Let's try to understand the problem step by step.



A sum of Rs. 9 is lent to be paid back in 10 equal monthly installments of Re. 1 each.



This means that the borrower is paying back Re. 1 per month for 10 months.



Now, let's calculate the interest paid in each installment.



1. In the first month, the borrower still owes Rs. 9, so no interest is paid.

2. In the second month, the borrower has already paid Re. 1, so he now owes Rs. 8. The interest paid would be on Rs. 8.

3. In the third month, the borrower has paid Rs. 2, so he now owes Rs. 7. The interest paid would be on Rs. 7.

4. This continues until the 10th month when the borrower has paid Rs. 9 and owes nothing.



Now let's calculate the total interest paid over the 10 months.



Total Interest Paid = (Interest on Rs. 8) + (Interest on Rs. 7) + ... + (Interest on Re. 1)



Let's assume the rate of interest is "R" percent per month.



Total Interest Paid = (8 * R) + (7 * R) + ... + (1 * R)



Now, we know that the total amount paid is Rs. 10 (10 installments of Re. 1 each), and the total amount lent is Rs. 9. So, the total interest paid is Rs. 1.



1 = (8 * R) + (7 * R) + ... + (1 * R)



Now we can simplify the equation:



1 = R * (8 + 7 + 6 + 5 + 4 + 3 + 2 + 1)



1 = R * 36



Now, let's find the value of R (the rate of interest per month):



R = 1/36



Since we need to calculate the rate of interest in percentage, we multiply R by 100:



R (%) = (1/36) * 100 = 2.78%



Now, we have the monthly rate of interest. To find the annual rate of interest, we multiply the monthly rate by 12:



Annual Rate of Interest = 2.78% * 12 = 33.33%