SOLUTION: 4. A client has asked for your advice on setting up two university education trust funds for his two children ages 4 and 6 respectively. He feels that an accumulated trust of $10,0

Question 1011421: 4. A client has asked for your advice on setting up two university education trust funds for his two children ages 4 and 6 respectively. He feels that an accumulated trust of $10,000 for each child on their 18th birthdays will be sufficient to provide a good education.
a) What amount must be placed in each trust account annually in advance to produce the desired trust, assuming that the deposits bear interest at 7% compounded annually?

Found 2 solutions by Boreal, MathTherapy:
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
10,000=Po{1+0.07}^t, where Po is the amount needing to be placed in the trust account.
ln of both sides
9.2103=ln Po+t ln(1.07); t=12 for the oldest child
9.2103-12ln(1.07)=8.3984. Don't round yet,
now take e of both sides
e^8.3984-e^(lnPo)=Po
$4440.12
===========same for the other child, only t=14
$3878.17

Answer by MathTherapy(10552) (Show Source): You can put this solution on YOUR website!
4. A client has asked for your advice on setting up two university education trust funds for his two children ages 4 and 6 respectively. He feels that an accumulated trust of $10,000 for each child on their 18th birthdays will be sufficient to provide a good education.
a) What amount must be placed in each trust account annually in advance to produce the desired trust, assuming that the deposits bear interest at 7% compounded annually?

Amount each year for 4 year-old: for 14 years
Amount each year for 6 year-old: for 12 years
This is the formula I used. It's set up in MS Excel. It may seem like 2 different formulae, but they're the same.
It's just that one is a little simpler, if I may say so.
, or , where:
= ANNUAL deposit
= FUTURE VALUE of an ordinary annuity (end-of-period deposit)
= ANNUAL INTEREST rate
= NUMBER of COMPOUNDING periods, per annum
= TIME (in years)
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