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

1 Answer

10 votes

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

User Josiah Kiehl
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