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2 Saved Live Forever Life Insurance Co. is selling a perpetuity contract that pays $1,100 monthly The contract currently sells for $107000. What is the monthly return on this investment vehicle? (Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) a. b. 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.) 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.) c. a. Monthly returm b. APR c. EAR 1.02% 12.33

Solution

Here we need to find the interest rate that equates the perpetuity cash flows with the PV of the cash flows. Using the PV of a perpetuity equation:

PV = C/r

$107,000 = $1,100/r

r = 0.01028 or 1.028% per month

The interest rate is 1.028% per month. To find the APR, we multiply this rate by the number of months in a year, so:

APR = (12)1.028% = 12.336%

3.

And using the equation to find an EAR:

EAR = [1 + (APR/m)]^m– 1

= (1 + 0.01028)¹² - 1

= 0.130579 or 13.58 %