Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 4 - Section 4.2 - The Natural Exponential Function - 4.2 Exercises - Page 343: 35

Answer

(a) Annually $\approx \$768.05$ (b) Semiannually $\approx\$769.22$ (c) Quarterly $\approx\$769.82$ (d) Continuously $\approx\$770.41$

Work Step by Step

*A quick review* For Compound Interest we have the following formula (Also explained in previous chapters): $A = P(1+\frac{r}{n})^{nt}$ $n$ - amount of interest compounded per year $t$ - number of years $r$ - interest rate per year $P$ - principal $A$ - amount of money after t years --- (a) For an annual compound we have: $A=600(1+\frac{0.025}{1})^{1\times10} \approx \$768.05 $ (b) For a semiannual compound we have the interest compounded $2$ times per year. So we have the following: $A=600(1+\frac{0.025}{2})^{2\times10}=600(1+\frac{0.025}{2})^{20}\approx\$769.22$ (c) In this case we have the interest compounded $4$ times per year, so we have: $A=600(1+\frac{0.025}{4})^{4\times10}=600(1+\frac{0.025}{4})^{40}\approx\$769.82$ (d) For continuously compounded interest we have another formula: $A=Pe^{rt}=600e^{0.025\times10}=600e^{0.25}\approx\$770.41$
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