Twenty-eight months ago, Rajeesh purchased a used vehicle and maxed out his credit card at $\$ 25000$. Shortly thereafter, he moved and failed to let the bank holding his credit card know where he moved. This morning, his luck changed when he received a letter from the bank stating that he owed $\$ 50000$. If the interest accrued was compounded monthly, what was the interest rate?

Step 1 ：Given that Rajeesh purchased a used vehicle and maxed out his credit card at $25000 twenty-eight months ago. Recently, he received a letter from the bank stating that he owed $50000. The interest accrued was compounded monthly.

Step 2 ：We are asked to find the monthly interest rate. We know that the initial amount was $25000 and after 28 months it became $50000. We can use the formula for compound interest to solve this problem.

Step 3 ：The formula for compound interest is: \(A = P (1 + \frac{r}{n})^{nt}\)

Step 4 ：Where: \(A\) is the amount of money accumulated after n years, including interest, \(P\) is the principal amount (the initial amount of money), \(r\) is the annual interest rate (in decimal), \(n\) is the number of times that interest is compounded per year, and \(t\) is the time the money is invested for in years.

Step 5 ：In this case, we are looking for \(r\) (the interest rate), so we need to rearrange the formula to solve for \(r\).

Step 6 ：Substituting the given values into the formula, we get: \(P = 25000\), \(A = 50000\), \(n = 12\), and \(t = 2.3333333333333335\)

Step 7 ：Solving for \(r\), we get: \(r = 0.025064211965874605\)

Step 8 ：Converting \(r\) to a percentage, we get: \(r_{\text{percent}} = 2.5064211965874605\)

Step 9 ：Final Answer: The monthly interest rate is approximately \(\boxed{2.51\%}\).