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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