Final answer:
To calculate the principal from the difference between compound and simple interest, we use respective interest formulas with an annual rate of 12% for two years. The given difference is ₹90. By solving the resulting equation, we find the principal to be ₹1,500.
Step-by-step explanation:
The question given refers to calculating the principal based on the difference between compound interest and simple interest over a period of two years with an interest rate of 12% per annum, where the difference is ₹90. We can use the formulas for simple and compound interest to find the principal amount.
To find the principal from the difference in interest rates, we use the compound interest formula Principal(1 + interest rate)^time and the simple interest formula Principal + (principal × rate × time). Since the rate is 12% or 0.12 and the time is 2 years, we can set up an equation where the difference between the compound interest formula and the simple interest formula equals to ₹90.
Compound Interest: P(1 + 0.12)^2
Simple Interest: P + (P × 0.12 × 2)
The difference in the formulas gives us the condition: P(1 + 0.12)^2 - (P + (P × 0.12 × 2)) = ₹90. Solving this equation will yield the principal P.
After calculating, we find that the principal sum is ₹1,500, which corresponds to option A. Thus, by understanding how compound interest can make a significant difference over time, even with small amounts of money, we're able to solve for the principal using the difference in interest methods.