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It looks like you uploaded an image of a math problem related to mortgage payments, specifically asking to compare interest savings between a 30-year fixed-rate loan at 7.5% and a 20-year fixed-rate loan at 7% for a mortgage of $190,000. The formula provided is for calculating the regular payment amount (PMT) using the annuity formula.

The key formula given is:
\[
PMT = \frac{P \cdot \frac{i}{12}}{1 - \left(1 + \frac{i}{12}\right)^{-n \cdot 12}}
\]
Where:
- $ P $ is the principal (in this case, $190,000),
- $ i $ is the annual interest rate (7.5% for the 30-year loan, 7% for the 20-year loan),
- $ n $ is the number of years (30 years or 20 years),
- The denominator represents the number of total payments for each loan.

### Steps to solve:
1. **Calculate Monthly Payments**: For each loan, we need to calculate the monthly payment.
2. **Determine Total Payments**: Multiply the monthly payment by the total number of months (for 30 years, it's $30 \times 12 = 360$; for 20 years, it's $20 \times 12 = 240$).
3. **Calculate Total Interest**: Subtract the principal ($190,000) from the total payments to find the total interest paid over the life of the loan.
4. **Compare**: The difference between the interest for each loan will tell us which is more economical and by how much.

Would you like me to go through the full calculation using these steps?

In terms of paying less in interest, which is more economical for a $190,000 mortgage: a 30-year fixed-rate at 7.5% or a 20-year fixed-rate at 7%? How much is saved in interest?

Learn how to calculate and compare the interest savings for a $190,000 mortgage with a 30-year loan at 7.5% interest and a 20-year loan at 7%. This example applies the loan amortization formula and demonstrates key financial concepts in mortgage payments.

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