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Unformatted text preview: F301 Problem Set 2 Solutions Spring 2011 Please show your work in a professional, businesslike fashion. It should be neither crowded nor illegibly tiny. Make this assignment look like something you could present to your boss. Show your work in the form requested in the problem: either calculations and equations, or calculator inputs with the TVM keys. No credit will be given without complete work. Each part of each problem is worth three points. Total possible points = 33. 1. You have decided to buy a car with the $10,000 gift you just received from your grandmother. That early Porsche Cayman will cost you $28,000. With your $10,000 cash as your down payment, you will need to borrow $18,000. Suppose this car loan is for four years, with a quoted interest rate of 9% compounded monthly. What will be the amount of your monthly payment? The rate is given as an APR with monthly compounding. Divide by m=12 to find R = 0.75% per month. Use this rate to solve for the monthly payment amount. 2. A bank is offering an amortized loan in the amount of $5,000 for 12 months, with a monthly payment of $432.27. a. What APR must the bank disclose on this loan? First solve for the rate of return for that monthly payment. So R = 0.57% per month. APR = R × m = 0.57% × 12 = 6.84% compounded monthly. b. What is the EAR on this loan? The EAR must be the annual rate which gives the same FV after one year. Solve for the EAR by setting the (1 + r) m terms equal to each other. ( ¡ ¢£¤¥¥¦¤§) ¨ © ( ¡ ¢£ª«¥¬§®) ¨¯ £ ¡ ¢£¤¥¥¦¤§ © ( ¡ °±±²³) ¨¯ £ ¡ ¢£¤¥¥¦¤§ © °±³±´£ µ¶· © ¸° ¹º» Alternatively, solve this as a TVM problem where the FV is the same. Find the FV using the monthly rate. Then solve for the rate which gives the same FV. Just change N and recompute. N I/Y PV PMT FV 48 0.75% 18,000 ? 447.93 N I/Y PV PMT FV 12 ? 5,000-432.27 0.570% N I/Y PV PMT FV 12 0.57%-100 ? 107.06 N I/Y PV PMT FV 1 ?-100 107.06 7.06% 3. Consider a five-year $10,000 Certificate of Deposit with an interest rate of 4.94%. a. If this rate is compounded annually, what will the CD be worth at the end of five years? APR = 4.94% compounded annually. R = 4.94% / 1 = 4.94% per year. FV = 10,000 × (1.0494) 5 FV = $12,726.39 b. If this rate is compounded weekly, what will the CD be worth at the end of five years? Assume 52 weeks per year. APR = 4.94% compounded weekly. R = 4.94% / 52 = 0.095% per week. FV = 10,000 × 1.00095 (52× 5) = 10,000 × 1.00095 260 FV = $12,800.29 4. See Question 1, above. It turns out your grandmother was only loaning you the money. She expects to be paid back at some point after you graduate. Let’s assume after you graduate you can begin depositing funds on a monthly basis into an account which will earn interest, so you can eventually pay her back. The account earns interest at the rate of 6.8% per year (EAR). If you deposit $345 per month, her back....
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This note was uploaded on 03/15/2012 for the course BUS-F 301 taught by Professor T during the Spring '12 term at IUPUI.
- Spring '12