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) $14,046
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 $120,000 discounted back 18 years using the given interest rates. For the last 8 years, the rate is 11% compounded annually. For the first 10 years, the rate is 14% compounded annually.First, calculate the present value of $120,000 after 8 years at 11%:$$ PV = \frac{FV}{(1 + r)^n} = \frac{120,000}{(1 + 0.11)^8} \approx 60,306.97 $$Then, calculate the present value of $60,306.97 (the amount needed in 10 years) at 14% for 10 years:$$ PV = \frac{60,306.97}{(1 + 0.14)^{10}} \approx 14,046 $$Therefore, an investment of approximately $14,046 today will grow to $120,000 in 18 years under the given conditions.

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