Question

Find the balance in the account after the given period. $3500 deposit 6.75% compounded monthly, after 6 months

Answer 1

Keeping in mind that 6 months is not even a year, since there are 12 months in a year, then is really just 6/12 of a year, or 1/2, thus

$\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\to &\ 3500\\ r=rate\to 6.75\%\to \frac{6.75}{100}\to &0.0675\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\to &12\\ t=years\to \frac{6}{12}\to &\frac{1}{2} \end{cases} \\\\\\ A=3500\left(1+\frac{0.0675}{12}\right)^{12\cdot \frac{1}{2}}\implies A=3500(1.005625)^6$