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# A deposit of 50 is made at the beginning of each month in an account that pays 8% interest. compounded monthly. The balance A in the account at the end of 5 years is given by$A=50\left(1+\frac{0.08}{12}\right)^{1}+\cdots+50\left(1+\frac{0.08}{12}\right)^{00}$. Find A.

Solution

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To find $A$, we have to use the formula for the sum of a finite geometric sequence:

\begin{align*} a_1, a_1r, a_1r^2,...,a_1r^{n-1} \end{align*}

with common ration $r\neq1$ that is:

\begin{align*} S_n&=\displaystyle\sum_{i=1}^n a_1r^{i-1}=a_1\cdot \left( \frac{1-r^n}{1-r} \right) \end{align*}

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