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Question

# Suppose you own a parcel of land whose value $t$ years from now will be $V(t)=8,000 e^{\sqrt{ }}$ dollars. If the prevailing interest rate remains constant at $6 \%$ per year compounded

Solution

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We start by finding the present value of land, $P(t).$

\begin{align*} P(t)&= V(t)e^{-0.06t}\\ &=8000e^{\sqrt{t}}e^{- 0.06t}\\ &=8000e^{\sqrt{t}- 0.06t}& \textrm {as }a^{m} \cdot a^n=a^{m+n}\\ \end{align*}

We get the first equality using the fact that present value of an amount $A$, compounded continuously at interest $r$ is $Ae^{-rt}.$

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