Asked by Kevin Buakuma-Sayers on Jul 08, 2024

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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

Post-secondary Education

Education that occurs after high school, including programs at colleges, universities, and technical schools.

Anticipate

To expect or predict something based on current knowledge or trends, often involving preparation for a known event or condition.

  • Determine the required initial investment to meet a future financial goal under varying interest rate conditions.
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Unathi Silinga

1 week ago

Final Answer :
A
Explanation :
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=FV(1+r)n=120,000(1+0.11)8≈60,306.97 PV = \frac{FV}{(1 + r)^n} = \frac{120,000}{(1 + 0.11)^8} \approx 60,306.97 PV=(1+r)nFV=(1+0.11)8120,00060,306.97 Then, calculate the present value of $60,306.97 (the amount needed in 10 years) at 14% for 10 years: PV=60,306.97(1+0.14)10≈14,046 PV = \frac{60,306.97}{(1 + 0.14)^{10}} \approx 14,046 PV=(1+0.14)1060,306.9714,046 Therefore, an investment of approximately $14,046 today will grow to $120,000 in 18 years under the given conditions.