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=(8500)/(e^(1.33)) \\ P_0=2248.056\approx2248.06 \end{gathered}`