Answer
The investment yields a greater return over three years when it is invested at 7% compounded monthly.
Work Step by Step
To find the total amount in the account after 3 years when we invest at 7% compounded monthly, 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
$A = P~(1+\frac{r}{n})^{nt}$
$A = (\$12,000)~(1+\frac{0.07}{12})^{(12)(3)}$
$A = \$14,795.11$
After 3 years, there will be \$14,795.11 in the account.
If the money is compounded continuously, we can use this formula:
$A = P~e^{rt}$
$A = (\$12,000)~e^{(0.0685)(3)}$
$A = \$14,737.67$
After 3 years, there will be \$14,737.67 in the account.
The investment yields a greater return when it is invested at 7% compounded monthly over three years.
