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The problem in the image asks to find the mortgage balance after the first three payments on a 30-year $160,000 mortgage, with an APR of 4.75%, and a monthly payment of $834.64. A table is provided that includes the breakdown of interest and principal payments for the first three payments.

Here’s a breakdown of the information:

- **Loan Amount (Principal):** $160,000
- **Annual Interest Rate (APR):** 4.75%
- **Monthly Payment:** $834.64
- **Payment 1:**
  - Interest Payment: $633.33
  - Principal Payment: $201.31
- **Payment 2:**
  - Interest Payment: $632.54
  - Principal Payment: $202.10
- **Payment 3:**
  - Interest Payment: $631.74
  - Principal Payment: $202.90

### Finding the Balance After Each Payment:
We can compute the mortgage balance after each payment as follows:

1. **Starting Balance:** $160,000
2. **Interest for Payment 1:** The first interest payment is $633.33, which is calculated on the full balance. The principal payment for the first month is $201.31.
   - **New Balance after Payment 1:** $160,000 - $201.31 = $159,798.69
3. **Interest for Payment 2:** The interest for the second payment ($632.54) is calculated on the remaining balance. The principal paid is $202.10.
   - **New Balance after Payment 2:** $159,798.69 - $202.10 = $159,596.59
4. **Interest for Payment 3:** The interest for the third payment ($631.74) is calculated on the updated balance. The principal paid is $202.90.
   - **New Balance after Payment 3:** $159,596.59 - $202.90 = $159,393.69

### Mortgage Balance after Three Payments:
The balance after the third payment is **$159,393.69**.

Would you like further details or explanations on how this calculation works?

### Related Questions:
1. How is the interest portion of the payment calculated for each month?
2. How does the monthly payment remain constant, while the interest and principal portions change?
3. How can you calculate the total interest paid over the life of a mortgage?
4. What impact does making an extra payment toward principal have on a mortgage?
5. How would a change in the interest rate affect the mortgage balance?

### Tip:
By making extra payments toward the principal, you can significantly reduce the total interest paid and shorten the term of the mortgage.

Find the mortgage balance after the first three payments on a 30-year $160,000 mortgage that was financed at an APR of 4.75% and has a monthly payment of $834.64.

This problem helps you calculate the mortgage balance after the first three payments on a $160,000 loan with a 4.75% APR and a monthly payment of $834.64. Key concepts include loan amortization, interest calculations, and principal repayments. Suitable for high school students in Grades 10-12.

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