Question

At the beginning of year 1, Jonah invests $300 at an annual
compound interest rate of 4%. He makes no deposits to or
withdrawals from the account.
Which explicit formula can be used to find the account's
balance at the beginning of year 6?

Answer 1

At the beginning of year 6, that means 5 years only have elapsed, thus t = 5.

$\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\ 300\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &5 \end{cases} \\\\\\ A=300\left(1+\frac{0.04}{1}\right)^{1\cdot 5}\implies A=300(1.04)^5$