Mathematics

Question

Martha is buying a house for $107,820. She is making 15 percent down payment and financing the remainder at 6.5 percent for 25 years. What are Martha's monthly payments?

2 Answer

  • $91,647 would be the answer
  • Answer:

    The monthly payment is $ 618.81 ( approx )

    Step-by-step explanation:

    Here,

    The price of house =  $ 107,820,

    Down payment percentage = 15 %,

    So, the down payment = 15 % of $ 107,820

    [tex]=\frac{15\times 107820}{100}[/tex]

    [tex]=\frac{1617300}{100}[/tex]

    = $ 16,173

    Thus, the principal amount of loan, P.V. = The price of house -  the down payment

    = $ 107,820 - $ 16,173

    = $ 91647

    Now, the annual rate = 6.5 % = 0.065

    ⇒ The rate per month, r = [tex]\frac{0.065}{12}[/tex]

    Time, n = 25 years = 300 months,

    Hence, the monthly payment of the loan is,

    [tex]P=\frac{P.V.(r)}{1-(1+r)^{-n}}[/tex]

    [tex]=\frac{91647(\frac{0.065}{12})}{1-(1+\frac{0.065}{12})^{-300}}[/tex]

    [tex]=\$ 618.80710716\approx \$ 618.81[/tex]

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