Peter Johnson invests $35,516.80 now for a series of $5,000 annual returns beginning one year from now.Peter will earn 10% on the initial investment.How many annual payments will Peter receive?

Question

Quizplus · Accepted Answer

To determine the number of annual payments that Peter will receive, we need to use the formula for the future value of an annuity:
FV = PMT x [(1 + r)^n - 1] / r
where FV is the future value, PMT is the annual payment, r is the annual interest rate, and n is the number of payments.
In this case, we know that FV = $35,516.80, PMT = $5,000, and r = 10% = 0.1. We can solve for n:
$35,516.80 = $5,000 x [(1 + 0.1)^n - 1] / 0.1
$7.10336 = (1.1)^n - 1
1.1^n = 8.10336
n = log(8.10336) / log(1.1) = 12.99
Since the number of annual payments must be a whole number, Peter will receive 13 annual payments. Therefore, the best choice is C.

Peter Johnson Invests $35,516