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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.

User Spiro
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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{(r)/(n)}{1-\left( 1+ (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 (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{(0.049)/(12)}{1-\left( 1+ (0.049)/(12)\right)^(-12\cdot 20)} \right]
User Beau Bouchard
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