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Chapter006_Formulas_2nd

# 1 1 m remember that the apr is the quoted

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Unformatted text preview: ample Suppose you want to earn an effective rate of Suppose 12% and you are looking at an account that compounds on a monthly basis. What APR must they pay? they [ APR = 12 (1 + .12) or 11.39% 1 / 12 − 1 = .1138655152 49 Computing Payments with Computing APRs APRs Suppose you want to buy a new computer system and Suppose the store is willing to sell it to allow you to make monthly payments. The entire computer system costs \$3,500. The loan period is for 2 years and the interest rate is 16.9% with monthly compounding. What is your monthly payment? monthly Monthly rate = .169 / 12 = .01408333333 Number of months = 2(12) = 24 3,500 = C[1 – (1 / 1.01408333333)24] / .01408333333 C = 172.88 50 Future Values with Monthly Future Compounding Compounding Suppose you deposit \$50 a month into an Suppose account that has an APR of 9%, based on monthly compounding. How much will you have in the account in 35 years? in Monthly rate = .09 / 12 = .0075 Number of months = 35(12) = 420 FV = 50[1.0075420 – 1] / .0075 = 147,089.22 51 Present Value with Daily Present Compounding Compounding You need \$15,000 in 3 years for a new car. If You you can deposit money into an account that pays an APR of 5.5% based on daily compounding, how much would you need to deposit? deposit? Daily rate = .055 / 365 = .00015068493 Number of days = 3(365) = 1,095 FV = 15,000 / (1.00015068493)1095 = 12,718.56 52 Continuous Compounding Sometimes investments or loans are figured Sometimes based on continuous compounding based EAR = eq – 1 The e is a special function on the calculator normally The denoted by ex denoted Example: What is the effective annual rate of Example: 7% compounded continuously? 7% EAR = e.07 – 1 = .0725 or 7.25% 53 Quick Quiz – Part V What is the definition of an APR? What is the effective annual rate? Which rate should you use to compare Which alternative investments or loans? alternative Which rate do you need to use in the time Which value of money calculations? value 54 Pure Discount Loans – Example Pure 6.12 6.12 Treasury bills are excellent examples of pure Treasury discount loans. The principal amount is repaid at some future date, without any periodic interest payments. interest If a T-bill promises to repay \$10,000 in 12 If months and the market interest rate is 7 percent, how much will the bill sell for in the market? market? PV = 10,000 / 1.07 = 9,345.79 55 Interest-Only Loan - Example Consider a 5-year, interest-only loan with a 7% Consider interest rate. The principal amount is \$10,000. Interest is paid annually. Interest What would the stream of cash flows be? • Years 1 – 4: Interest payments of .07(10,000) = 700 • Year 5: Interest + principal = 10,700 This cash flow stream is similar to the cash This flows on corporate bonds and we will talk about them in greater detail later. them 56 Amortized Loan with Fixed Principal Amortized Payment - Example Payment Consider a \$50,000, 10 year loan at 8% Consider interest. The loan agreement requi...
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