What is the rate of interest per annum if a sum of money invested at compound interest amounts to Rs. 2400 in 3 years and to Rs. 2520 in 4 years, with annual compounding?

Introduction / Context:
This question asks us to determine the compound interest rate from the way a sum grows between the third and fourth years. We are told that the amount after 3 years is Rs. 2400 and after 4 years is Rs. 2520. Because compounding is annual, the growth from year 3 to year 4 directly indicates the yearly rate of interest. This is a standard type of reverse compound interest question.

Given Data / Assumptions:

• Amount after 3 years A3 = Rs. 2400.
• Amount after 4 years A4 = Rs. 2520.
• Compounding is annual at a fixed rate r percent per annum.
• The principal is the same for both calculations; only time differs.

Concept / Approach:
Under annual compounding at rate r percent, the amount each year is multiplied by the factor (1 + r/100). Thus the ratio of A4 to A3 is: A4 / A3 = 1 + r/100 We can therefore find r by dividing 2520 by 2400 and then converting the resulting factor into a percentage rate.

Step-by-Step Solution:
A3 = 2400, A4 = 2520 Compute the ratio: A4 / A3 = 2520 / 2400 2520 / 2400 = 1.05 Therefore, 1 + r/100 = 1.05 r/100 = 1.05 - 1 = 0.05 r = 0.05 * 100 = 5 percent Hence the rate of interest per annum is 5 percent

Verification / Alternative check:
We can quickly check by assuming a principal P and verifying both amounts. Let the annual factor be 1.05. Then: A3 = P * (1.05)^3 A4 = P * (1.05)^4 = A3 * 1.05 If A3 is 2400, then A4 should be 2400 * 1.05 = 2520, which matches the given data. This confirms that a yearly rate of 5 percent is consistent with the information provided.

Why Other Options Are Wrong:
A rate of 3.5 percent or 4 percent would give smaller growth between the third and fourth year and would not produce a ratio of 1.05. A rate such as 6 percent or 6.5 percent would yield a higher ratio, for example 1.06 or 1.065, leading to larger final amounts than stated. Only 5 percent matches the exact ratio 2520 / 2400 = 1.05.

Common Pitfalls:
Some students try to work backwards all the way to the principal using more complicated algebra than necessary. Others mistakenly average across multiple years or confuse the situation with simple interest. Recognizing that the ratio between successive annual amounts directly reveals the compound factor is the key insight. Careful handling of the ratio and keeping track of the meaning of each quantity prevents confusion.

Final Answer:
The rate of interest per annum is 5 percent.