The parents of a child have just come into a lare inheritance and wish to establish a trust fund for the child's college education. If they estimate that they will need $100000 in 13 years, how much should they set aside in the trust now if they can invest the money at 8.5% per year compounded semiannually?
x(1. 0425)^26 = 100 000
solve for x
To calculate the amount the parents should set aside in the trust now, we can use the concept of compound interest. The formula for the future value of an investment with compound interest is:
Future Value = Present Value × (1 + interest rate/number of compounding periods)^(number of compounding periods × number of years)
In this case, the future value (FV) is $100,000, the interest rate (r) is 8.5% or 0.085, the number of compounding periods per year (n) is 2 (semiannually), and the number of years (t) is 13.
Let's plug the values into the formula:
$100,000 = Present Value × (1 + 0.085/2)^(2 × 13)
Now we can solve for the Present Value (PV):
Present Value = $100,000 / [(1 + 0.085/2)^(2 × 13)]
Calculating this using a calculator or spreadsheet will give us the amount the parents should set aside in the trust now to reach $100,000 in 13 years with an 8.5% interest rate compounded semiannually.