Question

You and your cousin Kristin were born on the same day. Today is your 25th birthday. Five years ago (when you turned 20) your aunt started depositing $2,500 into Kristin's account. She did this every year and she just made a sixth deposit. Your aunt will make forty more $2,500 payments until a 46th and final payment is made on Kristin's sixty fifth birthday. Your aunt has had a change of heart and now wants to make an equivalent provision for you. She will make the first payment to your account today. She plans to make forty additional (and equal) annual payments until you too turn sixty five, when the forty first and final payment will be made. If both accounts earn an annual return of 8 percent, how much must your aunt put into your account today and the next 40 years to enable you to have the same retirement fund as Kristin after the last payment is made on your sixty fifth birthday?

Answer 1

We have:
Amount Deposited annually in Kristen's Account				2500
Total number of payments until Kristen's 65th Birthday				45
Annual Interest Earned				0.08
We need to determine the value in Kristen's account at the end of day, on her 65th birthday.
We can do this by using the Future Value of an annuity formula:

where,

P = constant periodic payment per period

r = rate of interest earned per period

n = number of periods

Plugging in the values we get,

The value in Kristen's account on her 65th birthday will be $9,66,264.04. Next we need to find the aunt's annual contribution for 40 years so that I will have the same Future Value as Kristen. We use the same formula as above but solve for P

We have:

Plugging in the values we get,

Hence my aunt has to invest $3,729.94 on my birthday each year for the next forty years so that the amount in my account on my 65th birthday is exactly same as the amount in Kristen's account on the same day.