable wages (on W-2), as well as any other forms of income such as interest. Next, fill out any adjusted values to your income if applicable. Next, file your deductions, whether standard or itemized. Your taxable income can be calculated by subtracting the total taxable wages (step 1) by the deductions. You can then find your tax using the IRS tax table to find out how much percent of your income will be taxed. Next, fill out any credits that may apply to taxes or any other taxes that need to be paid. Finally, you can calculate your refund or the total amount you owe, depending on how much tax you already paid. Prepare a 1040 A using W2 and 1099 Interest form. ind info here from MBA Research Modules: FI:074.Form 1040 A tax forms were technically discontinued after 2018 and replaced with the 1040 form, but it can still be good to know how to use it. Firstly, we can fill out your taxable income by using the W-2 sheet. The 1099-INT form shows how much interest your earned, so you must write it down, as it can be taxed. We can find the adjusted gross income by adding all the income made from the two forms. Next fill out deductions, such as standard deduction or any other adjustments. Then, find the taxable income and use the IRS tax table to find how much tax is owed. Finally, look for any other taxes that may apply, and find the total amount owed, whether it is a refund or a payment. Complete basic tax forms such as W2 and W4.The W2 is used by an employer to measure wages earned and taxes withheld by the employee. Firstly, the employer's personal information needs to be input, such as Social security number, EIN, name, address, etc. We then need some of the employee's information, such as name or address. Then the employee's total wages are calculated, and the federal tax that is withheld. A certain percentage of the wages will be subject to taxes such as social security or Medicare, which will be listed down and calculated. Finally, additional information can be recorded, such as benefits, retirement plans, tips, etc. A W4 is used by employees to give their employers their preferences on tax. Firstly, information is given (name, address, SSN, etc). Next list whether special conditions in work apply, such as multiple jobs. Then claim dependents, or find how much people you have (for example children) in your family that can reduce taxes. Finally, list any extra income or deductions to the form, and then sign it. Bank RecordsCompare different types of banking options such as credit unions and other banks.Some types of banks include credit unions, traditional banks, or online banks. Credit unions are different from other banks typically because it uses a membership based system, which can include criteria for membership such as an individual's job information or affiliation. These banks are usually non-profit, which can allow for benefits such as higher interest rates on bank accounts or lower interest on loans. Credit unions are more community-oriented, meaning they are more personalized and typically charge lower fees. Traditional banks are more focused on profits, meaning they can charge higher fees than credit unions. It also can have lower saving rates and higher loan rates. These banks do not usually have a membership system, but allow more access to funds through the use of mortgages and large scale business banking. Online banks are similar to traditional banks, but are primarily operated online, This can cause limitations in services, but makes up for it in easy access online and typically less fees and more interest.Identify the types of banking services and their costs for meeting various needs.Banks can include checking accounts, which allow for transactions and money to be put into an account to be used for payments instead of physical cash. This allows for transactions to occur, whether to deposit or withdraw money, but can also be used to digitally pay bills. This can include fees from the bank, such as for maintenance, usually monthly. Savings accounts are another form of account where money slowly grows as interest accumulates over time. This account also can contain maintenance fees and other charges. Banks also offer loans, which are grants of money in exchange for repayments later with interest. This allows for quick access to cash but overall a larger payment back to the bank. Credit cards are used for money being borrowed quickly on a lower scale, but contains fees, typically annually for using the card as well as interest for money owed to the bank. Write a check, prepare deposits, and prepare withdrawal slips.Writing a check requires information, including the date, the person the check is being paid to, the amount of money being paid (written in numbers and words) and the signature of the payee. It is also possible to add optional notes about the purpose of the check when necessary. This allows the check to be paid to someone, which is later processed by the bank. A deposit slip requires different information, such as the date, the account number of the holder, the amount of cash or value of check(s) being deposited, and the total amount of money being deposited. Some of these might require the signature of the person being paid, but in the end will be processed by the bank. A withdrawal slip is used to withdraw money from the bank. On the slip, information is required such as the date, account number, amount being withdrawn, and the signature of the account holder. A reason for the withdrawal might be required, but in the end will allow the holder to withdraw money from their account. Maintain a check register including proper procedures for ATM and automatic payment withdrawals.A check register is used to track the balance of an individual's account, which can be used to manage finances and ensure the proper amount of cash is used. For every entry on the check register, it should include a date, a description of the transaction, the type of transaction, (types of deposits/withdrawals) the net amount of money (added or subtracted) and the final balance after the transaction. This allows for updates to the balances accurately to make sure all money is in check. For ATM procedures, make sure to list the description as related to an ATM, as well as the type of transaction. Also include fees if applicable from the ATM. Do this immediately after use to ensure accuracy. For automatic payment withdrawals, record payments whenever paid out, recording the description and type as automatic payment. Reconcile a bank statement. ind info here from MBA Research Modules: FI:070.A bank statement might not be the same as the check register, requiring reconciliation. First, look at the information on the bank statement and check register. Compare the deposits and withdrawals, looking for discrepancies that are missing on the bank statement. Also check for other potential errors, such as fees by the bank. In the end, make sure to change the value of the bank statement by adding outstanding deposits and subtracting outstanding checks. For the check register, change any additional fees not added, such as potentially a bank service charge fee. In the end, the two values should be the same, which would make them reconciled. Utilize online banking and bill payment options securely.When using online banking, make sure the account is secure. For example, make sure the address of the website or app is correct to ensure not paying money to a scam website. Use a strong password to avoid guesses, and maybe consider changing passwords somewhat frequently. Get extra security using a two-factor authentication system using either a phone number or email. Try to use a secure and private network when using the bank, and do not use a public WiFi network, which could be non-secure. Check your accounts regularly to find any transactions not made by the user to avoid others stealing money from your account. Make sure that bill payment options are verified to make sure you are paying the correct account/person by using a trusted service. Finally, make sure to carefully review automatic payments to not make mistakes, and if suspicious activity arises, report it to the bank and freeze your accounts immediately to prevent losses. InsuranceIdentify and compare types of insurance.One type of insurance is life insurance, where the individual will pay money at a certain rate called premiums to the insurance company, where they will pay the money at a date once the person paying the insurance dies, where the people you choose (called beneficiaries) will obtain the money later. This form of interest is good as it grows over time (basically it has interest) and will allow the holder to be able to gain a lot of money over the course of their lifetime to be spent by their family later. Health insurance is another type of insurance that helps with very expensive medical bills. In this insurance, a person will pay a premium (usually monthly or yearly) to the insurance company, who will pay for a large majority of expenses related to health or medicine, such as emergency surgeries and other operations that are expensive. There is usually a deductible, or an amount a person needs to pay that the insurance will not cover, as well as the other percentages that the insurance doesn't cover, but this allows for a safety net against costly medical treatment for a small amount per period. Auto insurance is paid in a similar way to the other types, but is focused on automobiles or vehicles. This insurance covers damage to cars, as well as any injury from an accident related to vehicles. It also usually has deductibles, but helps a lot against major and expensive accidents. Read insurance premium charts and determine the cost of a particular policy.An insurance premium chart will contain information on the cost of an insurance policy, or premium. An individual will need to look at the chart to see what applies to them, and plan their costs accordingly. For example, age is a category to be considered, as insurance typically increases with age for life insurance policies. The total value of the policy also plays a factor, as a higher policy typically costs more. By taking other factors into account, such as gender, salary, and other variables, it is possible to look at a chart and determine an accurate premium for a policy. Analyze insurance proposals for auto and determine the cost of compulsory insurance and costs of optional coverage.Insurance proposals for auto basically include information about the individual buying the insurance and their vehicle. This is used to help inform the client about the cost of their policy, including factors that might increase the price, such as being accident prone or unsafe. When looking at insurance, compulsory insurance must be paid, as it is illegal otherwise, while optional coverage is a decision that could be made, but is not necessary. The purpose of the optional coverage is to pay a higher premium, but more protection if there is ever damage. For example, a certain amount, such as 15,000 for injury insurance is required by law to be purchased, but collision or comprehensive insurance are optional, as they will provide extra protection from damage, but is not legally required to be purchased. Analyze health insurance premiums and calculate based on selected options.There are many types of health insurance premiums based on the individual's preference, such as paying a higher premium for access to more medical facilities (such as PPO) or paying a lower premium at the cost of having limited access (such as HMO). Other plans, such as EPO require the individual to use only a specific health provider in its system. Looking at the premiums for health insurance, some insurance plans may cost more depending on the benefits it gives, while others might cost less for limited benefits. In the end, it depends on what the individual prefers or needs, which will help them to calculate the insurance policy that they need. Compute the costs and benefits of specific insurance plans.Specific insurance plans will have different costs depending on their benefits. For example, an insurance with a more flexible coverage might have a higher deductible or premium payment, while an insurance with more limited coverage or benefits will typically cost less, with a lower deductible or premium payment. Additionally, some plans include varying deductibles with premiums, such as a higher monthly premium with a lower deductible, or a higher deductible with a lower monthly premium. These plans depend on the client's preference and rate of injury, as frequent injuries would make the lower deductible better, while less frequent injuries would prefer the lower monthly payment. In total, different insurance plans will vary in costs and benefits, and it depends on the client's situation to determine the best one for them. Analyze deductibles and their effect on policy.Deductibles are payments that the client of a policy will use, which is not covered by insurance and must be paid by the client whenever insurance is used to cover damages. The price of a deductible can change per policy, but will likely change other factors, such as the premium. For example, a higher deductible payment might come with a lower premium, while a lower deductible payment could come with a higher or more expensive premium. A lower deductible would be better for more frequent injuries, which could save you money, while a higher deductible should be preferred for less frequent injuries, which would save money on monthly payments. Deductibles can change the price of a policy overall, depending on the client's preference and situation. DepreciationDistinguish between straight-line method, declining balance method, sum of the year’s digits method, and MACRS method.Straight line depreciation is found by simply dividing the total depreciation by the number of time units (usually years) it spent deprecating. This method usually accounts for the salvage value, which is how much the item sells for at the end of its useful life. The declining balance method finds the depreciation value by the total value of the asset per time units (usually years). This method does not usually account for a salvage value, which makes it cost more for earlier years than later years, as the book value will be higher earlier. The sum of the year's digits method adds all of the years together. (use the summation formula n(n+1)/2, as every year is not worth the same in the method) Depreciation is then weighted higher in the beginning (ex. 5/15 for first of 5 years) and multiplied by the book value (includes salvage value) which creates a method of depreciation that decreases over time. The MACRS method is used in the United States by the IRS. This method determines depreciation rates per year as defined by the government, instead of using mathematical values such as the other methods. Depreciation in this method usually is higher in the beginning and lower at the end. Determine straight-line depreciation for a year.For straight line depreciation for a year, simply find how much that asset depreciated if only for one year. For many years, find the total depreciation (include the salvage value) and divide it by the total amount of years. By using this method, we can find the straight-line depreciation for one year on average, even if the depreciation changes per year. Determine the depreciation expense on plant assets by the sum of the year’s digits and declining balance.For the declining balance method, the salvage value is not considered for calculating depreciation. With the method, multiply the rate of depreciation by the book value of the asset each year. This means that depreciation will be increased in the beginning, but will decrease over time. The sum of the digits methods adds up all the years (each year is worth as much as its number value) and reverses the fractions for each year. This means that for 5 years, it will go from 5/15 to 4/15 to 3/15 and so on. Multiply the rates by the total depreciation (include salvage value) to get the depreciation per year. This means that the depreciation, similar to the declining balance method is higher in the beginning but lower towards the end. Determine modified accelerated cost recovery system depreciation.The MACRS system used by the US is determined by the IRS to find the amount of depreciation. This system classes assets differently, giving a different amount of years per type of asset. The system mainly uses double declining balance (declining balance method but double the straight line method's rates) or the straight line method, but has some alternate methods for certain scenarios . MACRS uses a fixed rate for every year, determined by the IRS which can be used to calculate depreciation by multiplying the total cost of the asset by the rate given (usually in a table). This method can be used to find annual depreciation expenses, which are usually decreasing over time. Use the straight-line depreciation method to find the value of an asset.The straight-line method can be used to find the value of an asset in terms of its original value or salvage value. For its salvage value, find the average depreciation by dividing its total depreciation over time (in years), where subtracting all the depreciation over the years would give us salvage value (final asset value), including the average depreciation. If we can find the average depreciation, we can add it to the salvage value, adding it as often as years to find the original value of an asset. InventoryDetermine the cost and value of inventory.The costs of maintaining inventory can contain purchasing inventory for selling later, as well as sometimes expenses for holding inventory that might occur, such as renting a storage facility. Other costs may occur from goods going bad over time, such as fresh produce or other perishable items. The value of inventory is how much it is worth, which can include the value of the items in the inventory (based on how much they sell for) and other assets that have a monetary value. To find the overall worth of an inventory, you can subtract the costs from the assets or value, which can either result in a positive inventory value or a negative one. Determine rate of inventory turnover.The rate of inventory turnover is how much a company sells in relation to its total inventory over the span of a time period, such as a year. For example, a rate of inventory turnover of 6 means that a company will sell their inventory out 6 times in the time period. The formula for the rate can be found by dividing the the costs of items sold in a period by the average inventory. This can also be calculated by dividing the sales by the costs of purchasing the items being sold. Generally, the first formula could be used to find the ratio of inventory turnover, but the second can be used to find the rate instead. These formulas help find out how efficient a business is in selling goods, which can determine how profitable a company is. Determine the value of ending inventory using Average Cost (weighted average), FIFO, and LIFO.Average cost method involves dividing the total value of the costs of goods by the number of items. This method finds just the average of all items, but weights can add additional value to some items. To clarify, the weight method needs to multiply every item by its total weight (out of 100%) of the inventory, which will make items that bear more weight worth more than those with less weight (on a singular scale). By adding up all the costs and dividing by the amount of goods, a weight average can be calculated. The FIFO method means First In, First Out. This method uses the idea of selling the first items received initially, and saving the last items for later. Since the first item is usually worth less than newer ones, it usually makes the ending value higher. For example, if the first 100 are worth , if 90 goods are sold it would count as 90*10 and 10015, where the first items are sold first. LIFO stands for Last in, First out. This is the exact opposite of the FIFO method, as the last items are sold first. This would result in the inverse of the ending value lower. In the example above, the final inventory would be 10*10, which is a lot less than the FIFO method. Ratios and ProportionsDefine the terms ratio and proportion. ind info here from MBA Research Modules: FI:097.A ratio is the numerical or quantitative relationship between two numerical values. This means that a ratio compares two numbers, where the numbers shown describes the relationship between the number. For example, a ratio of 3:2 means that for every 2 quantities of the second value, there is 3 quantities of the first. A proportion describes the size or number of something compared to the size or number of something else. To be more specific, a proportion is not a ratio, but instead equates two ratios. For example, making a 1:2 ratio equal to a 2:4 ratio is a proportion, as it compares both ratios (can be used to compare two fractions)Use ratios to evaluate profitability, efficiency, and leverage. ind info here from MBA Research Modules: FI:097.Ratios can be used to compare certain aspects, such as assets and liabilities. This ratio would help determine if a company is in debt or has assets left over for other use. To determine a profitability ratio, you can mathematically divide the total net income (revenue - operating/other expenses) by the total amount of sales. This ratio would tell you how profitable the company is, by measuring how much money the company is making in profit divided by the total amount of money made, which show the profit margin. The efficiency ratio can be calculated by dividing the total expenses by the revenue made. This ratio (between 0 and 1) tells you how much the company spends to make one dollar, effectively giving an accurate estimation on how efficient the company is in making money. The leverage ratio compares a company's debt to another financial amount, such as assets. This tells you the financial risk of the company, as it will tell you how much the company uses debt. Create ratios to express the quantitative relationship between two amounts. ind info here from MBA Research Modules: FI:097.Ratios are used to measure the quantitative relationship between two amounts by writing their relationship in the #:# format, telling you how much of each would be equivalent. For example, if there were 20 apples and 30 oranges, we could simplify a fraction to get a ratio, in this case 2:3. This tells us the quantitative relationship between apples and oranges: 2 apples for every 3 oranges. Use ratios, proportions, and percents to solve problems involving financial calculations. ind info here from MBA Research Modules: FI:097.Financial calculations often use a lot of variables, such as assets, liabilities, debt, equity, cost, sales price, markup, etc. We can use ratios and proportions to create a relationship between two mathematical values. For example, if there is a 2:1 ratio of sales to cost, we can find out that the company makes double its operating costs, showing profitability. A 9:4 ratio of selling price to cost price tells us that the markup is 9/4 or 225% of cost, where we can also relate the ratios of comparing markup to cost or selling price. Ratios, proportions, and percents all have unique uses in solving financial problems. Analyze and explain methods for solving problems involving proportions such as scaling and finding equivalent ratios.Proportions can be used with scaling and equivalent ratios to solve problems. For example, if we know that one company has a 5:3 sales to cost ratio, and another company has 30000 in cost, we can use a proportion of 5/3=x/30000, where we can find the value of x using cross multiplication and division. For scaling, we could use a ratio and increase both values accordingly. For example, if there was a ratio of 3:2 for side lengths, if we have side length 8, we can increase the other (3) by 4 to get 12:8, an equivalent ratio. These techniques can be used to compare and change proportions to find missing values.