## Thinking Mathematically (6th Edition)

Published by Pearson

# Chapter 8 - Personal Finance - 8.4 Compound Interest - Exercise Set 8.4: 51

#### Answer

The amount of money that should be deposited in Account A is $\$38,754$The amount of money that should be deposited in Account B is$\$41,162$

#### Work Step by Step

This is the formula we use when we make calculations with compound interest. $A = P~(1+\frac{r}{n})^{nt}$ $A$ is the final amount in the account $P$ is the principal (the amount of money invested) $r$ is the interest rate $n$ is the number of times per year the interest is compounded $t$ is the number of years We can find the amount $P_A$ that should be deposited in Account A. $A = P_A~(1+\frac{r}{n})^{nt}$ $P_A = \frac{A}{(1+\frac{r}{n})^{nt}}$ $P_A = \frac{\$75,000}{(1+\frac{0.045}{1})^{(1)(15)}}P_A = \$38,754$ The amount of money that should be deposited in Account A is $\$38,754$We can find the amount$P_B$that should be deposited in Account B.$A = P_B~(1+\frac{r}{n})^{nt}P_B = \frac{A}{(1+\frac{r}{n})^{nt}}P_B = \frac{\$75,000}{(1+\frac{0.04}{360})^{(360)(15)}}$ $P_B = \$41,162$The amount of money that should be deposited in Account B is$\$41,162$

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