To determine which mortgage option is more economical in terms of paying less interest, we'll calculate the total amount of interest paid over the life of each loan using the formula for the monthly payment:

$PMT = \frac{P \left( \frac{r}{n} \right)}{1 - \left(1 + \frac{r}{n}\right)^{-nt}}$

Where:

• $P$ is the loan amount ($80,000),
• $r$ is the annual interest rate (expressed as a decimal),
• $n$ is the number of payments per year (12 for monthly payments),
• $t$ is the term of the loan (in years).

We'll calculate the monthly payment for each loan, then compute the total payment over the loan period, and finally subtract the loan amount to find the total interest paid.

Let's calculate that now.Here are the results for both mortgage options:

1. 30-year loan at 7%:

   • Monthly payment: $532.24
   • Total interest paid: $111,607

2. 15-year loan at 6.5%:

   • Monthly payment: $696.89
   • Total interest paid: $45,439

Interest savings: By choosing the 15-year loan, the buyer would save approximately $66,168 in interest compared to the 30-year loan.

Therefore, Option A is correct: the 15-year loan at 6.5% is more economical, saving the buyer around $66,000 in interest.

Let me know if you'd like any further details, or if you have additional questions. Here are five related questions to consider:

1. How does increasing the down payment affect the interest paid over the loan term?
2. What would be the effect of paying an extra $100 per month on either of these loans?
3. How would the total interest change if the 30-year loan had an interest rate of 6% instead of 7%?
4. Can refinancing during the term of the loan lead to further interest savings?
5. How does the loan amortization schedule differ between a 15-year and a 30-year loan?

Tip: Paying more than the required monthly payment on a mortgage can significantly reduce the total interest paid over time.