Eighteen years from now I will need to have $120,000 to pay for my child's post-secondary education. I anticipate being able to earn 14% compounded annually for the first 10 years and 11% compounded annually for years #11 through #20. What amount of money should I invest today in order to meet my goal?
A) $11,046
B) $16,380
C) $21,750
D) $29,600
E) $30.790

Question

Quizplus · Accepted Answer

To meet the goal of having $120,000 in 18 years with different interest rates for the periods, we need to calculate the present value of that future amount. For the last 8 years, the interest rate is 11% compounded annually. First, we find the present value of $120,000 at the end of 18 years for the last 8 years using the formula for present value: PV = FV / (1 + r)^n, where FV is the future value, r is the annual interest rate, and n is the number of years. For the first 10 years, the interest rate is 14% compounded annually. We calculate the present value of the amount needed at the beginning of the 11th year to reach $120,000 by the end of 18 years, and then find how much needs to be invested today to reach that amount in 10 years at 14% interest. The correct calculation shows that investing approximately $11,046 today will achieve the goal, considering the two different interest rates over the two periods.

Eighteen Years from Now I Will Need to Have $120,000