Simple interest on sum of money ios 36/81 of the principal and no of years is equal to the rate of interest. Find the rate of interest per annum.

Sure, let's solve this step by step.

Step 1: Understand the problem The problem states that the simple interest on a sum of money is 36/81 of the principal. It also states that the number of years is equal to the rate of interest. We are asked to find the rate of interest per annum.

Step 2: Use the formula for simple interest The formula for simple interest is I = PRT/100, where I is the interest, P is the principal, R is the rate of interest, and T is the time in years.

Step 3: Substitute the given values into the formula We know that I = 36/81P and T = R. Substituting these into the formula gives us 36/81P = PR^2/100.

Step 4: Simplify the equation Multiplying both sides by 100 gives us 3600/81P = PR^2. Dividing both sides by P gives us 3600/81 = R^2.

Step 5: Solve for R Taking the square root of both sides gives us R = sqrt(3600/81) = 20/3 = 6.67 (approx).

So, the rate of interest per annum is approximately 6.67%.