Question

Draper College predicts that in 16 years it will take $300,000 to attend the college for four years. Alexis has a substantial amount of cash and wishes to invest a lump sum of money for her child’s college fund. How much should Alexis put aside in an account with an APR of 9% compounded monthly in order to have $300,000 in the account in 16 years? Round the answer to nearest cent, if necessary.

Answer 1

Alexis needs to invest approximately $83,177.57 now in an account with an APR of 9% compounded monthly to have $300,000 available for college in 16 years. The formula for future value of a lump-sum investment was utilized to calculate this amount.

Step-by-step explanation:

To determine how much Alexis should put aside now in an account with an APR of 9% compounded monthly to have $300,000 in 16 years, we can use the formula for the future value of a lump-sum investment:

FV = PV (1 + r/n)^(nt)

Where:

• FV is the future value of the investment
• PV is the present value (initial investment)
• r is the annual interest rate (in decimal form)
• n is the number of times interest is compounded per year
• t is the number of years the money is invested

We know that FV = $300,000, r = 0.09, n = 12 (monthly compounding), and t = 16. We need to solve for PV. Rearranging the formula for PV gives us:

PV = FV / (1 + r/n)^(nt)

Substituting the known values, we get:

PV = $300,000 / (1 + 0.09/12)^(12*16)

After solving, we find that Alexis needs to invest approximately $83,177.57 now to have $300,000 in 16 years with a 9% APR compounded monthly.