Questions: Use PMT = P(r/n) / [1-(1+r/n)^(-nt)] to determine the regular payment amount, rounded to the nearest cent, if a home is financed with a 130,000 30-year fixed-rate mortgage at 4.5%. a. Find the monthly payments and the total interest for the loan. b. Prepare a loan amortization schedule for the first three months of the mortgage. a. The monthly payment is 658.69 The total interest for the loan is 107128.72 b. Fill out the loan amortization schedule for the first three months of the mortgage below. Payment Number Interest Principal Loan Balance 1 2 3

Solution Steps

To solve this problem, we need to calculate the monthly payment using the PMT formula for a fixed-rate mortgage. Then, we will calculate the total interest paid over the life of the loan. Finally, we will prepare a loan amortization schedule for the first three months, which involves calculating the interest and principal portions of each payment and updating the loan balance accordingly.

Using the PMT formula for a fixed-rate mortgage, we have:

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

Substituting the values \( P = 130000 \), \( r = 0.045 \), \( n = 12 \), and \( t = 30 \):

\[ PMT = \frac{130000 \left( \frac{0.045}{12} \right)}{1 - \left(1 + \frac{0.045}{12}\right)^{-360}} \approx 658.69 \]

The total payment over the life of the loan is given by:

\[ \text{Total Payment} = PMT \times nt = 658.69 \times 360 \approx 237128.72 \]

The total interest paid is:

\[ \text{Total Interest} = \text{Total Payment} - P = 237128.72 - 130000 \approx 107128.72 \]

For the first three months, we calculate the interest and principal payments as follows:

1. Month 1:

   • Interest Payment: \( 130000 \times \frac{0.045}{12} \approx 487.50 \)
   • Principal Payment: \( 658.69 - 487.50 \approx 171.19 \)
   • Remaining Balance: \( 130000 - 171.19 \approx 129828.81 \)

2. Month 2:

   • Interest Payment: \( 129828.81 \times \frac{0.045}{12} \approx 486.86 \)
   • Principal Payment: \( 658.69 - 486.86 \approx 171.83 \)
   • Remaining Balance: \( 129828.81 - 171.83 \approx 129656.98 \)

3. Month 3:

   • Interest Payment: \( 129656.98 \times \frac{0.045}{12} \approx 486.21 \)
   • Principal Payment: \( 658.69 - 486.21 \approx 172.48 \)
   • Remaining Balance: \( 129656.98 - 172.48 \approx 129484.50 \)

Final Answer