Question

Bob deposits $20 every month into a money market account with an APR of 8%. How much money will be in the account after 40 years?

(Please round your answer to the nearest dollar.)

Answer 1

`~~~~~~~~~~~~\stackrel{\textit{payments at the beginning of the period}}{\textit{Future Value of an annuity due}} \\\\ A=pmt\left[ \cfrac{\left( 1+(r)/(n) \right)^(nt)-1}{(r)/(n)} \right]\left(1+(r)/(n)\right)`

`\qquad \begin{cases} A=\textit{accumulated amount} \\ pmt=\textit{periodic payments}\dotfill & 20\\ r=rate\to 8\%\to (8)/(100)\dotfill &0.08\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &40 \end{cases} \\\\\\ A=20\left[ \cfrac{\left( 1+(0.08)/(12) \right)^(12 \cdot 40)-1}{(0.08)/(12)} \right]\left(1+(0.08)/(12)\right) \implies A \approx 70286`