The principal that amounts to Rs. 4913 in 3 years at 6 1/4% per annum compound interest, compounded annually, is equal to how much?

Introduction / Context:
In this question, we are given the final amount after 3 years under compound interest and must find the original principal. The rate is 6 1/4% per annum, which has a convenient fractional form. Recognizing standard numeric patterns makes this question faster to solve.

Given Data / Assumptions:

• Amount after 3 years, A = Rs. 4913.
• Rate of interest r = 6 1/4% per annum, that is, 6.25%.
• Time t = 3 years.
• Interest is compounded annually.
• Principal P is to be found.

Concept / Approach:

We use the compound interest formula A = P * (1 + r / 100)^t and rearrange it to P = A / (1 + r / 100)^t. The rate 6.25% can be written as the fraction 1/16, so 1 + r / 100 becomes 17 / 16. Thus A and P are related by a simple rational power, making the arithmetic easier.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

Values such as Rs. 3096, Rs. 4076, and Rs. 4085 do not produce Rs. 4913 in 3 years at 6 1/4% compound interest. Only Rs. 4096 leads to an amount that matches the given figure.

Common Pitfalls:

Learners may misinterpret the rate 6 1/4% and fail to recognize the nice fractional form 1 / 16, leading to more cumbersome decimal calculations. Others may not notice the cube relationship between 4913 and 4096, which is an intentional pattern in this type of question.

Final Answer:

The required principal is Rs. 4096.