Question

Live Forever Life Insurance Co. is selling a perpetuity contract that pays $1,150 monthly. The contract currently sells for $67,000.

Required: (a) What is the monthly return on this investment vehicle?

(b) What is the APR? (Do not round your intermediate calculations.)

(c) What is the effective annual rate? (Do not round your intermediate calculations.)

Answer 1

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

$67,000 = $1,150/ r

We can now solve for the interest rate as follows:

r = $1,150/$67,000 = .0172 or 1.72% per month

The interest rate is 1.72% per month. To find the APR, we multiply this rate by the number of months in a year, so:

APR = (12)1.72% = 20.64%

And using the equation to find an EAR:

EAR = [1 + (APR/ m )] m – 1

EAR = [1 + .0172]^12 – 1 = 22.71%