Question

I put $500 in a saving account that earns 6% interest compounded semi-annually. How much interest will be in the account after 2 years?
I would to see it solved using the formula.

Answer 1

$\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\to &\ 500\\ r=rate\to 6\%\to \frac{6}{100}\to &0.06\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{semi-annually, thus twice} \end{array}\to &2\\ t=years\to &2 \end{cases} \\\\\\ A=500\left(1+\frac{0.06}{2}\right)^{2\cdot 2}\implies A=500(1.03)^4\implies A=562.754405$

now, "A" is the accumulated amount, including the earned interest, how much interest was it earned?  well, is just A - P.