Let's calculate the monthly payment and the total interest paid for the mortgage using the Finance tab of a TI-84 calculator.

Step 1: Gather the relevant inputs

• Loan amount (PV): $175,000
• Annual interest rate (APR): 7.7%
• Loan term (N): 30 years
• Number of payments per year: 12 (monthly payments)

Step 2: Break down the formula for monthly payment (PMT)

The formula for calculating monthly payment $PMT$ is:

$PMT = \frac{PV \cdot \frac{r}{12}}{1 - \left(1 + \frac{r}{12}\right)^{-12N}}$

Where:

• $PV$ = Present Value (loan amount)
• $r$ = annual interest rate (as a decimal)
• $N$ = loan term in years

Plugging in the numbers:

• $PV = 175,000$
• $r = 0.077$
• $N = 30$

Let's calculate the monthly payment.The monthly payment needed to amortize the $175,000 mortgage loan over 30 years at an annual interest rate of 7.7%, compounded monthly, is approximately $1,247.68.

Step 3: Calculate the total interest paid on the loan

The total interest paid can be found using:

$\text{Total Interest} = (\text{Monthly Payment} \times \text{Total Number of Payments}) - \text{Loan Amount}$

Let's calculate the total interest paid.The total interest paid over the life of the loan is approximately $274,164.91.

Summary:

• Monthly payment: $1,247.68
• Total interest paid: $274,164.91

Would you like further details on the calculations, or do you have any other questions?

Here are 5 related questions for you:

1. What happens to monthly payments if the interest rate changes?
2. How would the loan term affect total interest?
3. How can extra monthly payments reduce interest?
4. What is the difference between simple and compound interest in loans?
5. How does refinancing a loan impact the overall payment?

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