A man leaves an estate of $50,000 which is invested at 9% compounded monthly. At the time of his death, he has two children aged 13 and 18. Each child is to receive an equal amount from the estate when they reach age 21. How much does each child get?
Let's say that he sets aside $x for the younger child, and 50000-x for the older one. Then we must have
x(1+.09/12)^96 = (50000-x)(1+.09/12)^36
x = 19488
so each child gets $39929
To find out how much each child will receive, we can use the future value formula for compound interest:
FV = PV * (1 + r/n)^(n*t)
Where:
FV is the future value or the amount each child will receive
PV is the present value or the initial investment of $50,000
r is the interest rate of 9% or 0.09
n is the number of times interest is compounded per year, which is 12 for monthly compounding
t is the time in years until the children reach age 21 (21 - current age)
Let's calculate the future value for each child:
For the first child aged 13:
t = 21 - 13 = 8 years
FV1 = $50,000 * (1 + 0.09/12)^(12*8)
For the second child aged 18:
t = 21 - 18 = 3 years
FV2 = $50,000 * (1 + 0.09/12)^(12*3)
Now, let's calculate the future value for each child:
FV1 = $50,000 * (1 + 0.0075)^(96)
FV1 ≈ $50,000 * (1.0075)^(96)
FV1 ≈ $50,000 * 1.87867
FV1 ≈ $93,933.33
FV2 = $50,000 * (1 + 0.0075)^(36)
FV2 ≈ $50,000 * (1.0075)^(36)
FV2 ≈ $50,000 * 1.34686
FV2 ≈ $67,343.07
Therefore, each child will receive approximately $93,933.33 and $67,343.07, respectively, from the estate.