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 $68,000 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 10.8 percent per year. Your salary will increase at 2 percent per year throughout your career. How much money will you have on the date of your retirement 35 years from today? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Please show all work. Do not use Excel.

Answer 1

Your expected salary next year = Current salary *(1+annual salary growth rate) = 68000*(1+0.02) = 69,360.00

Out of this salary, you will deposit 10% next year. The amount of deposit = 0.10*69,360.00 = 6936.00

Since your annual deposit amount grows @ 2%, the PV of your annual deposits can be calculated from the following formula:

PV =(Initial Deposit/(r-g)) * [1-(((1+g)/(1+r))^n)], where:

• r = rate of return on investment = 10.80%
• g = growth rate = 2%
• n = number of periods over which deposits are made = 35

PV₀ =(6936/(0.108-0.02))*(1-(((1+0.02)/(1+0.108))^35)) = $74.465.66

Since this is the PV and you need the FV, we need to compond it @10.8 % for 35 years = 74.465.66*((1+0.108)^35) = $2,696,793.28, which is  money will you have on the date of your retirement.

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