## anonymous one year ago Engineering Economy(Not sure if it belongs here just need help): A rich man put up a trust fund in the bank with instructions to give his son the earnings of 400,000 at the end of every four (4) years and to continue until the twentieth (20th) year of the deposit when the son could get the 400,000 earning and the principal. What is the amount of money placed in the trust fund if guaranteed interest is 16% per year?

1. phi

earnings of 400,000 What is the amount of money placed in the trust fund ? Is this a trick question? If you want the earnings of 400,000 then you should put 400,000 into the fund.

2. anonymous

@phi i'm not so sure, but the answer is 493,340. I've been using the compounding interest formula and still can't solve for it.

3. anonymous

i think this is annuity problem? but still can't solve for it.

4. dumbcow

this is present value problem using geometric series the amount in trust is present value of 5 400,000 payments over next 20 years $PV = 400,000(v +v^2 + ...+v^5) = 400,000 (\frac{v (1-v^5)}{1-v})$ where "v" is present value of 1 dollar at 16% over 4 yrs $v = \frac{1}{(1.16)^4}$

5. phi

The best I can come up with is to interpret the problem as saying " an amount P is deposited into an account which provides 16% interest, compounded yearly, for 4 years. The total accrued interest of 400,000 is paid out. .. What amount is P ?" (the info about 20 years, etc is not relevant) using r= 0.16, we write P+400,000 = P(1.16)^4 400,000= P(1.16^4 - P = P(1.16^4 -1) and P = 400,000/(1.16^4 - 1) this gives a value of P= 493,438 which is close to your 493,340 value.

6. anonymous

@phi @dumbcow thank you very much for helping me solve the problem. i understand it now. :)