Questions: Use PMT = P(r/n) / [1 - (1 + r/n)^(-nt)] to determine the regular payment amount, rounded to the nearest cent. The cost of a home is financed with a 160,000 20-year fixed-rate mortgage at 3.5%. 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.

Use PMT = P(r/n) / [1 - (1 + r/n)^(-nt)] to determine the regular payment amount, rounded to the nearest cent. The cost of a home is financed with a 160,000 20-year fixed-rate mortgage at 3.5%. 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.
Transcript text: Use PMT $=\frac{P\left(\frac{r}{n}\right)}{\left[1-\left(1+\frac{r}{n}\right)^{-n t}\right]}$ to determine the regular payment amount, rounded to the nearest cent. The cost of a home is financed with a $\$ 160,000$ 20-year fixed-rate mortgage at $3.5 \%$. 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.
failed

Solution

failed
failed

Solution Steps

To solve this problem, we need to use the given PMT formula to calculate the monthly payment amount for the mortgage. Then, we can determine the total interest paid over the life of the loan. Finally, we will prepare a loan amortization schedule for the first three months.

Part (a): Monthly Payments and Total Interest
  1. Use the PMT formula to calculate the monthly payment.
  2. Calculate the total amount paid over the life of the loan.
  3. Subtract the principal amount from the total amount paid to find the total interest.
Part (b): Loan Amortization Schedule for the First Three Months
  1. Calculate the interest and principal portions of the monthly payment for each of the first three months.
  2. Update the remaining balance after each payment.
Step 1: Calculate Monthly Payment

Using the formula for the monthly payment \( PMT \):

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

Substituting the values \( P = 160000 \), \( r = 0.035 \), \( n = 12 \), and \( t = 20 \):

\[ PMT = \frac{160000 \left( \frac{0.035}{12} \right)}{1 - \left(1 + \frac{0.035}{12}\right)^{-240}} \approx 927.94 \]

Step 2: Calculate Total Amount Paid and Total Interest

The total amount paid over the life of the loan is given by:

\[ \text{Total Paid} = PMT \times nt = 927.94 \times 240 \approx 222704.53 \]

The total interest paid is calculated as:

\[ \text{Total Interest} = \text{Total Paid} - P = 222704.53 - 160000 \approx 62704.53 \]

Step 3: Prepare Amortization Schedule for the First Three Months

For the first three months, we calculate the interest and principal portions of the payment:

  1. Month 1:

    • Interest Payment: \( 160000 \times \frac{0.035}{12} \approx 466.67 \)
    • Principal Payment: \( PMT - \text{Interest Payment} \approx 927.94 - 466.67 \approx 461.27 \)
    • Remaining Balance: \( 160000 - 461.27 \approx 159538.73 \)

  2. Month 2:

    • Interest Payment: \( 159538.73 \times \frac{0.035}{12} \approx 465.32 \)
    • Principal Payment: \( PMT - \text{Interest Payment} \approx 927.94 - 465.32 \approx 462.61 \)
    • Remaining Balance: \( 159538.73 - 462.61 \approx 159076.12 \)

  3. Month 3:

    • Interest Payment: \( 159076.12 \times \frac{0.035}{12} \approx 463.97 \)
    • Principal Payment: \( PMT - \text{Interest Payment} \approx 927.94 - 463.97 \approx 463.96 \)
    • Remaining Balance: \( 159076.12 - 463.96 \approx 158612.15 \)

Final Answer

  • Monthly Payment: \( \boxed{927.94} \)
  • Total Interest Paid: \( \boxed{62704.53} \)

Amortization Schedule for the First Three Months:

  • Month 1: Payment = \( 927.94 \), Interest = \( 466.67 \), Principal = \( 461.27 \), Remaining Balance = \( 159538.73 \)
  • Month 2: Payment = \( 927.94 \), Interest = \( 465.32 \), Principal = \( 462.61 \), Remaining Balance = \( 159076.12 \)
  • Month 3: Payment = \( 927.94 \), Interest = \( 463.97 \), Principal = \( 463.96 \), Remaining Balance = \( 158612.15 \)
Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
Cuatro vectores se encuentran en el plano xy. El módulo del vector A es de 20 unidades y forma un ángulo de 40° con el eje x. El vector B, tiene magnitud de 15 unidades y forma un ángulo de 30° respecto del eje y negativo. El vector C, tienen 10 unidades de módulo y un triángulo rectángulo de catetos 4 y 3 puede formarse bajo él, tal como se indica en la figura. Un vector D parte en el origen y termina en el punto (-6,-7). Obtener en ángulo entre el vector A y el vector C.
failedAnswered
Calculate the future value of 9,000 earning 5% interest compounded quarterly for 7 years. (Round your answer to the nearest cent.) Enter a number.
failedAnswered
What is the slope of the line that passes through the points (6,-8) and (6,-3)? Write your answer in simplest form.
failedAnswered
Rank the following in order of most-liked to least-liked:
failedAnswered
Laura took out a 9000 loan for 7 months and was charged simple interest. The total interest she paid on the loan was 336. As a percentage, what was the annual interest rate of Laura's loan? Do not round any intermediate computations. If necessary, refer to the list of financial formulas.