Certainly! Let's go through the detailed steps to find the mortgage balance after each of the first three monthly payments.
Mortgage Details:
- Initial mortgage amount: \[tex]$100,000
- Annual Percentage Rate (APR): 4.25%
- Monthly payment amount: \$[/tex]491.94
Payment Details:
- Payment Number 1:
- Interest Payment: \[tex]$354.17
- Principal Payment: \$[/tex]137.77
- Payment Number 2:
- Interest Payment: \[tex]$353.68
- Principal Payment: \$[/tex]138.26
- Payment Number 3:
- Interest Payment: \[tex]$353.19
- Principal Payment: \$[/tex]138.75
### Step-by-Step Calculation:
1. Initial Mortgage Balance:
[tex]\[
\text{Initial Balance} = \$100,000
\][/tex]
2. After First Payment:
- Principal Payment for first month: \[tex]$137.77
\[
\text{Balance after first payment} = \$[/tex]100,000 - \[tex]$137.77 = \$[/tex]99,862.23
\]
3. After Second Payment:
- Principal Payment for second month: \[tex]$138.26
\[
\text{Balance after second payment} = \$[/tex]99,862.23 - \[tex]$138.26 = \$[/tex]99,723.97
\]
4. After Third Payment:
- Principal Payment for third month: \[tex]$138.75
\[
\text{Balance after third payment} = \$[/tex]99,723.97 - \[tex]$138.75 = \$[/tex]99,585.22
\]
### Summarized Results:
- Balance after the 1st payment: \[tex]$99,862.23
- Balance after the 2nd payment: \$[/tex]99,723.97
- Balance after the 3rd payment: \[tex]$99,585.22
Thus, the balances after the first three payments are as follows:
\[
(\text{Balance 1}, \text{Balance 2}, \text{Balance 3}) = (\$[/tex]99,862.23, \[tex]$99,723.97, \$[/tex]99,585.22)
\]
These are the mortgage balances after the first three monthly payments.
