Final answer:
The compound interest on the given sum of money for 2 years at 5% p.a. is Rs. 262.50. The correct answer is option (A).
Step-by-step explanation:
To find the compound interest on a certain sum of money for 2 years at 5% p.a., we can use the formula:
Compound Interest = P(1 + r/n)^(nt) - P,
where P is the principal amount, r is the interest rate, n is the number of times interest is compounded per year, and t is the time in years.
In this case, we know that the difference between compound interest and simple interest for 2 years is Rs. 12.50. Let's assume the principal amount is P.
Using the formula for simple interest, we can calculate the simple interest as follows:
Simple Interest = P * r * t =
* 0.05 * 2
= 0.1P
Now, let's calculate the compound interest:
Compound Interest = P(1 + r)^t - P
= P(1 + 0.05)^2 - P = 1.1025P - P
= 0.1025P
Given that the difference between compound interest and simple interest is Rs. 12.50, we can set up the following equation:
0.1025P - 0.1P = 12.50
Solving this equation, we find that P = 250.
Now, we can calculate the compound interest:
Compound Interest = 0.1025 * 250
= Rs. 25.62.50.