Question

1.) The Maybe Pay Life Insurance Co. is trying to sell you an investment policy that will pay you and your heirs $30,000 per year forever. If the required return on this investment is 4.3 percent, how much will you pay for the policy? (Hint: Find PV of perpetuity)

2.) Find the EAR in each of the following cases:

a. APR 9% with quarterly compounding

b. APR 18% with monthly compounding

c. APR 14% with semi-annual compounding

3.) Find the APR, or stated rate, in each of the following cases:

a. EAR 11.5%, semi-annual compounding

b. EAR 12% with quarterly compounding

4.) Consider a 3-year bond with a face value of $1,000 that has a coupon rate of 7%, with semi-annual payments.

a. What is the dollar amount of each coupon from this bond?

b. How many times of coupon payments will be made to the maturity?

SHOW HOW YOU GOT ANSWERS PLEASE!

Answer 1

Answer to Question 1:

Present Value of Perpetuity = Annual Payment / Required Return
Present Value of Perpetuity = $30,000 / 0.043
Present Value of Perpetuity = $697,674.42

Answer to Question 2:

EAR = [1 + (APR/n)]^n - 1, where n is number of compounding per year

Answer a.

EAR = [1 + (APR/n)]^n - 1
EAR = [1 + (0.09/4)]^4 - 1
EAR = 1.0225^4 - 1
EAR = 1.0931 - 1
EAR = 0.0931 or 9.31%

Answer b.

EAR = [1 + (APR/n)]^n - 1
EAR = [1 + (0.18/12)]^12 - 1
EAR = 1.015^12 - 1
EAR = 1.1956 - 1
EAR = 0.1956 or 19.56%

Answer c.

EAR = [1 + (APR/n)]^n - 1
EAR = [1 + (0.14/2)]^2 - 1
EAR = 1.07^2 - 1
EAR = 1.1449 - 1
EAR = 0.1449 or 14.49%