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

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

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