Mathematics

Question

Follow the steps above and find c, the total of the payments, and the monthly payment. Choose the right answers. Jane Smart buys a new SUV. The price, including tax, is $22,500.00. She finances the vehicle over 60 months after making a $2,000 down payment. The true annual interest rate is 12%. What are Jane's monthly payments (principal plus interest)?

2 Answer

  • To the nearest penny c
    (0.12×20,500×61)÷(2×12)
    =6,252.5
    Total of payments
    20,500+6,252.5
    =26,752.5
    Monthly payments
    26,752.5÷60
    =445.875
  • Answer:

    Jane's monthly payment is $455.6

    Step-by-step explanation:

    Given :

    The price, including tax, of SUV is $22,500.00.

    She finances the vehicle over 60 months after making a $2,000 down payment.

    The true annual interest rate is 12%.

    To Find : What are Jane's monthly payments

    Solution :

    Since we are given that he made a down payment of $2000

    So, After making the down payment the amount becomes : 22500-2000

                                                                                                      =$20500

    Now, Formula of monthly payment :

    Monthly payment, [tex]M=\frac{\text{Amount}}{\text{Discount factor}}[/tex]  

    Discount factor [tex]D=\frac{1-(1+i)^{-n}}{i}[/tex]  

    Where, Amount = $20500

    Rate r= 12%=0.12

    [tex]i=\frac{0.12}{12}=0.01[/tex]

    [tex]n=60[/tex]

    Now, substituting all the values we get,

    [tex]D=\frac{1-(1+i)^{-n}}{i}[/tex]

    [tex]D=\frac{1-(1+0.01)^{-60}}{0.01}[/tex]

    [tex]D=\frac{1-(1.01)^{-60}}{0.01}[/tex]

    [tex]D=\frac{1-0.55}{0.01}[/tex]

    [tex]D=\frac{0.45}{0.01}[/tex]  

    [tex]D=45[/tex]

    Monthly payment, [tex]M=\frac{\text{Amount}}{\text{Discount factor}}[/tex]

    [tex]M=\frac{20500}{45}[/tex]

    [tex]M=455.6[/tex]

    Hence , Jane's monthly payment is $455.6

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