Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 7 - Exponential Functions - 7.5 Compound Interest and Present Value - Exercises - Page 355: 3


(a) $ 1.0508$ (b) $ 1.0513 $

Work Step by Step

Since $$ r=0.05 $$ (a) The rate is compounded three times ($M=3 $), continuously, so we have \begin{aligned} P(t)&=P_{0}\left(1+\frac{r}{M}\right)^{M t}\\ &= \left(1+\frac{0.05}{3}\right)^{3} \\ &\approx 1.0508 \end{aligned} (b) The rate is compounded continuously, so \begin{aligned} P&=P_{0} e^{r t} \end{aligned} Thus, the yearly multiplier is: $$ e^{r}=e^{0.05} \approx 1.0513 $$
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