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+(r)/(n)\right)^(nt) \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\to &\$3500\\ r=rate\to 6.75\%\to (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 (6)/(12)\to &(1)/(2) \end{cases} \\\\\\ A=3500\left(1+(0.0675)/(12)\right)^{12\cdot (1)/(2)}\implies A=3500(1.005625)^6`