Question

Assume that you are 25 years old today, and that you are planning on retirement at age 65. You expect your salary to be $55,000 one year from now and you also expect your salary to increase at a rate of 3% per year as long as you work. To save for your retirement, you plan on making annual contributions to a retirement account. Your first contribution will be made on your 26th birthday and will be 12% of this year's salary. Likewise, you expect to deposit 12% of your salary each year until you reach age 65. Assume that the rate of interest is 5%.

The future value (FV) (at age 65) of your retirement savings is closest to:________
a. $1,091,733.20
b. $1,246,723.80
c. $988,452.90
d. $1,225,821.20

Answer 1

FV= $1,246,723.8

Step-by-step explanation:

To calculate the future value of this growing annuity, we need to use the following formula:

FV= A*{[(1+i)^n - (1+g)^n] / (i-g)}

A= annual deposit= 55,000*0.12= 6,600

i= 0.05

g=0.03

n= 40 years

FV= 6,600* {[(1.05^40) - (1.03^40)] / (0.05 - 0.03)}

FV= $1,246,723.8