Your job pays you only once a year for all the work you did over the previous 12
ID: 2724588 • Letter: Y
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 $55,000 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 9.5 percent per year. Your salary will increase at 3 percent per year throughout your career. How much money will you have on the date of your retirement 40 years from today?
Explanation / Answer
Answer: Since your salary grows at 3% per year, your next year’s salary is:
=$55000*(1+0.03)=$56650
Therefore, your deposit into your retirement account next year will be:
Next year Deposit is =$56650*0.10=$5665
Since your salary grows at a constant 3% per year and you put in a constant 10% of your salary into your retirement account, your annual deposit into the retirement account grows at 3% per year. Therefore, we can use the present value of a growing perpetuity equation to find the present value of your deposits today:
PVGP=$5665*[(1/(0.095-0.03)-(1/(0.095-0.03)*(1.03/1.095)^40]
=79616.6333
Now, we can find the value of this lump sum in 40 years:
FV=PV(1+r)^t
FV=$79616.6333*(1.095)^40
=$3003091.577
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