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The image presents a problem asking to calculate the savings in interest between two mortgage options for a $220,000 loan:

1. A 30-year fixed-rate mortgage at 8%.
2. A 20-year fixed-rate mortgage at 7.5%.

The formula provided is the payment formula for an amortizing loan:

\[
\text{PMT} = \frac{P \cdot \frac{r}{n}}{1 - \left(1 + \frac{r}{n}\right)^{-nt}}
\]

Where:
- $ P $ = Principal (loan amount, $220,000),
- $ r $ = Annual interest rate (0.08 for 30 years and 0.075 for 20 years),
- $ n $ = Number of payments per year (typically 12 for monthly payments),
- $ t $ = Term of the loan in years (30 years or 20 years).

The goal is to determine which loan results in less interest paid over time and how much is saved.

### Steps:
1. Calculate the monthly payment (PMT) for both mortgage options.
2. Compute the total payment for each mortgage by multiplying the monthly payment by the total number of payments.
3. Subtract the loan principal ($220,000) from the total payment to get the interest paid.
4. Compare the interest from the two options to find the savings.

Let me calculate the total interest paid for both mortgage options and determine which is more economical.### Results:

1. **30-year mortgage (8% interest):**
   - Monthly payment: \$1,614.28
   - Total payment over 30 years: \$581,141.54
   - Total interest paid: \$361,141.54

2. **20-year mortgage (7.5% interest):**
   - Monthly payment: \$1,772.31
   - Total payment over 20 years: \$425,353.21
   - Total interest paid: \$205,353.21

### Interest Savings:
By choosing the 20-year mortgage at 7.5%, the buyer would save approximately **\$155,788** in interest compared to the 30-year mortgage at 8%.

Thus, the 20-year 7.5% loan is more economical. You can fill in choice B with the savings of approximately \$155,788.

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Do you need further details or have any questions?

### Related questions:
1. How would the savings change with a different principal amount?
2. How would changes in the interest rate affect the monthly payments?
3. What happens if payments are made biweekly instead of monthly?
4. How is the monthly payment affected by a shorter loan term?
5. What are the long-term benefits of paying extra each month?

**Tip:** Paying a bit extra each month can significantly reduce the total interest paid over the life of the loan.

In terms of paying less in interest, which is more economical for a $220,000 mortgage: a 30-year fixed-rate at 8% or a 20-year fixed-rate at 7.5%? How much is saved in interest?

Compare a 30-year 8% mortgage and a 20-year 7.5% mortgage for a $220,000 loan. Learn how much can be saved in interest and which option is more economical using the amortization formula.

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