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# EAR / APR

1.)The Maybe Pay Life Insurance Co. is trying to sell you an investment policy that will pay you and your heirs \$25,000 per year forever. If the required return on the investment is 7.2 percent, how much will you pay for the policy?

2.)In the previous problem, suppose a sales associate told you the policy costs \$375,000. At what interest rate would this be a fair deal?

3.) Find the EAR in each of the following cases:
Stated Rate (APR) # of times compounded Effective rate (EAR)
8% Quarterly
16% Monthly
12% Daily
15% Infinite

4.)Find the APR, or stated rate, in each of the following cases:
Stated Rate (APR) # of times compounded Effective rate (EAR)
Semiannually 8.6%
Monthly 19.8%
Weekly 9.4%
Infinite 16.5%

5.)You want to buy a new sports coupe for \$68,500 and the finance office at the dealership quoted you a 6.9 percent APR loan for 60 months to buy the car. What will your monthly payments be? What is the effective annual rate on the loan?

#### Solution Preview

1. Since the policy pays forever it is a perpetuity. What we would pay is the present value of the payments from the policy. For a perpetuity, present value is calculated as
Present Value = Annual Payment/required return = 25,000/7.2% = \$347,222.20
We would pay \$347,222.20 for the policy

2. In this case we are given the present value and we have to find the rate. Using the same formula
Rate = Annual payment/Amount = 25,000/375,000 = ...

#### Solution Summary

The solution explains some questions relating to Annual Pecentage Rate and Equivalent Annual Rate

\$2.19