Final answer:
To find the original sum for which the difference between compound interest and simple interest over two years at 5% is 12 rupees, we use the formulas for both compound and simple interests to set up an equation. By solving this equation, we find the principal amount.
Step-by-step explanation:
The difference between compound interest and simple interest for a certain amount over two years at an interest rate of 5% per annum is given as rupees 12. To find the original sum, we can use the formulas for simple interest and compound interest. The formula for simple interest is SI = P * R * T / 100, where P is the principal amount, R is the rate of interest per annum, and T is the time in years. For compound interest, it is calculated on the principal plus the accumulated interest, and its formula over two years at an annual compounding rate is CI = P * (1 + R/100)2 - P.
Since we know the difference between compound interest and simple interest is rupees 12, we can set up an equation as follows:
- CI - SI = 12
- P * (1 + 0.05)2 - P - (P * 0.05 * 2) = 12
By solving the equation, we can find the value of P, which is the original sum of money.