Mathematics

Question

Sue Stitch buys a sewing machine. The price, including tax, is $575.00. She finances the sewing machine over 24 months after making a $25 down payment. The true annual interest rate is 15%. What are Sue's monthly payments (principal plus interest)?

To the nearest penny, c = $

Total of payments = amount financed + c = $

Total of payments ÷ number of payments = monthly payment = $

2 Answer

  • Hi there!

    To the nearest penny, c = $85.94.

    Total of payments = amount financed + c = $635.94.

    Total of payments ÷ number of payments = monthly payment = $26.50

    Your friend, ASIAX
  • Answer:

    c = $85.94

    Total payment = $635.94

    Total payment ÷ Number of payment = $26.5.

    Step-by-step explanation:

    We are given that,

    The tax on the machine = $575 with down payment = $25. Also, the rate of interest = 15% i.e. 0.15 and time period = 24 months.

    Now, the principal amount = tax - down payment = $575 - $25 = $550.

    Then, the monthly payment by the annuity formula is given by,

    [tex]c=\frac{r \times PV}{1-(1+r)^{-n} }[/tex]

    i.e. [tex]c=\frac{0.15 \times 550}{1-(1+0.15)^{-24} }[/tex]

    i.e. [tex]c=\frac{82.5}{1-(1.15)^{-24} }[/tex]

    i.e. [tex]c=\frac{82.5}{1-0.035 }[/tex]

    i.e. [tex]c=\frac{82.5}{0.965}[/tex]

    i.e. [tex]c=85.94[/tex]

    Hence, c = $85.94

    Thus, total payment = amount financed + c = $550 + $85.94 = $635.94.

    So, Total payment ÷ Number of payment = [tex]\frac{635.94}{24}[/tex] = $26.5.

NEWS TODAY