Question

How do I solve for future value of annuities??? I have this problem and apparently the answer is $7274.41, but I can’t figure out how that is correct. Can someone help please?

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 &20\\ r=rate\to 1.5\%\to (1.5)/(100)\dotfill &0.015\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &25 \end{cases}`

`A=20 \left[ \cfrac{\left( 1+(0.015)/(12) \right)^(12 \cdot 25)-1}{(0.015)/(12)} \right]\implies A\approx 20\left[ \cfrac{0.45465}{0.00125} \right]\implies A \approx 7274.41`

now, how much did you put in?

well, for 25 years every month 20 bucks will be (25)(20)(12) = 6000.