Question

Maybepay Life Insurance Co. is selling a perpetual annuity contract that pays $3,000 monthly. The contract currently sells for $326,000. What is the monthly return on this investment vehicle? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Monthly return % What is the APR? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Annual percentage rate % What is the effective annual return? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Effective annual return %

Answer 1

Solution:

1 : The interest rate that fits the lifetime cash flows to the PV of cash flows is expected here.  

PV of an equation of perpetuity:

PV = C/ r

$326,000 = $3,000 / r

With the interest rate, we could now solve the following:

r= $3,000 / $326,000

r= 0.0092 or 0.92% per month

2 :The interest rate per month is 0.92 percent.  

In order to calculate the APR, the number of months in a year is determined by:

APR = (12) 0.92%

APR = 11.04%

3 : And using the equation to find the EAR, we find:

EAR = [1 + (APR / m)]m– 1

EAR = [1 + 0.0092]12– 1

EAR = 0.1162 or 11.62%