Question

To plan for retirement, Maya deposits $106 each month in an annuity that pays 7.6% interest, compounded monthly. Payments will be made at the end of each

month. Find the total value of the annuity in 26 years.

Answer 1

`~~~~~~~~~~~~\stackrel{\textit{payments at the end of the period}}{\textit{Future Value of an ordinary annuity}} \\\\ A=pmt\left[ \cfrac{\left( 1+(r)/(n) \right)^(nt)-1}{(r)/(n)} \right] \\\\\\ ~~~~~~ \begin{cases} A=\textit{accumulated amount}\\ pmt=\textit{periodic payments}\dotfill &106\\ r=rate\to 7.6\%\to (7.6)/(100)\dotfill &0.076\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &26 \end{cases}`

`A=106 \left[ \cfrac{\left( 1+(0.076)/(12) \right)^(12 \cdot 26)-1}{(0.076)/(12)} \right]\implies A\approx 106\left[ \cfrac{6.16902}{0.00633} \right] \\\\\\ ~\hfill~ {\Large \begin{array}{llll} A \approx 103249.91 \end{array}}~\hfill~`