Question

Julian and Jonathan are twin brothers (and so were born on the same day). Today, both turned 25. Their grandfather began putting $2,500 per year into a trust fund for Julian 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 Julian's 65th birthday. The grandfather set things up this way because he wants Julian to work, not be a "trust fund baby," but he also wants to ensure that Julian is provided for in his old age. Until now, the grandfather has been disappointed with Jonathan and so has not given him anything. However, they recently reconciled, and the grandfather decided to make an equivalent provision for Jonathan. He will make the first payment to a trust for Jonathan today, and he has instructed his trustee to make 40 additional equal annual payments until Jonathan 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 Jonathan's trust today and each subsequent year to enable him to have the same retirement nest egg as Julian after the last payment is made on their 65th birthday? a. $3,912 b. $4,313 c. $4,107 d. $4,528 e. $3,726

Answer 1

Julian's trust will receive 46 installments of $2,500 each @ 8%. This will give a total of $ 1,046,065.
Calculation details:
: 2,500*(1+8%)^(45)+2,500*(1+8%)^(44)+2,500*(1+8%)^(43)+.............2,500*(1+8%)^(1)+2,500=1,046,065
This can also be achieved more simply by using finance formula for FV in M.S.Excel
FV(rate,nper,pmt,[pv],[type])
where;

rate: 8%
nper: 46
pmt: 2500
pv: not relevant in this case as we are using pmt to find FV, so we leave this blank
type: end of period. Since the payment is made on Julians birthday and the fund matures on his 65th birthday, its hence understood that payment are made at the end of period.

Now we know that Jonathan's fund shpuld also have the same balance on his 65th birthday. This has to be achieved in fewer number of installments, we need to find out this installment.
We have the Future Value (FV=1,046,065), Rate, number of payments, what we need to find out here is installment ie. pmt

Here we use the finance formula of PMT (M.S.Excel)
PMT(rate, nper, pv, [fv],[type])
rate: 8%
nper: 41
pv: here we leave this blank as there is no one single amount, rather a series of payments which we intend to find
fv: 1046065
type: end of period

Solving for PMT we get an installment amount of 3,725.55 which is 3,726

Answer: e. 3,726