The compound interest on a certain sum of money for 2 years is Rs. 1260 and the simple interest on the same sum for the same period and at the same rate of interest is Rs. 1200. Find the principal.
Question
The compound interest on a certain sum of money for 2 years is Rs. 1260 and the simple interest on the same sum for the same period and at the same rate of interest is Rs. 1200. Find the principal.
Solution
Sure, let's solve this step by step.
Step 1: Understand the problem We know that the difference between compound interest and simple interest for two years is given by the formula: Difference = P*(R/100)^2 Where P is the principal amount and R is the rate of interest.
Step 2: Set up the equation In this case, the difference between the compound interest and simple interest is Rs. 60 (i.e., Rs. 1260 - Rs. 1200). So, we can set up the equation as follows: 60 = P*(R/100)^2
Step 3: Solve for P We don't know the rate of interest, but we know that it's the same for both the simple and compound interest calculations. So, we can express R in terms of P and substitute it into the equation.
From the simple interest formula (SI = PRT/100), we know that Rs. 1200 = PR2/100. Solving for R, we get R = 1200100/(2P).
Substituting R into the equation from step 2, we get: 60 = P*[(1200100/(2P*100))^2] Solving this equation for P, we get P = Rs. 25000.
So, the principal amount is Rs. 25000.
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