Question

A regular sumof 2500 is invested at the beginning of every year at 3.5% interest companies pounded annually . Find thetltal amount invested at the end of 10 years

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 & 2500\\ r=rate\to 3.5\%\to (3.5)/(100)\dotfill &0.035\\ n= \begin{array}{llll} \textit{times it compounds per year} \end{array}\dotfill &1\\ t=years\dotfill &10 \end{cases}`

`A=2500\left[ \cfrac{\left( 1+(0.035)/(1) \right)^(1 \cdot 10)-1}{(0.035)/(1)} \right]\left(1+(0.035)/(1)\right)\\\\\\ A=2500\left[ \cfrac{0.4106}{0.035} \right](1.035)\implies A \approx 30354.98`