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 $\$41,162$
