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Question

Find the present value of $59,673 due in 5 years at an interest rate of$8% / yea compounded continuously.

Solution

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We will find the present value from the formula

A=Pert\begin{equation*} \boxed{\pmb{A=Pe^{rt}}} \end{equation*}

where

A=$59673t=5r=0.08\begin{align*} A&=\$59673\\ t&=5\\ r&=0.08 \end{align*}

From

59673=Pe50.08\begin{equation*} 59673=P\cdot e^{5\cdot 0.08} \end{equation*}

we proceed to solve for PP

P=59673e50.08P=$40000\begin{align*} P&=59673\cdot e^{-5\cdot 0.08}\Rightarrow\textcolor{#c34632}{P=\$40000} \end{align*}

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