Answer
(a) After 1 year, there will be \$10,457.65 in the account.
(b) The effective annual yield is 4.5765%
Work Step by Step
(a) 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
$A = P~(1+\frac{r}{n})^{nt}$
$A = (\$10,000)~(1+\frac{0.045}{4})^{(4)(1)}$
$A = \$10,457.65$
After 1 year, there will be \$10,457.65 in the account.
(b) This is the formula we use when we make calculations with simple interest:
$A = P~(1+rt)$
$1+rt = \frac{A}{P}$
$r = \frac{\frac{A}{P}-1}{t}$
$r = \frac{\frac{\$10,457.65}{\$10,000}-1}{1}$
$r = 0.045765$
The effective annual yield is 4.5765%
