Find the mortgage balance after the first three payments on a 30-year \[tex]$100,000 mortgage that was financed at an APR of 4.25\% and has a monthly payment of \$[/tex]491.94.

\begin{tabular}{|l|l|l|l|}
\hline
\begin{tabular}{l}
Payment \\ Number
\end{tabular} & \begin{tabular}{l}
Interest \\ Payment
\end{tabular} & \begin{tabular}{l}
Principal \\ Payment
\end{tabular} & \begin{tabular}{l}
Mortgage \\ Balance
\end{tabular} \\
\hline
1 & \[tex]$354.17 & \$[/tex]137.77 & Balance 1 \\
\hline
2 & \[tex]$353.68 & \$[/tex]138.26 & Balance 2 \\
\hline
3 & \[tex]$353.19 & \$[/tex]138.75 & Balance 3 \\
\hline
\end{tabular}



Answer :

To find the mortgage balance after the first three payments, we need to calculate the remaining balance after each payment step-by-step. Let's start with the initial balance and successively subtract the principal portions of each payment.

1. Initial Balance:
[tex]\[ \text{Initial Balance} = \$100,000 \][/tex]

2. First Payment:
- Interest Payment: \[tex]$354.17 - Principal Payment: \$[/tex]137.77
- Mortgage Balance after First Payment:
[tex]\[ \text{Balance 1} = \text{Initial Balance} - \text{Principal Payment 1} \][/tex]
[tex]\[ \text{Balance 1} = \$100,000 - \$137.77 = \$99,862.23 \][/tex]

3. Second Payment:
- Interest Payment: \[tex]$353.68 - Principal Payment: \$[/tex]138.26
- Mortgage Balance after Second Payment:
[tex]\[ \text{Balance 1} = \$99,862.23 \][/tex]
[tex]\[ \text{Balance 2} = \text{Balance 1} - \text{Principal Payment 2} \][/tex]
[tex]\[ \text{Balance 2} = \$99,862.23 - \$138.26 = \$99,723.97 \][/tex]

4. Third Payment:
- Interest Payment: \[tex]$353.19 - Principal Payment: \$[/tex]138.75
- Mortgage Balance after Third Payment:
[tex]\[ \text{Balance 2} = \$99,723.97 \][/tex]
[tex]\[ \text{Balance 3} = \text{Balance 2} - \text{Principal Payment 3} \][/tex]
[tex]\[ \text{Balance 3} = \$99,723.97 - \$138.75 = \$99,585.22 \][/tex]

Hence, the mortgage balances after the first three payments are:

- Balance 1: \[tex]$99,862.23 - Balance 2: \$[/tex]99,723.97
- Balance 3: \$99,585.22

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