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]
