## Thinking Mathematically (6th Edition)

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.