Question

An engineer expects to earn a $70,000 salary after she graduates. She anticipates that her salary will increase by an average of 4% each year until she retires 50 years later. If she deposits 10% of her salary into a retirement account at the end of each year, and the account earns 6% annual interest, how much will she have saved on the day she retires?

Answer 1

First deposit = 0.1*70000 = 7000

g = 0.04

i = 0.06

n = 50

Future worth of geometric series = A *[(1+i)^n - (1+g)^n]/(i-g)

Future worth of account = 7000*[(1+0.06)^50 - (1+0.04)^50]/(0.06-0.04)

= 7000*[(1.06)^50 - (1.04)^50]/(0.02)

= 7000 * 565.6735464

= 3959714.82 ~ 3959715