# Ashley deposits $500 into an account that earns 2% interest compounded 3 times per year. How much money will Ashley have in her account after 4 years? ##### 1 Answer Sep 17, 2016 Note that the 2% is not stated as "per annum" (per year) Based on 2% per year ->$541.50 rounded to 2 decimal places
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$\textcolor{m a \ge n t a}{\text{ This one is not very likely!}}$
Based on 2% per $\frac{1}{3}$ year ->$634.12 rounded to 2 decimal places. #### Explanation: $\textcolor{red}{\text{Assumption: the 2% is per annum}}$$\implies P {\left(1 + \frac{2}{100 \times 3}\right)}^{3 n}$where $n$is the number of years and the $\frac{2}{100 \times 3}$converts the percentage to $\frac{1}{3}$year equivalent. =>$500(302/300)^(3xx4)

=$541.4997 ~~$541.50 rounded to 2 decimal places

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$\textcolor{red}{\text{Assumption: the 2% is per "1/3 " year}}$

$\implies P {\left(1 + \frac{2}{100}\right)}^{3 n}$ where $n$ is the number of years

=>$500(102/100)^(3xx4) =$634.1208~~\$634.12 rounded to 2 decimal places.