Answer
(a) After 1 year, there will be \$12,799.22 in the account.
(b) The effective annual yield is 6.66%
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
$A = P~(1+\frac{r}{n})^{nt}$
$A = (\$12,000)~(1+\frac{0.065}{4})^{(4)(1)}$
$A = \$12,799.22$
After 1 year, there will be \$12,799.22 in the account.
(b) This is the formula we use when we make calculations with simple interest:
$A = P~(1+rt)$
$1+rt = \frac{A}{P}$
$r = \frac{\frac{A}{P}-1}{t}$
$r = \frac{\frac{\$12,799.22}{\$12,000}-1}{1}$
$r = 0.0666$
The effective annual yield is 6.66%
