Question

Mr. and Mrs. Hill hope to send their son to college in fourteen years. How much money should they invest now at an interest rate of 9.5% per year, compounded continuously, in order to be able to contribute $8500 to his education?Round your answer to the nearest cent.

Answer 1

continuouslyUsing the formula for a compounded continously

$P=P_0\cdot e^{r\cdot t}$

where P is the amount on the account after t years compounded at an interest rate r when Po is invested in an account.

then,

$\begin{gathered} 8500=P_0\cdot e^{0.095\cdot14} \\ 8500=P_{0^{}}\cdot e^{1.33} \\ P_0=\frac{8500}{e^{1.33}} \\ P_0=2248.056\approx2248.06 \end{gathered}$