Mathematics, 24.01.2020 14:31 hamada11617
A20-year, $148,000 mortgage is taken out with a 4.9% apr. if payments are scheduled monthly and there are no additional costs, determine the balance on the account after the first month's payment has been made.
Answers: 2
![\bf \qquad \qquad \textit{Amortized Loan Value} \\\\ pymt=P\left[ \cfrac{\frac{r}{n}}{1-\left( 1+ \frac{r}{n}\right)^{-nt}} \right]](/tpl/images/0468/9362/b386b.png)
![\bf \qquad \begin{cases} P= \begin{array}{llll} \textit{original amount deposited}\\ \end{array}\to & \begin{array}{llll} 148,000 \end{array}\\ pymt=\textit{periodic payments}\\ r=rate\to 4.9\%\to \frac{4.9}{100}\to &0.049\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{payments are monthly, thus} \end{array}\to &12\\ t=years\to &20 \end{cases} \\\\\\ pymt=148000\left[ \cfrac{\frac{0.049}{12}}{1-\left( 1+ \frac{0.049}{12}\right)^{-12\cdot 20}} \right]](/tpl/images/0468/9362/38f63.png)
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