Peter Johnson invests $35516.80 now for a series of $5000 annual returns beginning one year from now. Peter will earn 10% on the initial investment. How many annual payments will Peter receive?
A) 10
B) 12
C) 13
D) 15

Question

Quizplus · Accepted Answer

Using the formula for the present value of an annuity due:

PV = C * [(1 - (1 + r/n)^(-nt))/ (r/n)] * (1 + r/n)

where PV is the present value, C is the periodic payment, r is the annual interest rate, n is the number of compounding periods per year, and t is the number of years.

We have PV = $35,516.80, C = $5,000, r = 10%, and n = 1 (annual payments). Solving for t, we get:

$35,516.80 = $5,000 * [(1 - (1 + 0.10/1)^(-t*1))/ (0.10/1)] * (1 + 0.10/1)

$35,516.80 = $5,000 * [(1 - 1/(1.1)^t)/ 0.10] * 1.1

$35,516.80 = $55,000 * (1 - 1/(1.1)^t)

(1 - 1/(1.1)^t) = $35,516.80 / $55,000

(1.1)^t - 1 = 0.6458

Using logarithms, we get:

t = log(1 + 0.6458)/log(1.1) = 13.03

Therefore, Peter will receive 13 annual payments. The closest answer choice is C (13).

Peter Johnson Invests $35516