Question

Live Forever Life Insurance Co. is selling a perpetuity contract that pays $1,400 monthly. The contract currently sells for $75,000.

a. What is the monthly return on this investment vehicle?

b.	What is the APR?

c.	What is the effective annual rate?

Answer 1

Answer;

a) Annual Percentage Rate ( APR )= 22.40%

b) Effective Annual Rate = 24.85%

Explanation;

Part a)

Formula ; Present value of perpetuity = Constant Cash flow / Interest Rate

Present value of perpetuity = $75000

Constant Cash Flow = $1400 Per month

Interest Rate = ?

So,

$75000 = $14000 / Rate

Rate x $75000 = $1400

Rate = $1400 / $75000

Rate = .018667 or 1.8667% per month

Annual Percentage Rate = Monthly rate x 12 month i.e. 1.8667 x 12 = 22.40%

Part b) Effective annual Rate = Formula: (1+rate)^n - 1

Rate = 1.8667% per month

n = 12 month

So,

Effective annual Rate = (1+ 1.8667%)^12 - 1

= (1.018667)^12 - 1

=1.2485 - 1

= 0.2485 or 24.85%

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