Austin Community College District



K-1. Finance: Simple and Compound Interest Simple and Compound Interest Summary Questions Explored:What is the difference between simple and compound interest?I want to deposit a lump sum of money into an account earning interest and leave it there. What will I have in the future?What lump sum should I deposit into an account earning interest in order to have a certain future value?What happens to my credit card balance if I don’t pay any of it for a period of time?Terms:Principal – initial amount of the investment or loanInterest – amount paid to you by the lender for investing with them, or, the fee you pay for borrowing moneySimple interest – interest paid only on the original principalCompound interest – interest paid on both the original principal and any interest that has been added to the original principalAnnual percentage rate (APR) - % of interest earned or owed each year; may need to be divided up for smaller time periods (i.e. monthly, quarterly, etc.), APR does not take compounding into accountCompounding period – period at the end of which interest is computedAnnually = once a yearSemiannually = twice a yearQuarterly = four times a yearMonthly = twelve times a yearDaily = 365 times a year (was 360 in the past before computers were readily available to make math easier for the banker)Savings accounts – accounts into which you deposit money Currently savings accounts have a very low interest rateStandard savings accounts, money market accounts, and CDs (certificate of deposit) are a few different types of savings accounts with different interest rates and withdrawal restrictions.FDIC – (Federal Deposit Insurance Corporation) guarantees safety of bank deposits currently up to $250,000 per depositor per bank (as of 2016)Bonds – when you purchase a bond, the bond issuer is in debt to the bond holder and pays the bond holder interest on the bond and/or repays the principal later to the holderThe bond holder is the lender and has loaned the bond issuer money, who is now the debtor.There are many types of bonds: Treasury bonds, corporate bonds, municipal bonds, etc.Bonds may have a fixed or variable interest rate.Interest may be simple or compound.Bonds may or may not be inflation-linked.Bonds may or may not have tax advantagesBonds may be low or high riskCredit card – system of payment that allows someone to purchase goods or services with the promise that the money will be repaidAnnual percentage yield (APY or effective annual yield or effective yield or yield) – actual percentage by which a balance increases in one year, slightly different than the APR since it takes compounding into accountRulesSimple interest: The amount of interest earned is the same percentage of the original principal every pound interest: The amount of interest earned in each time period is computed on the accumulated amount of money in the account at the beginning of that time period.Annual Percentage Yield: The annual percentage yield of an investment is computed by finding the relative change from the initial balance to the balance at the end of the same year. Simple & Compound Interest Practice ExercisesUse a table to contrast simple and compound interest. Suppose we are modeling in each case a principal of $1000, one model using 4% simple interest and the other model using 4% compound interest. 4% Simple InterestYearStarting BalanceInterest Ending Balance1234% Interest Compounded AnnuallyYearStarting BalanceInterest Ending Balance123An investor purchases a corporate investment bond worth $10,000 with an annual coupon rate of 6% (simple interest). Assuming interest gets paid every six months, how much will the investor get paid every six months? Over the whole five years? Use the table below.Period Ending Year…Interest Earned that Period0.511.522.533.544.55Sarah puts $5000 into a savings account that pays 2% compounded annually. Rolando puts $5000 into a savings account that pays 2% semiannually. Complete the following tables that compare the amounts in their accounts. Summarize your findings regarding the same APR with different numbers of compoundings.Sarah: 2% APR is ______% AnnuallyRolando: 2% APR is ______% SemiannuallyValue after…Value after…6 months1 year1year1.5 years2 years2 years2.5 years3 years3 yearsExcel Activity: Simple & Compound Interest Spreadsheets Suppose that you purchase a US Series EE bond online at full face-value with an APR of 3.15%, compounded monthly. If you buy the bond originally for $100, how much will it be worth after 20 years when you decide to cash it out? Suppose you invest $500 into a CD with an interest rate of 2% compounded monthly. How much will be in the account after 60 months?How much should you deposit into a savings account with an APR of 4% compounded quarterly if you wish to have $50,000 in the account after 20 years? Assuming you make an investment for one year, you might think that increasing the number of compoundings per year on your investment would give you significantly higher returns. Let’s check that hypothesis. Fill in the table below. Assume that you invest $10,000 with APR 5% for one pounding Periods…Amount in account after one yearAnnually SemiannuallyQuarterlyMonthlyDaily (use 360 periods)What do you notice about the differences between the values as you increase the number of compoundings? The annual percentage yield (APY) on an investment is slightly higher than the APR since the APY takes compoundings into account. To compute the APY, find the relative change (as a percent) from the initial balance to the final balance over one year. For example, an investment grows from $5000 to $5415.00 over the course of one year. Compute the APY of this investment. Given that the APR of this investment was 8%, would a bank be more likely to advertise the APR or the APY for an investment? Explain. Suppose that you have a balance of $8500 on your credit card. With the permission of your credit card company you suspend payments (and don’t use the card) for one year. How much will you owe at the end of the year? Assume the company uses an APR of 21% compounded daily.You deposit $2000 into an account earning 3% interest compounded monthly. How long will it take for the account to grow to $3000? Simple & Compound Interest Excel ActivityPart I: Simple InterestOpen up the Excel file for this simple interest section and save the file in a location you know. Using your knowledge from the in-class exercises you just did, create formulas in Excel to populate the table and obtain ending balances using what you learned from our discussion and presentation up front. The formulas should contain an absolute reference for the interest rate cell location so that the table will reflect any changes in the interest rate percentage Notice: On what amount are you always computing simple interest? Why is this not the amount on which you want the bank to compute interest? _________________________________________________________________________________________________________________________________________________________________________________Part II: Compound Interest Let’s discuss how you would fix your Excel table so that it would compute interest on the most recent ending balance. In the same Excel workbook, open up the Compound Interest worksheet. Enter formulas for each column in order to model compound interest.Notice: What type of growth model is reflected with simple interest? With compound interest? _______________________________________________________________Part III: Compound Interest with WithdrawalIn the same Excel workbook, open up the Compound Interest Withdrawal worksheet. What would happen if—either regularly or just a few times—you wanted to withdraw an amount from the account once at the end of the year? What column would that withdrawal affect and how would you model this? After you modify the formulas to reflect an end-of-year withdrawal, experiment with different withdrawal values at different times to see how that affects the ending balances.Part IV: Interest Compounded More Than Once Per YearIn the same Excel workbook, open up the Compound Interest Withdrawal N worksheet. Now suppose that interest isn’t compounded just once per year, but more than one time per year. In that case, the APR must be divided into as many pieces as the number of compoundings per year. This gives the interest rate per period. Below, fill in the interest rate per period. APR Number of Compoundings per YearInterest Rate per Period12%1 (annually)12%2 (semiannually)12%4 (quarterly)12%12 (monthly)At the top of the spreadsheet you have an Interest Rate Per Period (%) box. Use the information above to provide a formula in this box that computes the interest rate per period. Notice that the first column is now labeled Period, not Year. For example, if you compound something quarterly, then one year comes after the 4th period. If you compound something monthly, then one year comes after the 12th period, etc.Now, discuss how you would create a formula under the Interest Paid column now that you have an interest rate per period. Pull down your formulas and use your spreadsheets to answer the remaining in-class exercises. ................
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