Answer
The investment yields a greater return over four years when it is invested at 8.25% compounded quarterly.
Work Step by Step
To find the total amount in the account after 4 years when we invest at 8.25% compounded quarterly, we can use this formula:
$A = P~(1+\frac{r}{n})^{nt}$
$A$ 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
$A = P~(1+\frac{r}{n})^{nt}$
$A = (\$6,000)~(1+\frac{0.0825}{4})^{(4)(4)}$
$A = \$8317.84$
After 4 years, there will be \$8317.84 in the account.
We can find the total amount in the account when we invest at 8.3% compounded semiannually.
$A = P~(1+\frac{r}{n})^{nt}$
$A = (\$6,000)~(1+\frac{0.083}{2})^{(2)(4)}$
$A = \$8306.64$
After 4 years, there will be \$8306.64 in the account.
The investment yields a greater return over four years when it is invested at 8.25% compounded quarterly.
