The present value of five uneven cash flows is $2,145. At a nominal rate of 10% compounded annually, what is the fifth payment if payment one is $500, payment two is $600, and payments three and four are $400?
A)$245
B)$1,000
C)$500
D)$600

Question

Quizplus · Accepted Answer

First, we need to calculate the present value of payments one to four. Using the formula for present value of uneven cash flows, we get:

PV = $500/(1 + 0.1)^1 + $600/(1 + 0.1)^2 + $400/(1 + 0.1)^3 + $400/(1 + 0.1)^4
PV = $500/1.1 + $600/1.21 + $400/1.331 + $400/1.4641
PV = $452.49 + $495.87 + $300.30 + $273.38
PV = $2,541.04

Since we know the present value of all five payments is $2,145, we can calculate the present value of the fifth payment:

$2,145 = $2,541.04/(1 + 0.1)^4 + X/(1 + 0.1)^5
$2,145 = $1,612.45 + X/1.61051
$532.55 = X/1.61051
X = $858.63

Therefore, the fifth payment is $858.63, which is closest to answer choice B ($1,000).

The Present Value of Five Uneven Cash Flows Is $2,145