Question

A 20-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.

Answer 1

So.... the account is at 0 at the beginning, after the 1st payment made to the account, the only balance it'd have, is the first payment amount, so namely, what's the monthly amortized payment

$\bf \qquad \qquad \textit{Amortized Loan Value} \\\\ pymt=P\left[ \cfrac{\frac{r}{n}}{1-\left( 1+ \frac{r}{n}\right)^{-nt}} \right]$

$\bf \qquad \begin{cases} P= \begin{array}{llll} \textit{original amount deposited}\\ \end{array}\to & \begin{array}{llll} 148,000 \end{array}\\ pymt=\textit{periodic payments}\\ r=rate\to 4.9\%\to \frac{4.9}{100}\to &0.049\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{payments are monthly, thus} \end{array}\to &12\\ t=years\to &20 \end{cases} \\\\\\ pymt=148000\left[ \cfrac{\frac{0.049}{12}}{1-\left( 1+ \frac{0.049}{12}\right)^{-12\cdot 20}} \right]$