Question

An engineer wants to contribute $5,000 per year to her retirement account out of her year-end bonus. However, she just got out of school and there are a lot of other things that need her attention. Suppose she starts contributing to the retirement account 10-years-post graduation, leaving her 25 years until retirement. The interest rate is 8%, compounded annually. How much money will she have in the account at retirement?
A. $622,910.
B. $365,530.
C. $568,432.
D. $315,250.

Answer 1

Answer:

The correct option is (B) $365,530.

Explanation:

In this problem we need to determine the future value, i.e. the amount at the retirement age.

The formula to commute the future value is:

$\\ FV=A[\frac{(1+r)^{n}-1}{r}]$

Here,

A = annual investment = $5,000

r = interest rate = 8%

n = number of periods = 25

The future value is:

$\\ FV=A[\frac{(1+r)^{n}-1}{r}]\\=5000\times[\frac{(1+0.08)^{25}-1}{0.08}]\\=365529.699\\\approx365530$

Thus, the amount of money the engineer will have in the account at retirement is $365,530.