Question

jayne purchased a home for 240000 with a down payment of 48000. The rate of interest was 5-3/4 for 30 years. What was her monthly mortgage payment

Answer 1

`\bf \qquad \qquad \textit{Amortized Loan Value} \\\\ pymt=P\left[ \cfrac{(r)/(n)}{1-\left( 1+ (r)/(n)\right)^(-nt)} \right]`



`\bf \begin{cases} P= \begin{array}{llll} \textit{original amount}\\ \end{array}\to & \begin{array}{rllll} 240,000\\ -downpayment\\ -48,000\\ -----\\ 192,000 \end{array}\\ pymt=\textit{periodic payments}\\ r=rate\to 5(3)/(4)\%\to (5(3)/(4))/(100)\to &0.0575\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{payments are monthly, thus} \end{array}\to &12\\ t=years\to &30 \end{cases}`



`\bf pymt=192000\left[ \cfrac{(0.0575)/(12)}{1-\left( 1+ (0.0575)/(12)\right)^(-12\cdot 30)} \right]`