## Info

Challenge

(continued)

PART THREE Valuation of Future Cash Flows

Now, Judy recognizes that coming up with \$1,481.54 all at once might be a strain, so she lets you make "low, low monthly payments" of \$1,481.54/36 = \$41.15 per month, even though this is extra bookkeeping work for her.

Is this a 14 percent loan? Why or why not? What is the APR on this loan? What is the EAR? Why do you think this is called add-on interest?

66. Calculating Annuity Payments This is a classic retirement problem. A time line will help in solving it. Your friend is celebrating her 35th birthday today and wants to start saving for her anticipated retirement at age 65. She wants to be able to withdraw \$80,000 from her savings account on each birthday for 15 years following her retirement; the first withdrawal will be on her 66th birthday. Your friend intends to invest her money in the local credit union, which offers 9 percent interest per year. She wants to make equal annual payments on each birthday into the account established at the credit union for her retirement fund.

a. If she starts making these deposits on her 36th birthday and continues to make deposits until she is 65 (the last deposit will be on her 65th birthday), what amount must she deposit annually to be able to make the desired withdrawals at retirement?

b. Suppose your friend has just inherited a large sum of money. Rather than making equal annual payments, she has decided to make one lump-sum payment on her 35th birthday to cover her retirement needs. What amount does she have to deposit?

c. Suppose your friend's employer will contribute \$1,500 to the account every year as part of the company's profit-sharing plan. In addition, your friend expects a \$30,000 distribution from a family trust fund on her 55th birthday, which she will also put into the retirement account. What amount must she deposit annually now to be able to make the desired withdrawals at retirement?

67. Calculating the Number of Periods Your Christmas ski vacation was great, but it unfortunately ran a bit over budget. All is not lost, because you just received an offer in the mail to transfer your \$10,000 balance from your current credit card, which charges an annual rate of 17.9 percent, to a new credit card charging a rate of 8.9 percent. How much faster could you pay the loan off by making your planned monthly payments of \$200 with the new card? What if there was a 2 percent fee charged on any balances transferred?

68. Future Value and Multiple Cash Flows An insurance company is offering a new policy to its customers. Typically, the policy is bought by a parent or grandparent for a child at the child's birth. The details of the policy are as follows: The purchaser (say, the parent) makes the following six payments to the insurance company:

 First birthday: \$750 Second birthday: \$750 Third birthday: \$850 Fourth birthday: \$850 Fifth birthday: \$950 Sixth birthday: \$950

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

III. Valuation of Future Cash Flows

6. Discounted Cash Flow Valuation