Question

Steve and Ed are cousins who were both born on the same day, and both turned 25 today. Their grandfather began putting $2,100 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 $2,100 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? retirement nest egg as Steve after the last payment is made on their 65th birthday? Assume that all payments are made at the end of the year.

a. $3,067

b. $2,660

c. $3,129

d. $3,036

e. $3,255

Answer 1

First, we will calculate how much Steve will have when he retires,

Interest(i) = 8%

Periods remaining(n) = 46

Payment made each year(pmt) = $2,100

We have to calculate Future Value(FV).

We can use the financial calculator and put in the above values or we can use excel,

i = 8%, n = 46, pmt = -2100, CPT FV = $948,990.32 (set the calculator at the beginning of the period)

interest	8%
no periods	46
pmt	2100
FV	$948,990.32	(=FV(8%,46,-2100,1)

Hence FV = $948,990.32.

Now we will solve backwards,

Interest - 8%

No of periods = 41

FV = $948,990.32

pmt = ?

interest	8%
no periods	41
FV	948990.32
pmt	3129.47	(=PMT(8%,41,0,-948,990.32,1)

Hence the annual payments are $3,129(approx). The answer is option c) $3,129.

If you have any doubts please let me know in the comments. Please give a positive rating if the answer is helpful to you. Thanks.