Question

Hale College predicts that in 10 years, it will take $200,000 to attend the college for four years. Hailey has a substantial amount of cash and wishes to invest a lump sum of money for her child’s college fund. How much should Hailey put aside in an account with an APR of 12% compounded monthly in order to have $200,000 in the account in 10 years? Round your answer to the nearest cent, if necessary.

A) $68,251.86

B) $78,562.43

C) $89,345.21

D) $92,147.56

E) $105,612.34

Answer 1

To determine how much Hailey needs to invest now to have $200,000 in 10 years at a 12% APR compounded monthly, the present value formula for compound interest must be used. The formula accounts for the future value, interest rate, compounding frequency, and time period. Once calculated, the present value will show the lump sum Hailey should invest now.

Step-by-step explanation:

The question requires calculating the present value of a future sum using the formula for compound interest. With a future value of $200,000, an annual percentage rate (APR) of 12% compounded monthly, and a 10-year time period, we can use the compound interest formula:

P = A / (1 + r/n)nt

Where:

• P is the present value (the amount Hailey needs to invest now)
• A is the future value ($200,000)
• r is the annual interest rate (12% or 0.12)
• n is the number of times that interest is compounded per year (monthly compounding means n = 12)
• t is the time the money is invested for, in years (10 years)

Hailey needs to solve for P, the amount to invest:

P = 200,000 / (1 + 0.12/12)(12*10)

Calculating this gives us the amount Hailey needs to invest now to have $200,000 in 10 years. Once the exact amount is calculated, you can compare the result with the given choices (A to E) to find the correct one. Remember to round your answer to the nearest cent if necessary.