Question

find the monthly mortgage p is the monthly R is the precent rate and T is the time/years. find the monthly mortgage. ​

Answer 1

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

`\begin{cases} P= \begin{array}{llll} \textit{original amount deposited}\\ \end{array}\dotfill & \begin{array}{llll} 857 \end{array}\\ pymt=\textit{periodic payments}\\ r=rate\to 6.5\%\to (6.5)/(100)\dotfill &0.065\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &30 \end{cases}`

`pymt=857\left[ \cfrac{(0.065)/(12)}{1-\left((12)/(12+0.065)\right)^(12 \cdot 30)} \right]\implies pymt=857\left[ \cfrac{(13)/(2400)}{1-\left((2400)/(2413)\right)^(360)} \right] \\\\[-0.35em] ~\dotfill\\\\ ~\hfill pymt\approx 5.42~\hfill`