Question

Patricia and Joe Payne are divorced. The divorce settlement stipulated that Joe pay $485 a month for their daughter Suzanne until she turns 18 in 4 years. Interest is 6% a year. How much must Joe set aside today to meet the settlement?

Answer 1

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

$\bf \begin{cases} A= \begin{array}{llll} \textit{original amount}\\ \textit{already compounded} \end{array} & \begin{array}{llll} \end{array}\\ pymnt=\textit{periodic payments}\to & \begin{array}{llll} 485\cdot 12\\ \underline{5280} \end{array}\\ r=rate\to 6\%\to \frac{6}{100}\to &0.06\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{a year, thus once} \end{array}\to &1\\ t=years\to &4 \end{cases}$

$\bf A=5280\left[ \cfrac{\left( 1+\frac{0.06}{1} \right)^{1\cdot 4}-1}{\frac{0.06}{1}} \right]$

Joe is making $485 payments monthly, but the amount gets interest on a yearly basis, not monthly, so the amount that yields interest is 485*12

also, keep in mind, we're assuming is compound interest, as opposed to simple interest