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
