Mathematics

Question

Mark borrowed $5,500 at 11.5 percent for five years. What is the amount of Mark's total payment?

2 Answer

  • Answer:

    The amount of Mark's Total payment is $7256.91.

    Step-by-step explanation:

    Given : Mark borrowed $5,500 at 11.5 percent for five years.

    To find : What is the amount of Mark's total payment?          

    Solution :

    First we find the monthly payment,

    Formula of monthly payment

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

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

    Where, Amount = $5500

    Rate r= 11.5%=0.115

    [tex]i=\frac{0.115}{12}=0.00958[/tex]

    Time = 5 years  

    [tex]n=5\times12=60[/tex]

    Now, put all the values we get,

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

    [tex]D=\frac{1-(1+0.00958)^{-60}}{0.00958}[/tex]

    [tex]D=\frac{1-(1.00958)^{-60}}{0.00958}[/tex]

    [tex]D=\frac{1-0.5643}{0.00958}[/tex]

    [tex]D=\frac{0.4357}{0.00958}[/tex]

    [tex]D=45.4739[/tex]

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

    [tex]M=\frac{5500}{45.4739}[/tex]

    [tex]M=120.948[/tex]

    Monthly payment is $120.948

    The amount is [tex]120.948\times 60=7256.91[/tex]

    Therefore, The amount of Mark's Total payment is $7256.91.

  • Answer:

    Mark's total payment is $7,257

    Step-by-step explanation:

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