Calculate how much you would need to invest now in order to fund a year of college twenty years from now, assuming a year of college costs $19,000 now and is inflating at 7%, and your investment will earn 11%. Assume continuous compounding.
A) $8537
B) $2105
C) $4685
D) $42,285

Question

Quizplus · Accepted Answer

To find the present value of the future cost of college, we use the formula for continuous compounding: $PV = FV \times e^{-rt}$, where $PV$ is the present value, $FV$ is the future value, $r$ is the rate, and $t$ is the time in years. First, calculate the future cost of college using the inflation rate: $FV = 19000 \times e^{0.07 \times 20}$. Then, calculate the present value needed to reach that future value using the investment rate: $PV = FV \times e^{-0.11 \times 20}$. Combining these steps into one, we get $PV = 19000 \times e^{(0.07-0.11) \times 20}$, which calculates to approximately $8537.

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