Question

If $\$1000$is invested at $4\%$per annum compounded semiannually, how much is in the account after 2 years?

Short answer

The amount available in account after 2 years will be$\$1082$.

Step-by-step solution

Step 1. Write the given information.

$\$1000$is invested at$4\%$per annum compounded semiannually.

Time - 2 years.

The formula for compound interest is $A=p{\left(1+\frac{r}{n}\right)}^{nt}$

Step 2. Find the compound interest.

$$\begin{gathered} A=1000{\left(1+\frac{0.04}{2}\right)}^{2.2} \\ =1000·{\left(1.02\right)}^4 \\ =1082.43216 \end{gathered}$$