Question

An investment will return $125 at the end of each month for 5 years and then $250 at the end of each month for the next 3 years. What is the present value of the earnings on this investment calculated at the annual rate of 7.50% per year compounded monthly (0.625% per month)?

Answer 1

Present Value of an investment returning Amount P at the end of month for n months

= P/(1+r) + P/(1+r)² + ..... P/(1+r)ⁿ = P[1 - (1+r)^-n]/r

where, r is the monthly interest rate (r = 0.00625)

Part 1
P = $125
n = 5*12 = 60 months
r = 0.00625
=> NPV1 = 125(1 - 1.00625^-60)/0.00625 = $6238.164

Part 2
P = $250
n = 3*12 = 36 months
r = 0.00625
=> PV2 at 5 years = 250(1 - 1.00625^-36)/0.00625 = $8036.978
NPV2 (at t = 0) = 8036.978/1.00625⁶⁰ = $5530.179

Hence, NPV = NPV1 + NPV2 = 6238.164 + 5530.179 = $11768.343