Question

18. Find the balance in your savings account at the end of 21 months if your initial savings of $500 earns 6% compounded quarterly.​

Answer 1

since a year has 12 months, after 21 months that'd be 21/12 of a year.

`~~~~~~ \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}\dotfill &\$500\\ r=rate\to 6\%\to (6)/(100)\dotfill &0.06\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\to (21)/(12)\dotfill &(7)/(4) \end{cases}`

`A=500\left(1+(0.06)/(4)\right)^{4\cdot (7)/(4)}\implies A=500(1.015)^7\implies A\approx 554.92`