## Calculus (3rd Edition)

Published by W. H. Freeman

# Chapter 7 - Exponential Functions - 7.5 Compound Interest and Present Value - Exercises - Page 355: 8

#### Answer

$r=0.08$; it is better to receive $\$ 1000$today$r=0.03$; it is better to receive$\$1300$ after $4$ years

#### Work Step by Step

Since $r= 0.08$, then for $t=4$ years and $P= \$ 1300, we have \begin{align*} P V&=P e^{-r t}\\ &=1300 e^{-0.08 (4)} \\ &\approx 943.99 \end{align*} Hence, it is better to receive\$1000$ today. For $r=0.03$, $t=4$ years, and $P= \$ 1300, we have \begin{align*} P V&=P e^{-r t}\\ &=1000 e^{-0.03 (4)} \\ &\approx 1152..99 \end{align*} Hence, it is better to receive\$1300$ in $4$ years.

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