Question

A $250,000 home loan is used to purchase a house. The loan is for 30 years and has a 5.4% APR. Use the amortization formula to determine the amount of the monthly payments.

Answer 1

`\bf ~~~~~~~~~~~~ \textit{Amortized Loan Value} \\\\ pymt=P\left[ \cfrac{(r)/(n)}{1-\left( 1+ (r)/(n)\right)^(-nt)} \right] \\\\\\ ~~~~~~ \begin{cases} P= \begin{array}{llll} \textit{original amount deposited}\\ \end{array}\to &250000\\ pymt=\textit{periodic payments}\\ r=rate\to 5.4\%\to (5.4)/(100)\to &0.054\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{since the payments are}\\ \textit{monthly, then twelve} \end{array}\to &12\\ t=years\to &30 \end{cases}`


`\bf pymt=250000\left[ \cfrac{(0.054)/(12)}{1-\left( 1+ (0.054)/(12)\right)^(-12\cdot 30)} \right] \\\\\\ pymt=250000\left[ \cfrac{0.0045}{1-\left( 1.0045\right)^(-360)} \right] \\\\\\ pymt\approx 250000\left[ \cfrac{0.0045}{0.80138080852472389274} \right]`