Question

5. What is the approximate monthly mortgage payment if the loan amount is $600,000,

the annual interest rate is 3%, and the loan duration is 30 years?

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} \$600000 \end{array}\\ pymt=\textit{periodic payments}\\ r=rate\to 3\%\to (3)/(100)\dotfill &0.03\\ 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=600000\left[ \cfrac{(0.03)/(12)}{1-\left((12)/(12+0.03)\right)^(12\cdot 30)} \right]\implies pymt=600000\left[\cfrac{0.0025}{1-\left( (12)/(12.03) \right)^(360)} \right] \\\\[-0.35em] ~\dotfill\\\\ ~\hfill pymt\approx 2529.62~\hfill`