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You need to purchase a car. You can only afford to make payments of $200 each month. What is the maximum amount you can afford to borrow if you take out a 60-month 5.5% loan from a bank for your car?

Respuesta :

Edufirst

Answer:

           [tex]\large\boxed{\large\boxed{\$10,470.57}}[/tex]

Explanation:

The monthly payment to pay a loan with constant rate is given by the formula:

      [tex]Payment=Loan\times \bigg[\dfrac{r(r+1)^t}{(r+1)^t-1}\bigg][/tex]

Where:

  • r is the monthly compounded rate and it is equal to the APR (annual percentage rate) divided by 12: r = 5.5%/12 = 0.055/12

  • t is the number of months: t = 60

Then, you can subsitute with the maximum payment to find the maximun amount you can afford  to borrow (loan):

     [tex]\$200=Loan\times \bigg[\dfrac{(0.055/12)((0.055/12)+1)^{60}}{((0.055/12)-1)^{60}-1}\bigg][/tex]

      [tex]\$200=Loan\times 0.01910116[/tex]

     [tex]Loan=\$200/0.01910116=\$10,470.57[/tex]

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