Financial Math Study Guide Notes #1

Financial Math NotesConsumer CreditIdentify the costs, benefits, and sources of various types of credit.Revolving creditTypes of credit that are available even after fully paying them backe.g. credit cardsCan have various rates and interest applied Can be pulled from infinitelyClosed-end creditMust be paid back in full and then no more money to draw from Interest rates can vary and applyInstallment creditBorrow a lump sum from a lenderMust pay back in periodic paymentse.g. mortgages, car paymentsCalculate sales tax and computer total price with sales tax.current price x 1+sales tax = total priceCompute total purchase price with interest/finance charges addedInitial price x 1+interest rate = final price. Add finance charges depending on if taxed or notCompute the costs involved in owning and buying an item such as an automobile, appliances, home, or furniture.Typically a long the lines of :Total cost - down payment = amount financed/principal amountPrincipal * interest rate * duration = total costtotal cost/payment times (amortization) = installation costsCompute finance charges for single payment loans.Finance charge can be a flat fee or percentage of money used.Same equation as above interest ratesCalculate installment loan costs such as amount financed, installment price, finance charge, and installment payment.Amount financed is the principal after the down payment if there is one.Installment price is usually total price of all down payment money and regular payments.Finance charge is the extra rate at which the money is loaned out. Typically the interest addedInstallment payment are the regularly scheduled payments. Find after total cost of principal + interest, and then divide by each interval paidFind the estimated annual percentage rate (APR) using a table.Year 11000Year 21010Year 31020Year 41030Interest is 1%Compare costs of leasing and buying.Leasing is more expensive in the long run than buyingBuying is typically a one-time payment but cheaper in long runFind the finance charge and new balance using the average daily balance method.Finance charge is the total amount of interest paid over the duration of the entire loan. Read amortization tables to determine payment, interest and balance.Initial1000Week11100Week2990Week3880Payment per week is 110Bc initial is 1000 and new principal is 1100, interest is 10%66556Compute Annual and monthly Percentage Rate for credit cards or loan.Use the rate aboveFind the monthly mortgage payment.Divide total amount and then divide per monthsFind the total interest on a mortgage and the PITI.Use the rate above principal, tax, interest r all easy.Prepare a partial amortization schedule of a mortgage.Each month just pay this muchCompare the total interest paid on a 15-year and 30-year fixed rate mortgage.Interest on a 15 year is either double (simple interest) or more than double (compound interest)Define and compare the interest only, fixed rate, and adjustable-rate loans.Fixed rate interest is the same throughout so you can compute the interest easilyAdjustable rate loans or Adjustable rate mortgages (arm) fluctuate from the current market index.Data Analysis and ReportingUsing a data set, determine mean, median, and mode.Mean: add all of them up, divide by number of terms- Median: arrange in numerical order: middle number of mean of two middle numbers - Mode: most common number. If there isn’t one, then no mode, and can be more than one.Distinguish between a simple average and a weighted average and calculate each.In calculating a simple average, or arithmetic mean, all numbers are treated equally and assigned equal weight. But a weighted average assigns weights that determine in advance the relative importance of each data point. Simple average is just calculating mean. Weighted average is used to balance all of the data points. For example, a test grade is 20% of your grade, but homework is only 10% of your grade. In any case, in a weighted average, each data point value is multiplied by the assigned weight, which is then summed.Identify and construct various types of graphs and charts.A bar chart, also known as a horizontal column chart, is popular for a reason — it’s easy on the eyes. With bar charts, you can quickly identify which bar is the highest or the lowest, including the incremental differences between bars. Line chartUse a line chart to plot continuous data or data with infinite value. For example, the line chart below highlights the increase of keyword searches for “remote work” across the US from February 1, 2020 to March 22, 2020. Area graphAn area graph is like a line chart as it also shows changes over time. One difference is that area graphs can represent volume which is typically filled with color. The area graph example by the BBC below shows a simple comparison of two data sets over a period of time. Scatter plot A scatter plot or a scatter chart helps show the relationship between items based on two different variables. Dots are plotted in an x-y coordinate system. In some cases, a trend line is added (like in the example below) to a scatter plot. Pie chartA pie chart highlights data and statistics in pie-slice format. This type of chart represents numbers in percentages, and the total sum of all pies should equal 100 percent. Pie charts are most impactful to your audience if you have a small data set. Pictograph A pictograph or a pictogram is a type of chart that uses pictures or icons to represent data. Each icon stands for a certain number of units or objects. For example, the infographic below contains a pictogram— each human icon represents 10 percent of CEOs. Column chart A column chart is ideal for presenting chronological data. Also known as the vertical bar chart, this type of chart works if there are only a few dates to highlight your data set like in the example below. Bubble chartA bubble chart or a bubble plot is a lot like a scatter plot. However, bubble charts have one or two more visual elements (dot size and color) than a scatter plot to represent a third or fourth numeric variable. Gauge chart A gauge chart, also known as a dial chart, is an advanced type of graph that shows whether data values fit on a scale of acceptable (good) to not acceptable (bad). For example, you can create a gauge chart to display current sales figures and use your quarterly sales targets as thresholds. Gauge charts are particularly helpful where the expected value of the data is already known. This helps organizations create actionable reports and help employees understand where they stand in terms of metrics by looking at the chart. Stacked Venn A stacked Venn chart is used to showcase overlapping relationships between multiple data sets. This type of graph is a variation of the original Venn diagram, where overlapping shapes or circles illustrate the logical relationships between two or more variables. Compile and arrange facts in organized manner for a table, chart, or figure.See if there is a common category or trend in the dataOrganize under these and find an appropriate graphExplain or prepare written summary of findings expressed in tables, charts, graphs and figures.See general rising, lowering, or stagnant trends Make predictions and decisions based on data and communicate their reasoning.See #5Explain the usage of statistics, probability, and systems of measurement in business.These statistics can be used to make business projections for future monetary gains, which can be used to make budgets and estimated costs. It can also evaluate the state of the market and predicted trends to make executive financial decisions. SWOT analysis are an exampleInterest RatesFigure rates, interest, and proceeds of bank discounts.Rates are applied per year (APR) unless otherwise specifiedInterest is calculated by multiplying principal times rate times timeDiscounts are 1-rateCalculate simple interest using the simple interest formula.See #1Interest = Principal (rate * years)Calculate any single variable – principal, interest rate, amount of interest, or time – given the other three.Amount of interest = Principal * Interest rate * Time (in years)Use ordinary interest (360 days)Explain the process of discounting a promissory note and calculate the proceeds of a discounted promissory note.Find the discount money off (discount = p * rate * time)Then subtract the discount from the principal to find the proceedsDefine maturity value and find the maturity value of a loan.Maturity value is the total value of the principal plus interest accrued over time.Maturity Value = Principal * (1 + rate) * Time (in years)Convert months to a fractional or decimal part of a year.Divide # months by 12Find the future value and compound interest by compounding manually.Future value (see formula for maturity value in #5)Compound interest = (Principal * (1 + rate)^(Time in years)) - PrincipalIgnore the final [ - principal] if you want final valueFind the interest compounded daily using a table.1000Year 01050Year 11102.5Year 2Subtract the amount from a year and the previous to find interestWe can see the growth is not linear, so it must be compound interest growthMark-ups and DiscountsIdentify the various types of discounts.Cash Discount:Seller will usually reduce the amount that the buyer owes by either a small percentage or a set dollar amount.Trade discount: A trade decided between retailers and not to the end consumer, but otherwise same as cash discount Buy one get one freePercentage discounts: ex: 70% off of 27. Formula=100%-discount=n, original value of product X n = discounted price.Early Payment discounts: Paying in advance or much earlier than the deadline gets you a discount. Determined between the two parties.Bundling: putting multiple products or services together as one priceFree shipping discounts: going over a certain amount will get you free shipping costs.Others include buying in bulk and seasonal discounts.Calculate chain, trade, and cash discounts and net selling price of each kind of discount.Formula to find new price: 100%-discount off=n, original value of product X n = discounted price.Formula to find discount: new price/old price=n, 100%-n%=discount off.Formula to find old price: 100%-discount off=n, n into a decimal, new price/n=old price.Chain discount: must calculate each one individually, cant just add them up. Original price X first discount X second discount X third discount X nth discount = final net selling price. Determine price of product after coupons and/or rebates.See #2Define and calculate markup and markdown.Markup/Markdown is money added or taken off respectively to gain profit or motivate buyers to buySee #2Determine the rate of the markup or markdown.See #2Find the cost, markup or selling price when any two of the three are known.See #2Find the amount of markdown, the reduced price and the percent of markdown of an item.See #2Calculate markup based on cost.See #2Calculate markup based on selling price.See #2Convert markups from cost to selling price or from selling price to costs.Cost plus markup (if in a dollar amount) = selling priceCost x (1 + markup rate) = selling pricePayrollCalculate pay based on piecework, salary, commissions, and graduated commissions.Piecework is pay per item manufacturedSalary is predetermined for each day, regardless of hours workedCommission is a flat pay or rate of items soldGraduated scales higher if the items sold evaluates to moreCalculate gross pay based on an hourly wage with an overtime policy.Hourly wage times (hours worked + hours worked overtime * overtime policy[usually 1.5])Calculate an employee’s net earnings per paycheck.Net earnings is gross pay minus all tax and withheld incomePrepare an individual payroll or earnings record.Individual payroll shows hours worked, pay per hour wage, taxes deducted, expensesFind federal tax withholding per paycheck using IRS tax tables and IRS percentage method.Calculate your total income for the year to see which tax bracket you are in. Then use the dollar amount or percentage of your total income to calculate.Calculate Social Security Tax and Medicare tax per paycheck.Add the two percentages to find total percentage then multiply by your paycheck. They are independent so they don't affect each other.Find an employer’s total deposit for withholding tax, social security tax, and Medicare tax per pay period and quarterly.Subtract all three of these items from each pay period to find the net pay. If don't quarterly or less than a year, be sure to adjust rates depending on the fraction of the year.Calculate federal and state unemployment taxes.Federal and state taxes are rate times pay and then subtract it for net pay.Compute business expenses related to employees: benefits, disability insurance, travel, and employee training.Employee benefits are usually paid for in lump sums or yearly fees. Most of these are, depend on period between recurring payments and amount of payment, multiply both to find total payments. InvestmentsDefine investment terms such as risk, yields, P/E ratio, and rate of return.Risk: The amount of liability you are able to accrue from an investment or action. Can come from changes in market, economy.Yield: the Amount of money gained on an investmentP/E Ratio: Price to earnings ratio which is for companies. Used by dividing current stock price by earnings per share, assessing levels of investors.Rate of Return: Percentage for profit or loss for an investment.Market Cap (Capitalization): Total value of a company, multiply stock numbers by stock price.Explain the effect compounding has in an investment and lending environment.Compounding is interest on interest, allowing valuations to grow exponentially. Items that are compounded more often or in more periods per year grow quicker.Compare investment decisions and make mathematical comparisons of investment alternatives.Investment decisions vary depending on principal amount, interest rate, and compounding period. Can also vary on simple or compound interest. Calculate both out with a random principal amount and determine final amounts.Calculate the net present value of an investment such as certificate of deposit, savings account, stocks, and mutual funds.Find principal amount and interest rate and time, same calculations as loans.Determine stock yield, earnings per share, and price-earnings ratio.Stock yield is typically dividend payments, which is a set amount or percentage per share. Earnings per share is a calculation of net income by number of shares outstanding. P/E ratio is current stock price divided by EPS.Compute the anticipated rate of return on specific investments and savings accounts using various factors such as simple or compound interest, dividends, fees, etc.Principal x interest rate x time Literally the most basic thingTaxesDefine tax terms such as standard deduction, itemized deductions, exemptions, and various types of taxes such as income tax, sales tax, and property tax.Standard Deduction: Fixed dollar amount taxpayers subtract from taxable income. Can vary due to age or health conditionsItemized deductions: Certain expenses that are able to be subtracted from taxable income (tax deductible)Exemption: A set amount deducted per each dependent or outlined personIncome Tax: Tax on any form of earnings, uses a graduated income tax system.Sales Tax: Extra percentage on sold items, often does not affect medications or groceries.Property Tax: Tax on real estate, rate given by governments. Payroll Tax: Tax taken out of an employees paycheck to pay for Social Security and Medicare.Define and calculate property taxes based on local percentages/guidelines.Assessed property value times the given tax rateCalculate sales tax on purchase.Bruh really.Complete a 1040 EZ Federal Income Tax Form with a W2 form.Ill just do 4-6 with my family when we do taxes or somethingPrepare a 1040 A using W2 and 1099 Interest form.Complete basic tax forms such as W2 and W4.Bank RecordsCompare different types of banking options such as credit unions and other banks.Credit Unions are member owned and non-profits, with a member service and exclusive benefits. They are more community-oriented and more tight-knit. Have higher interest rates and fewer fees, lower credit rates.Banks are more accessible but are for-profit. They are open to the general public with ATM services but have higher rates and worse services.Identify the types of banking services and their costs for meeting various needs.Making savings and checking accountsWithdraw/deposit money through online or ATMSTaking out loans, require charge through interestWrite a check and prepare deposits and withdrawal slips.Maintain a check register including proper procedures for ATM and automatic payment withdrawals.Give customer the right amount of change?Reconcile a bank statement.Compare bank account balance with other financial records (balance sheet, income statement, etc.)Check that change in your bank account since the last time reconciled matches records.Make sure all deposits and withdrawals are accurate, resolve discrepancies. Utilize online banking and bill payment options securely.Make sure to pay and track bank account regularly, don't give out personal informationInsuranceIdentify and compare types of insurance.Property Insurance: protects physical assets like buildings or property from fire or theft. Does not always include items like natural disasters, unless explicitly stated. Insurance may pay back the full cost (replacement cost) or the value of the depreciated item (Actual Cash Value [ACV])Liability Insurance: Insures others or other peoples' property due to your actions. Can pay for medical bills, legal fees, or property. Can be seen in auto insurance or business insuranceHealth Insurance: Covers medical bills and payments for the insured. Gives access to healthcare and some early diagnosis benefits. Can be done through family plans or employment. Has monthly premiums, and requires deductibles and copay.Disability Insurance: Gives a source of income for workers who are unable to work. Short term disability is limited to 6 months and long term disability can be as long as retirement. Typically comes in the form of a percentage of income (60-80%)Life Insurance: Covers costs to beneficiaries after the insured's death. Can cover items such as mortgage, education, and cost of living. Can also cover funeral expenses. Term life insurance is a period of 10, 20 etc years that only counts if the insured dies within the time period. Whole life insurance is lifelong coverage and consistent premiums and cash growth. Universal life insurance is similar but is more flexible. Premiums can also different due to age, health, and policy.Read insurance premium charts and determine the cost of a particular policy.Premium is a flat charge per month, can vary depending on the services offered.Analyze insurance proposals for auto and determine the cost of compulsory insurance and costs of optional coverage.Analyze coverage of the auto insurance, deductibles, and monthly premiums. Compulsory insurance depends on similar items, same with optional.Analyze health insurance premiums and calculate based on selected options.Health insurance varies (See above)Compute the costs and benefits of specific insurance plans.See above #1Analyze deductibles and their effect on policy.Deductibles are payments per each financial loss that is insured. Lower deductible typically has less coverage and/or higher premiums, vice versaDepreciationDistinguish between straight-line method, declining balance method, sum of the year’s digits method, and MACRS method.Straight-Line MethodAssumes constant depreciation per yearDepreciation per year = (Principal value - Salvaged value)/ Lifespan (in yrs)Declining Balance MethodHigher depreciation in early years, lower expenses in later yearsDepreciation per year = Book value at start of year x Depreciation rateSum of the Year's Digits MethodWeighted like the declining balance methodDepreciation = Remaining life of asset/Sum of Years x (Book value - Salvaged ValueFor example if the asset had 5 years of useful life, year 1 = 5/(1 + 2 + 3 + 4 + 5), year 2 = 4/(same sum of 15)...MACRS (Modified Accelerated Cost Recovery SystemBased on tables provided by the IRS and their recovery periods.Initially uses the Declining balance method, but later uses a straight line instead.First decide which category the asset is under, then use the IRS chart of percentages, varies per yearCan receive tax benefitsDetermine straight-line depreciation for a year.Depreciation per year = (Principal value - Salvaged value)/ Lifespan (in yrs)Determine the depreciation expense on plant assets by the sum of the year’s digits and declining balance.See #1 for how to use these methodsDetermine modified accelerated cost recovery system depreciation.See #1Use the straight-line depreciation method to find the value of an asset.See #1InventoryDetermine the cost and value of inventory.Add up total units by their values, repeat with other typesDetermine rate of inventory turnover.Cost of Goods Sold / Average InventoryHigher shows stronger salesDetermine the value of ending inventory using Average Cost (weighted average), FIFO, and LIFO.Weighted Ave Cost Per Unit = Total Cost of Inventory/Total Units available for SaleEnding Value = Weighted Ave x Units in ending inventoryFIFO (First in First Out Method)Uses the cost of the most recent purchases (assumes oldest inventory sold 1st) to value ending inventoryLIFO (Last in First Out)Same as above but instead values the oldest purchases (Assumes the newest purchases are sold first)Ratios and ProportionsDefine the terms ratio and proportion.Comparing one value to another, depending on the size of the originalUse ratios to evaluate profitability, efficiency, and leverage.Higher ratios tend to mean better profit margins or valuesCreate ratios to express the quantitative relationship between two amounts.32:4 - 8:1Use ratios, proportions, and percents to solve problems involving financial calculations.Use them wellAnalyze and explain methods for solving problems involving proportions such as scaling and finding equivalent ratios.Scale each side by the same amount to find equal ratios, like fractions.