Jing borrowed $\$ 22000$ for a second-hand vehicle. She pays $\$ 450$ per month for 6 years on a monthly basis. What is the monthly compound interest rate on this loan?

Step 1 ：Given that Jing borrowed $22000 for a second-hand vehicle and she pays $450 per month for 6 years on a monthly basis, we are asked to find the monthly compound interest rate on this loan.

Step 2 ：We are given the principal amount (P) which is $22000, the monthly payment (A) which is $450, and the number of payments (n) which is 6*12 = 72 months.

Step 3 ：The formula for the monthly payment on a loan with compound interest is: \(A = P * r * (1 + r)^n / [(1 + r)^n - 1]\)

Step 4 ：We can rearrange this formula to solve for r: \(r = (A / P) * [(1 + r)^n - 1] / (1 + r)^n\)

Step 5 ：However, this is a transcendental equation and cannot be solved algebraically for r. We will need to use a numerical method to solve for r.

Step 6 ：Using an initial guess of 0.01 for r, we find that the solution is approximately 0.01143089, which is the monthly interest rate.

Step 7 ：To convert this to a percentage, we multiply by 100: \(r_{percent} = 1.143089144043192\)

Step 8 ：Final Answer: The monthly compound interest rate on the loan is approximately \(\boxed{1.143\%}\).