4. Steve and Ed are cousins who were both born on the same day, and both turned

Question

4. Steve and Ed are cousins who were both born on the same day, and both turned 25 today. Their grandfather began putting $2,500 per year into a trust fund for Steve on his 20th birthday, and he just made a 6th payment into the fund. The grandfather (or his estate's trustee) will make 40 more $2,500 payments until a 46th and final payment is made on Steve's 65th birthday. The grandfather set things up this way because he wants Steve to work, not be a "trust fund baby," but he also wants to ensure that Steve is provided for in his old age.
Until now, the grandfather has been disappointed with Ed, hence has not given him anything. However, they recently reconciled, and the grandfather decided to make an equivalent provision for Ed. He will make the first payment to a trust for Ed today, and he has instructed his trustee to make 40 additional equal annual payments until Ed turns 65, when the 41st and final payment will be made. If both trusts earn an annual return of 8%, how much must the grandfather put into Ed's trust today and each subsequent year to enable him to have the same retirement nest egg as Steve after the last payment is made on their 65th birthday?
a. $3,726 b. $3,912 c. $4,107 d. $4,313 e. $4,528

Explanation / Answer

Step 1 find how much Steve will have when he retires:

financial calculator steps
press g 7 (to set the calculator to assume payments are made at the beginning of the period)

8 i (interest earned)
46 n (periods remaining)
-2500 pmt (payment made into the account each period)
0 PV (starting balance of account)
solve for FV
FV = $1,129,750.38

We can now use this value to solve backwards

8 i
41 n (only 41 more payments here)
0 PV (starting balance)
1,129,750.38 FV (ending value)
solve for pmt
pmt = 3,725.55 ~ 3,726 so answer A

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