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?

Answer 1

For Julian

PMT= 2500

The first depsoit occured at 6th payment and we have 40 years to do, so a total of (N) =46 years

Interest rate=8%

Future value of annuity= (PMT/r) *[(1+r)^N-1] = (2500/46)*[(1+0.08)^46-1]= $1046065.17

Now look at Jonathan

His grandfather wants to have the same amoutn of julian, so we will use that future value to find the deposts to be made

Here total of 40 payments + additional payment made today= 41 years

PMT= (FV*r) / [(1+r)^N-1] = 1046065.17 / [(1+0.08)^41-1]

The deposits to be made are $3725.55