a mother leaves $10000 to her tow children with the no vision that they are to get equal mounts when they reach age 21 . if the children are 12 and 17 when the women dies how much will each receive ? the money is invested at 8% compounded quarterly .
+37170 We will have to assume that they are both EXACTLY 12 and 17 today (they both had birthdays today)
then we have 10,000 invested at 2% per quarter and that 1/2 of the amount will be distributed in 16 quarters and the remaining will be distributed in 36 quarters and the amounts can be different????? Well there is a whole bunch of possibilites depending on how it is split when the first kid turns 21 !
Wouldn't it be better to split the accumulated amount EQUALLY when the first kid turns 21 and then let the remainder continue to grow until final disbursement to the second child when she/he turns 21 ???? We'll need some more info to proceed.....BUT here is the way I would do it
10000(1+.02)^16 = 13727.86 when the 17 y/o turns 21......give half of the money to them $6863.93
6863.93 will continue to grow for 20 more quarters before being disbursed to the younger child
6863.93(1.02)^20 = 10199.44 to the younger child when she/he turns 21
This MAY seem unfair, but it is NOT....the FIRST child could leave the money deposited and get the same amount if she/he waits until the younger turns 21 to receive the money.
ElectricPavlov:
Good effort ElectrcPavlov but no cigar!!. Read the following carefully and try to undersrand it.
1) Since each child is to receive the same amount when they turn 21, then will have to find the PV of $1 in each case:
PV=FV [1 + R ]^-N
In the case of the 17-year old we have:
PV=1[1 + .08/4 ]^-(4*4)-He/she has 4 more years or 16 quartes to reach 21.
PV=.728445813714
In the case of the 12-year old we have:
PV=1 [1 + .08/4 ]^-(9*4)--He/she has 9 more years or 36 qurters to reach 21
PV=.490223150352
Now, will add these two PV's together and will get:
=.728445813714 + .490223150352
=1.21866896406. Next, will divide $10,000 by this figure, which is what each child will receive:
$10,0000 / 1.21866896406
=$8,205.67--Which is the the amount that each child will receive when they turn 21.
2) Check:
The $10,000 will grow for 4 more years until the 17-year old turns 21. At the time, it will be worth:
=13,727.86. Then will subtract his/her inheritance of $8,205.67 from this amount and the balance is:
$13,727.86 - $8,205.67=$5,522.19.
This balance of $5,522.19 will continue to grow @ 8% comp. quarterly for another 5 years or 20 quarters until the 12-year old, who is now 16, turns 21.
FV=$5,522.19[1.02]^20
=$8,205.67. And that is what the 12-year old will receive at 21, which is the same amount that the other child received. And that is the end of this saga!!!!.
+37170 Sorry , Guest....this WAS addressed in the Question AND the naswer EP gave.
"no vision that they are to get equal mounts when they reach age 21"
and
"..and the remaining will be distributed in 36 quarters and the amounts can be different????? Well there is a whole bunch of possibilites depending on how it is split when the first kid turns 21 ! "
IF the question said they were to receive the same amounts when they turn 21 , that would be different...BUT IT DOESN'T SAY THAT !
The fairest way of distributing the money would be as follows:
When the mother died, she should have left instuctions in her Will that the $10,000 be split evenly between the two children, or $5,000 per child. At the same time, she should have put a provision in her Will that the money is to be distributed ONLY when each child turns 21.
In that case, the 17-year old would have received $6,863.93 when he/she turned 21.
And the 12-year old would have received $10,199.44, when he/she turned 21.
Even though there is a difference of $3,335.51 between the two amounts, in reality they are equivalent, because their PV was equivalent when she died. The difference of $3,335,51 in FV is because of the extra 5 years that the money grew @ 8% comp. quarterly.
+37170 THIS IS WHAT HAPPENS WHEN QUESTIONS ARE WRITTEN UNCLEARLY OR WITH MISTAKES
OK....if you want them BOTH to receive the SAME amont when they EACH turn 21
Amount available when 17 y/o turns 21 = 10,000(1.02)^16 = 13727.86
x = amount they BOTH will get
Money after 17y/o gets first share = 13727.86-x
Money when the 12 y/o turns 21 is the same 'x ' and this equals :
x = (13727.86-x)(1.02)^20 Solve for 'x'
x = (13727.86-x)(1.4859473) then x = 8205.68 THey BOTH will get this amount when they EACH turn 21
OK.....done BOTH ways ....THIS is the end of the 'saga'
~THE END hahahahahaha
