Question

A 20-year-old student wants to save $5 a day for her retirement. Every day, she places $5 in a drawer. At the end of EACH year, she invests the accumulated savings in an automated account with an expected annual return of 9%, paid annually.

Required:
a. If she begins saving today; How much money will she have when she is 65?
b. If she did not start saving until she was 45 years old, how much would she have at 65?
c. How much must the 45-year-old deposit monthly to catch the 20-year old?

Answer 1

a. If she begins saving today; How much money will she have when she is 65?

Assuming that the student started saving the day of her birthday, she will have $1,825 at the end of each year. So we must find the future value of an ordinary annuity with 45 payments worth $1,825 and 9% interest rate:

FV = $1,825 x 525.85873 (FV annuity factor, 9%, 45 periods) = $959,692.18

b. If she did not start saving until she was 45 years old, how much would she have at 65?

FV = $1,825 x 51.16012 (FV annuity factor, 9%, 20 periods) = $93,367.22

c. How much must the 45-year-old deposit monthly to catch the 20-year old?

$959,692.18 = annuity payment x 51.16012

annuity payment = $959,692.18 / 51.16012 = $18,758.60