Steve and Ed are cousins who were both born on the same day.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 sixth payment into the fund.The grandfather (or his estate's trustee) will continue with these $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 to 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 later today,and he has instructed his trustee to make additional equal annual payments each year 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

Question

Steve and Ed are cousins who were both born on the same day.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 sixth payment into the fund.The grandfather (or his estate's trustee) will continue with these $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 to 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 later today,and he has instructed his trustee to make additional equal annual payments each year 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

Quizplus · Accepted Answer

The grandfather needs to put $3,726 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. This is because the present value of the 41 annual payments of $2,500 at an 8% annual return is $65,000. The present value of the 46 annual payments of $2,500 at an 8% annual return is $75,000. Therefore, the grandfather needs to put in an additional $10,000 over the 41 years to make up the difference. This works out to $10,000/41 = $244 per year. Adding this to the $2,500 annual payment, the grandfather needs to put in $2,500 + $244 = $3,726 into Ed's trust today and each subsequent year.

Steve and Ed Are Cousins Who Were Both Born on the Same