Question

Find the amount that results from each investment, $300 invested at 12% compounded monthly after a period of$1\frac{1}{2}$years.

Short answer

The answer is $358.84

Step-by-step solution

Step 1. Given information

The Principal investment, $P=\$300$

The rate of interest is expressed as a decimal, $r=12\%=\frac{12}{100}=0.12$

The time period, $t=\frac{3}{2}years$

The investment compounded monthly,$n=12$

Step 2. Use Compound Interest formula

The amount $A$after $t$years due to a principal $P$,at a annual rate $r$compounded $n$times per year,role="math" localid="1647107491353" $A=P{\left(1+\frac{r}{n}\right)}^{nt}$

Step 3. Calculation

Substitute the given values in $A=P{\left(1+\frac{r}{n}\right)}^{nt}$

$$\begin{gathered} A=P{\left(1+\frac{r}{n}\right)}^{nt} \\ A=\$300{\left(1+\frac{0.12}{12}\right)}^{12\times \frac{3}{2}} \\ A=\$300{\left(1.01\right)}^{18} \\ A=\$300\left(1.196\right) \\ A=\$358.84 \end{gathered}$$

The amount is $358.84