Question

Calculate the present value annuity of 5000per annum for 12years and interested being 4% per annually compounded annually

Answer 1

`~~~~~~~~~~~~\underset{\textit{payments at the end of the period}}{\textit{Future Value of an ordinary annuity}}\\ \\\\ A=pymnt\left[ \cfrac{\left( 1+(r)/(n) \right)^(nt)-1}{(r)/(n)} \right] \\\\\\ ~~~~~~ \begin{cases} A=\textit{accumulated amount} \\ pymnt=\textit{periodic payments}\dotfill &\$5000\\ r=rate\to 4\%\to (4)/(100)\dotfill &0.04\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &12 \end{cases}`

`A=5000\left[ \cfrac{\left( 1+(0.04)/(1) \right)^(1\cdot 12)-1}{(0.04)/(1)} \right]\implies A=5000\left( \cfrac{1.04^(12)~~ - ~~1}{0.04} \right) \\\\[-0.35em] ~\dotfill\\\\ ~\hfill A\approx 75129.03~\hfill`