Question

Sarafina is making monthly payments into an annuity. She wants to have ​$900 in the fund to buy a new convection range in six ​months, and the account pays 8.4​% annual interest. What are her monthly payments to the​ account?

Answer 1

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


$\bf \begin{cases} A= \begin{array}{llll} \textit{accumulated amount}\\ \end{array}\to & \begin{array}{llll} 900 \end{array}\\ pymnt=\textit{periodic payments}\\ r=rate\to 8.4\%\to \frac{8.4}{100}\to &0.084\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly payments, thus} \end{array}\to &12\\ t=years\to \frac{6}{12}\to &\frac{1}{2} \end{cases} \\\\\\ 900=pymnt\left[ \cfrac{\left( 1+\frac{0.084}{12} \right)^{12\cdot \frac{1}{2}}-1}{\frac{0.084}{12}} \right]$


solve for "pymnt"