Question

Find the amount that results from each investment, $100 invested at 4% compounded quarterly after a period of 2 years.

Short answer

The answer is $108.28

Step-by-step solution

Step 1. Given information

The Principal investment, $P=\$100$

The rate of interest is expressed as a decimal, $r=4\%=\frac{4}{100}=0.04$

The time period,$t=2$

The investment compounded quarterly,$n=4$

Step 2. Use Compound interest formula

$P$The amount $A$after $t$years due to a principal ,at a annual rate $r$compounded $n$times per year,role="math" localid="1647108689822" $A=P{\left(1+\frac{r}{n}\right)}^{nt}$

Step 3. Calculation

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

$$\begin{gathered} A=\$100{\left(1+\frac{0.04}{4}\right)}^{4\times 2} \\ A=\$100{\left(1+0.01\right)}^8 \\ A=\$100{\left(1.01\right)}^8 \\ A=\$100(1.0828) \\ A=\$108.28 \end{gathered}$$

The amount is $108.28