Question

Jorgen made deposits of $250 at the end of each year for 12 years. The rate received was 6% annually. What's the value of the investment after 12 years? A. $3,000 B. $2,028 C. $4,200 D. $4,217.48

Answer 1

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

`\bf ~~~~~~ \begin{cases} A= \begin{array}{llll} \textit{accumulated amount}\\ \end{array}\dotfill & \begin{array}{llll} \end{array}\\ pymnt=\textit{periodic payments}\dotfill &250\\ r=rate\to 6\%\to (6)/(100)\dotfill &0.06\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &12 \end{cases}`

`\bf A=250\left[ \cfrac{\left( 1+(0.06)/(1) \right)^(1\cdot 12)-1}{(0.06)/(1)} \right]\implies A=250\left(\cfrac{1.06^(12)-1}{0.06} \right) \\\\\\ A\approx 250(16.86994)\implies A\approx 4217.485`