## With The First Payment Occuring Today Your Child S 18th Birthday

After the child's sixth birthday, no more payments are made. When the child reaches age 65, he or she receives \$175,000. If the relevant interest rate is 10 percent for the first six years and 6 percent for all subsequent years, is the policy worth buying?

69. Calculating a Balloon Payment You have just arranged for a \$300,000 mortgage to finance the purchase of a large tract of land. The mortgage has a 9 percent APR, and it calls for monthly payments over the next 15 years. However, the loan has a five-year balloon payment, meaning that the loan must be paid off then. How big will the balloon payment be?

70. Calculating Interest Rates A financial planning service offers a college savings program. The plan calls for you to make six annual payments of \$5,000 each, with the first payment occurring today, your child's 12th birthday. Beginning on your child's 18th birthday, the plan will provide \$15,000 per year for four years. What return is this investment offering?

71. Break-Even Investment Returns Your financial planner offers you two different investment plans. Plan X is an \$8,000 annual perpetuity. Plan Y is a 10-year, \$20,000 annual annuity. Both plans will make their first payment one year from today. At what discount rate would you be indifferent between these two plans?

72. Perpetual Cash Flows What is the value of an investment that pays \$5,200 every other year forever, if the first payment occurs one year from today and the discount rate is 14 percent compounded daily? What is the value today if the first payment occurs four years from today?

73. Ordinary Annuities and Annuities Due As discussed in the text, an annuity due is identical to an ordinary annuity except that the periodic payments occur at the beginning of each period and not at the end of the period (see Question 56). Show that the relationship between the value of an ordinary annuity and the value of an otherwise equivalent annuity due is:

Annuity due value = Ordinary annuity value X (1 + r)

### Show this for both present and future values.

74. Calculating Annuities Due A 10-year annual annuity due with the first payment occurring at date t = 7 has a current value of \$50,000. If the discount rate is 13 percent per year, what is the annuity payment amount?

75. Calculating EAR A check-cashing store is in the business of making personal loans to walk-up customers. The store makes only one-week loans at 11 percent interest per week.

a. What APR must the store report to its customers? What is the EAR that the customers are actually paying?

b. Now suppose the store makes one-week loans at 11 percent discount interest per week (see Question 60). What's the APR now? The EAR?

c. The check-cashing store also makes one-month add-on interest loans at 8 percent discount interest per week. Thus, if you borrow \$100 for one month (four weeks), the interest will be (\$100 X 1.084) - 100 = \$36.05. Because this is discount interest, your net loan proceeds today will be \$63.95. You must then repay the store \$100 at the end of the month. To help you out, though, the store lets you pay off this \$100 in installments of \$25 per week. What is the APR of this loan? What is the EAR?

Challenge

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## Sell Your Annuity

Do you have annuity you dont want? Discover When is it Time to Sell Your Annuity? What can I do? Where can I get the money I need? I have an annuity, but I dont know that I can sell it. Is there a good time to sell my annuity? I already have a home improvement loan, but it was used before the roof needed replacing.

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