A man estimates that the computer he plans to buy in 15 months will cost $2,400.To meet this goal, how much should he deposit in an account paying 9.6%, compounded monthly?
A)$2,099.63
B)$2,109.63
C)$2,129.63
D)$2,133.63
E)none of the above

Question

Quizplus · Accepted Answer

First, we need to find the future value of the $2,400 in 15 months with 9.6% annual interest rate, compounded monthly. Using the formula:

$FV=P\cdot(1+r/n)^{nt}$

where:
P = principal amount (the amount we need to deposit)
r = annual interest rate (as a decimal)
n = number of times the interest is compounded per year
t = time (in years)

We have:
P = ?
r = 0.096/12 = 0.008
n = 12
t = 15/12 = 1.25

$FV = 2,400\cdot(1+0.008)^{12\cdot1.25} = 2,613.95$

Therefore, the amount he needs to deposit now is $2,613.95/(1+0.008)^{12\cdot1.25} = $2,129.63, which is closest to choice C.

A Man Estimates That the Computer He Plans to Buy