Question

You are buying a sofa. You will pay $200 today and make three consecutive annual payments of $300 in the future. The real rate of return is 7.5 percent, and the expected inflation rate is 4 percent. What is the actual price of the sofa? (Round intermediate calculation and final answer to 2 decimal places, e.g. 15.25.)

Actual price

$

Answer 1

Given,

Payment today = $200

Consecutive annual payments (A) = $300

No. of consecutive annual payments (n) = 3

Real rate of return = 7.5% or 0.075

Expected inflation rate = 4% or 0.04

Solution :-

Nominal rate of return (r) = [(1 + real rate of return) x (1 + nominal rate of return)] - 1

= [(1 + 0.075) x (1 + 0.04)] - 1

= [(1.075) x (1.04)] - 1

= 1.118 - 1 = 0.118

Actual price

= payment today + [A/r x {1 - (1 + r)^-n}]

= $200 + [$300/0.118 x {1 - (1 + 0.118)^-3}]

= $200 + [$300/0.118 x {1 - (1.118)^-3}]

= $200 + [$300/0.118 x {1 - 0.71560701517}]

= $200 + [$300/0.118 x 0.28439298483]

= $200 + $723.03

= $923.03