Question

Lance Rice has decided to invest $1,200 quarterly for eight years in an ordinary annuity at 4%. The total cash value of the annuity at end of year 8 is

Answer 1

`\bf \qquad \qquad \textit{Future Value of an ordinary annuity} \\\\ A=pymnt\left[ \cfrac{\left( 1+(r)/(n) \right)^(nt)-1}{(r)/(n)} \right] \\\\`


`\bf \begin{cases} A= \begin{array}{llll} \textit{original amount}\\ \textit{already compounded} \end{array}\begin{array}{llll}\end{array}\\ pymnt=\textit{periodic payments}\to &1200\\ r=rate\to 4\%\to (4)/(100)\to &0.04\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, meaning } \end{array}\to &4\\ t=years\to &8 \end{cases} \\\\\\ A=1200\left[ \cfrac{\left( 1+(0.04)/(4) \right)^(4\cdot 8)-1}{(0.04)/(4)} \right]`