Question

Antonio invests $3,000, at 10% interest, compounded semiannually for 12 years. Use the compound interest formula to calculate the compound amount for his investment.

Answer 1

$\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\ 3000\\ r=rate\to 10\%\to \frac{10}{100}\dotfill &0.10\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{semi-annually, twice} \end{array}\dotfill &2\\ t=years\dotfill &12 \end{cases} \\\\\\ A=3000\left(1+\frac{0.10}{2}\right)^{2\cdot 12}\implies A=3000(1.05)^{24}\implies A\approx 9675.2998$