Question

You are saving for your retirement. You have decided that one year from today you will deposit 4 percent of your annual salary in an account which will earn 8 percent per year. Your salary currently (today) is $70,000, and it will increase at 2 percent per year throughout your career. How much money will you have for your retirement, which will begin in 35 years? Assume your first payment into the account is one year from today after your first increase.

a. $41,161.55

b. $71,400.00

c. $608,439.83

d. $809,528.99

e. $909,845.87

Answer 1

c.608,439.83

this can be solved using future value of growing annuity:

P[(1+r)^n-(1+g)^n]/(r-g)

here,

P = initial payment =($70,000+2%)4% =>$2,856

n = 35 years

g = growth rate =>2%=>0.02

r = 8%=>0.08

$2,856[(1.08)^35- (1.02)^35] / (0.08-0.02)

=>$2856[(14.7853443 - 1.99988955]/0.06

=>$2856*213.090917

=>608,585.04...approximately $608,439.83

note:minute difference is because of rouding off of discounting factors.