## Calculating Ear With Points

85,000

55. Calculating Present Values A 5-year annuity of ten \$8,000 semiannual payments will begin 9 years from now, with the first payment coming 9.5 years from now. If the discount rate is 14 percent compounded monthly, what is the value of this annuity five years from now? What is the value three years from now? What is the current value of the annuity?

56. Calculating Annuities Due As discussed in the text, an ordinary annuity assumes equal payments at the end of each period over the life of the annuity. An annuity due is the same thing except the payments occur at the beginning of each period instead. Thus, a three-year annual annuity due would have periodic payment cash flows occurring at Years 0, 1, and 2, whereas a three-year annual ordinary annuity would have periodic payment cash flows occurring at Years 1, 2, and 3.

Ross et al.: Fundamentals of Corporate Finance, Sixth Edition, Alternate Edition

III. Valuation of Future Cash Flows

6. Discounted Cash Flow Valuation

CHAPTER 6 Discounted Cash Flow Valuation a. At a 10.5 percent annual discount rate, find the present value of a six-year ordinary annuity contract of \$475 payments.

b. Find the present value of the same contract if it is an annuity due.

57. Calculating Annuities Due You want to buy a new sports car from Muscle Motors for \$48,000. The contract is in the form of a 48-month annuity due at a 9.25 percent APR. What will your monthly payment be?

58. Amortization with Equal Payments Prepare an amortization schedule for a five-year loan of \$20,000. The interest rate is 12 percent per year, and the loan calls for equal annual payments. How much interest is paid in the third year? How much total interest is paid over the life of the loan?

59. Amortization with Equal Principal Payments Rework Problem 58 assuming that the loan agreement calls for a principal reduction of \$4,000 every year instead of equal annual payments.

60. Discount Interest Loans This question illustrates what is known as discount interest. Imagine you are discussing a loan with a somewhat unscrupulous lender. You want to borrow \$20,000 for one year. The interest rate is 11 percent. You and the lender agree that the interest on the loan will be .11 X \$20,000 = \$2,200. So the lender deducts this interest amount from the loan up front and gives you \$17,800. In this case, we say that the discount is \$2,200. What's wrong here?

Calculating EAR with Discount Interest You are considering a one-year loan of \$13,000. The interest rate is quoted on a discount basis (see the previous problem) as 16 percent. What is the effective annual rate? Calculating EAR with Points You are looking at a one-year loan of \$10,000. The interest rate is quoted as 12 percent plus three points. A point on a loan is simply 1 percent (one percentage point) of the loan amount. Quotes similar to this one are very common with home mortgages. The interest rate quotation in this example requires the borrower to pay three points to the lender up front and repay the loan later with 12 percent interest. What rate would you actually be paying here? Calculating EAR with Points The interest rate on a one-year loan is quoted as 14 percent plus two points (see the previous problem). What is the EAR? Is your answer affected by the loan amount?

EAR versus APR There are two banks in the area that offer 30-year, \$150,000 mortgages at 8.5 percent and charge a \$1,000 loan application fee. However, the application fee charged by Insecurity Bank and Trust is refundable if the loan application is denied, whereas that charged by I. M. Greedy and Sons Mortgage Bank is not. The current disclosure law requires that any fees that will be refunded if the applicant is rejected be included in calculating the APR, but this is not required with nonrefundable fees (presumably because refundable fees are part of the loan rather than a fee). What are the EARs on these two loans? What are the APRs?

65. Calculating EAR with Add-On Interest This problem illustrates a deceptive way of quoting interest rates called add-on interest. Imagine that you see an advertisement for Crazy Judy's Stereo City that reads something like this: "\$1,000 Instant Credit! 14% Simple Interest! Three Years to Pay! Low, Low Monthly Payments!" You're not exactly sure what all this means and somebody has spilled ink over the APR on the loan contract, so you ask the manager for clarification.

Judy explains that if you borrow \$1,000 for three years at 14 percent interest, in three years you will owe:

Intermediate

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