Financial Math Study Guide Notes #7

Financial Math NotesConsumer CreditIdentify the costs, benefits, and sources of various types of credit. The three main types of credit are revolving credit, installment credit, and open credit. Revolving Credit - Costs: Gives interest on balances that are unpaid. Annual fees, late fees, over-limit fees.Benefits: Allows you to have flexibility in how you borrow and pay money. Builds your credit history.Sources: You can get revolving credit from banks and credit unions.Installment Credit- Costs: Fixed interest over a period of time.Benefits: Assists in very big purchases such as a car or house.Sources: Banks and credit unions.Open Credit - Costs: Late fees if not paid in time.Benefits: No interest given if paid in time and provides services to the borrower without having to pay upfront.Sources: Charge card issuers such as American Express. Calculate sales tax and computer total price with sales tax.Sales Tax = (Price of item) x (Sales Tax Rate)Total Price = (Price of item) + (Sales Tax)Compute total purchase price with interest/finance charges addedFinance Charges = (Purchase Price) x (Interest Rate) x (Times in Years)Total Purchase Price = (Purchase Price) + (Finance Charges)Compute the costs involved in owning and buying an item such as an automobile, appliances, home, or furniture.Automobile - Buying: purchase price, sales tax, registration fees, loan interest. Owning: Insurance, maintenance, fuel. Home - Buying: purchase price, mortgage interest, property tax. Owning: insurance, maintenance. Appliances/Furniture - Buying: purchase price, delivery, installment. Owning: maintenance. Compute finance charges for single payment loans.Finance Charges = (Loan Amount) x (Interest Rate) x (Time in Years).Calculate installment loan costs such as amount financed, installment price, finance charge, and installment payment.Amount financed = (Purchase Price) - (Down Payment) - (Trade-in Value)Finance Charge = (Amount Financed) x (Interest Rate) x (Time in Years)Installment Price = (Amount Financed) + (Finance Charge)Installment Payment = (Installment Price) / (Number of Payments in Months)Find the estimated annual percentage rate (APR) using a table.APR =((Finance Charges) / (Amount Financed)) x ((365) / (Loan Term in Days)) x (100)Compare costs of leasing and buying.Leasing is better for people who plan on having lower monthly payments and returning the product at the end of the term. They don't plan on keeping the product for that long of a period of time. Buying is better for people who want to own the product as soon as they buy it and can pay higher monthly payments. They plan on keeping the product for a long period of time.Find the finance charge and new balance using the average daily balance method. Finance Charge = (Average Daily Balance) x (Daily Periodic Rate) x (Number of Days in Billing Cycle)Read amortization tables to determine payment, interest and balance. Amortization tables are used to track your loan payments over a period of time. This shows the amount of money that goes towards the interest for each payment and also shows the loan balance in total. Compute Annual and monthly Percentage Rate for credit cards or loan.APR = (Finance Charges/Amount FInanced) x 100MPR = (APR/12)Find the monthly mortgage payment. M = (P) x ((r(1+r)^n)/(1-r)^n-1))M = monthly mortgage payment, P = amount borrowed, r = monthly interest rate, n number of payments. Find the total interest on a mortgage and the PITI.Total Interest = (Monthly Payment x Number of Payments) - Loan PrincipalPITI = (Principal Payment + Interest Payment + Taxes + Insurance) Prepare a partial amortization schedule of a mortgage.First identify the loan principal, interest rate, loan term, and payment frequency. Second, calculate the monthly payment with the PMT formula: M = P x ((r(1+r)^n)/(1+r)^n-1))Third, create the amortization schedule. For every month, calculate the interest payment, principal payment, and remaining balance. Fourth, use the amortization schedule for any months that you need. Compare the total interest paid on a 15-year and 30-year fixed rate mortgage. A 15-year loan will result in lower interest paid but will have higher monthly payments. Define and compare the interest only, fixed rate, and adjustable-rate loans.Interest only loans are loans that require the borrower to only pay the interest required for the principal for a certain amount of time. Fixed-rate loans are loans where the interest rate stay the same for the entire span of the loan. Adjustable-rate loans are loans that have an interest rate that changes from time to time depending on many factors. Interest only loans have lower payments but have risks of higher payment when the principal is due. Fixed-rate loans have loans that remain constant which is appealing for borrowers who want consistency in payments.Adjustable-rate loans have lower rates at first but the rate change from time to time can be very unpredictable.Data Analysis and ReportingUsing a data set, determine mean, median, and mode.Mean = (Sum of all values/Number of values in total)Median = The middle value in a set of numbers. If the total number of numbers is odd, the median is the middle number. If it's even, the median is the two middle numbers divided by two.Mode = The number that appears the most in a set of numbers.Distinguish between a simple average and a weighted average and calculate each.The simple average is when all numbers are treated equally without an external factor. A weighted average is when you multiply a value by a weight depending on its importance. Simple Average = (Sum of all values/Number of values)Weighted Average = (SigmaNotation(value x weight)) / (SigmaNotation(weights))Identify and construct various types of graphs and charts.Bar Chart: Make an x and y-value chart. Label the categories on the x and y values. X is independent, y is dependent. A rectangle is put vertically on the x-value as it shows the value of the variable. Often shows the value of something.Pie Chart: Make a circle and divide the circle depending on how many variables there are. Make the divisions on the circle smaller or bigger depending on what the percentage is on one of the variables. Often shows percentages of something.Line Graph: Make an x and y-value chart with the x-value being the time. The y-value can be whatever variable you need as the x is independent and the y is dependent. Connect the lines on the graph with a line. Often shows where the value of something is headed depending on the circumstance.Scatter plot: Make an x and y-value chart. The x is independent and the y is dependent. Graph points on the scatter plot depending on whatever information you have. Do not connect them with lines. Often shows randomized events.Compile and arrange facts in organized manner for a table, chart, or figure.Step 1: Collect data. Step 2: Create a table depending on what data you have.Step 3: Put x and y values for the table with the x being independent and the y being dependent. Step 4: Put the values you have on the table. Explain or prepare written summary of findings expressed in tables, charts, graphs and figures.Step 1: Give background information on what the table is about.Step 2: Explain the key data in the table.Step 3: Explain the tendency of a variable on the table. (For Ex: show the tendency of the stock to either go up or down.)Step 4: Reflect on what the data on the table shows. (For Ex: if a stock is doing really well, keep on investing in the stock.)Step 5: Point out the outliers in the table. (For Ex: if a stock spikes up in value, this might be because of an external factor).Step 6: Draw a conclusion from the table. (For Ex: if a stock has been doing really well for a long time, keep that stock and it'll keep on rising.)Make predictions and decisions based on data and communicate their reasoning.If you have a piece of information, you can make predictions and decisions based on that piece of information. For example, if you have a piece of stock that's doing really well, you can make a prediction that that stock will continue to rise, therefore you can make the decision to buy that stock and keep onto it for a while.The information you get from data can communicate their reasoning with you as it'll help tell you the destined outcome of something and therefore you can make a decision from that.Explain the usage of statistics, probability, and systems of measurement in business.The usage of statistics, probability, and systems of measurement in business is key to helping a business thrive as a business can use statistics to analyze their past, current, and future sales. Using probability can help them determine what the percentage of something happening is and can therefore help them capitalize on that. They also use systems of measurement in business to help keep track of company records which helps to ensure consistency throughout the business. Interest RatesFigure rates, interest, and proceeds of bank discounts.Figure rates/D = (M) x (r) x (t)D = discount, M = maturity value, r = discount rate annually, t = period of time in yearsProceeds/P = (M) - (D)Proceeds are what the borrower receives after the discount is deducted. Calculate simple interest using the simple interest formula.(I) = (P) x (r) x (t)I = interest, P = principal, r = annual interest rate in decimal form, t = period of time in years.Calculate any single variable – principal, interest rate, amount of interest, or time – given the other three.Principal: P = (I) / ((r) x (t))Interest rate: r = (I) / ((P) x (t))Time: t = (I) / ((P) x (r))Explain the process of discounting a promissory note and calculate the proceeds of a discounted promissory note.The process of discounting a promissory note is where the person who gives money says that they'll pay a certain amount of cash at a future's given time. D: D = (M) x (r) x (t) M: P = (M) - (D)Define maturity value and find the maturity value of a loan.The maturity value is the total amount of money due at the end of the loan term. This includes the principal and the interest.Simple interest: M = (P) + (I)I = (P) x (r) x (t)M = P(1 + r x (t))Convert months to a fractional or decimal part of a year.Amount of time in years = (Number of months)/12Find the future value and compound interest by compounding manually.FV = P(1 + (r/n))^n(t)FV = future valueP = Principalr = annual interest raten = number of compounding periods per yeart = time in years Find the interest compounded daily using a table.FV = P x (1 + (r/365))^365(t)To find the interest compounded daily by using a table, look at the table as it provides the pre-calculated future value factors for different rates and time periods, then multiply the principal by the table factor for the given rate and time.