Question

Brenda invests $\$4,848$ in a savings account with a fixed annual interest rate of $5\%$ compounded $2$ times per year. What will the account balance be after $6$ years?

Answer 1

Calculate the account balance after $\mathbf{6}$ years:

Given, Principal value, $P=\$4,848$, Rate of interest, $r=5\%$, Time period, $t=6\mathrm{years}$, Number of times interest applied per time period, $n=2\mathrm{times}$,

We know that, $\mathit{A}\mathbf{=}\mathit{P}{\left(1+\frac{r}{n}\right)}^{\mathbf{n}\mathbf{t}}$

where, $A$ is final amount

$P$ is Principal value

$r$ is interest rate

$n$ is number of times interest applied per time period

$t$ is time period

$$\begin{gathered} A=4848{\left(1+\frac{0.05}{2}\right)}^{2\times 6} \\ =4848{\left(1+\frac{0.05}{2}\right)}^{12} \\ \approx \$6,520 \end{gathered}$$

Therefore, the account balance will be $\mathbf{\$}\mathbf{6}\mathbf{,}\mathbf{520}$ after $\mathbf{6}$ years.