The Maybe Pay Life Insurance Co. is trying to sell you an investment policy that will pay you and your heirs $33,000 per year forever. Suppose a sales associate told you the policy costs $478,000. At what interest rate would this be a fair deal?

Problem 6-11 Calculating Perpetuity Values [LO1]

The Maybe Pay Life Insurance Co. is trying to sell you an investment policy that will pay you and your heirs $33,000 per year forever. Suppose a sales associate told you the policy costs $478,000. At what interest rate would this be a fair deal? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Interest rate

%

 

Explanation:

The time line is:

0	1									∞
−$478,000	$33,000	$33,000	$33,000	$33,000		$33,000	$33,000	$33,000	$33,000	$33,000

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

$478,000 = $33,000 / r

We can now solve for the interest rate as follows:

r = $33,000 / $478,000

r = .0690, or 6.90%