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 $54,000 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 10 percent of your annual salary in an account that will earn 9.4 percent per year. Your salary will increase at 4 percent per year throughout your career.

  

How much money will you have on the date of your retirement 45 years from today? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

Answer:

Today yearly salary received = $54,000

One year from now year salary = 54000 * (1 + 4%) = $56160

1st deposit one year from now = 56160 * 10% = $5616

Salary growth rate / deposit growth rate = 4%

Discount rate = 9.4%

Time period = 45 years

First we will calculate present value of this growing annuity

The formula is:

PV = C * 1/ (r - g) * [1- {(1 + g) / (1 + r)} ^N]

C = Cash flow

r = Discount rate

g = Growth rate

N = Number of years

PV = 5616 * 1 / (9.4% - 4%) * (1- ((1 + 4%) / (1 + 9.4%)) ⁴⁵ )

=93340.0757676975

Now we can calculate future value of this present value:

FV = 93340.0757676975 * (1 + 9.4%) ⁴⁵

= $5,319,216.16

Money you will have on the date of your retirement 45 years from today = $5,319,216.16