Question

Your job pays you only once a year for all the work you did over the previous 12 months. Today, December 31, you just received your salary of $53,000 and you plan to spend all of it. However, you want to start saving for retirement beginning next year. You have decided that one year from today you will begin depositing 3 percent of your annual salary in an account that will earn 10 percent per year. Your salary will increase at 4 percent per year throughout your career. Required: How much money will you have on the date of your retirement 35 years from today?

Answer 1

The amount of money you will have on the date of your retirement 35 years from today is $640,143.22.

Step-by-step explanation:

This can be determined using the formula for calculating the future value of growing annuity as follows:

FV = M * (((1 + r)^n - (1 + g)^n) / (r - g)) ...................................... (1)

Where

FV = Amount on the date of retirement = ?

M = Annual deposit = Annual salary * Deposit percentage = $53,000 * 3% = $1,590

r = annual interest rate = 10%, or 0.1

g = salary growth rate = 4%, or 0.04

n = number of years = 35 years

Substituting all the values into equation (1), we have:

FV = $1,590 * (((1 + 0.1)^35 - (1 + 0.04)^35) / (0.1 - 0.04))

FV = $1,590 * ((1.1^35 - 1.04^35) / 0.06)

FV = $1,590 * ((28.1024368480643 - 3.94608899421194) / 0.06)

FV = $1,590 * (24.1563478538524 / 0.06)

FV = $1,590 * 402.605797564207

FV = $640,143.22

Therefore, the amount of money you will have on the date of your retirement 35 years from today is $640,143.22.