29.03.2023 - 22:48

You plan to purchase a $310,000 house using a 15-year mortgage obtained from your local credit union. The mortgage rate offered to you is 7.75 percent. You will make a down payment of 20 percent of the purchase price. a. Calculate your monthly payments on

Question:

You plan to purchase a $310,000 house using a 15-year mortgage obtained from your local credit union. The mortgage rate offered to you is 7.75 percent. You will make a down payment of 20 percent of the purchase price.

a. Calculate your monthly payments on this mortgage. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

b. Construct the amortization schedule for the first six payments. (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Answers (1)
  • Galanet
    April 3, 2023 в 08:45

    a. To calculate the monthly payments on this mortgage, we first need to calculate the loan amount. The down payment is 20% of the purchase price, so it is:

    Down payment = 20% × $310,000 = $62,000

    Therefore, the loan amount is:

    Loan amount = $310,000 - $62,000 = $248,000

    The mortgage rate is 7.75% and the term of the mortgage is 15 years, or 180 months. Using the formula for monthly payments on a mortgage, we can calculate the monthly payment:

    Monthly payment = [Loan amount x (mortgage rate/12)] / [1 - (1 + mortgage rate/12)^(-term in months)]

    Plugging in the values, we get:

    Monthly payment = [$248,000 x (0.0775/12)] / [1 - (1 + 0.0775/12)^(-180)] = $2,336.19

    Therefore, the monthly payment on this mortgage is $2,336.19.

    b. To construct the amortization schedule for the first six payments, we need to calculate the interest and principal components of each payment.

    For the first payment, the interest is calculated by multiplying the loan balance at the beginning of the period by the monthly interest rate. The principal component is the difference between the monthly payment and the interest.

    Using the values from part a, the interest for the first payment is:

    Interest = $248,000 x (0.0775/12) = $1,604.17

    The principal component is:

    Principal = $2,336.19 - $1,604.17 = $732.02

    The loan balance at the end of the first payment period is:

    Loan balance = $248,000 - $732.02 = $247,267.98

    For the second payment, we repeat the process using the new loan balance:

    Interest = $247,267.98 x (0.0775/12) = $1,595.85

    Principal = $2,336.19 - $1,595.85 = $740.34

    Loan balance = $247,267.98 - $740.34 = $246,527.64

    We can repeat this process for the remaining payments to construct the amortization schedule. Here is the complete schedule for the first six payments:

    PaymentInterestPrincipalLoan Balance
    1$1,604.17$732.02$247,267.98
    2$1,595.85$740.34$246,527.64
    3$1,587.50$748.69$245,778.95
    4$1,579.11$757.08$245,021.87
    5$1,570.68$765.51$244,256.36
    6$1,562.22$773.97$243,482.39

    Note that the interest component decreases and the principal component increases over time, as the loan balance decreases.

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