A certain principal is invested at compound interest. The amount after 1 year is Rs. 2400 and the amount after 2 years is Rs. 2880. Based on these two consecutive yearly amounts, what is the annual rate of interest in percent for this compound interest investment?

Introduction / Context:
This question is a classic example of finding the rate of compound interest when successive yearly amounts are given. The key idea is that under compound interest with annual compounding, each year the amount is multiplied by the factor (1 + r/100). When we know the amount at the end of one year and at the end of the next year, the ratio of these amounts directly reveals the interest factor and hence the annual rate. This is a quick and important shortcut in competitive exams.

Given Data / Assumptions:

• Amount after 1 year, A₁ = Rs. 2400.
• Amount after 2 years, A₂ = Rs. 2880.
• Principal P is the same underlying amount, but we are not directly asked to find it.
• Interest is compounded annually at rate r percent.
• We need to find the value of r in percent per annum.

Concept / Approach:
If interest is compounded annually at rate r percent, then:
A₁ = P * (1 + r/100),
A₂ = P * (1 + r/100)^2.
Therefore, the ratio A₂ / A₁ equals (1 + r/100). This relationship allows us to find the yearly growth factor and hence the rate without first computing the principal. Once we compute A₂ / A₁, we can subtract 1 and convert to a percentage to get the annual rate of interest.

Step-by-Step Solution:
Step 1: Write the relationship between consecutive amounts under annual compounding: A₂ = A₁ * (1 + r/100). Step 2: Therefore, (1 + r/100) = A₂ / A₁. Step 3: Substitute the given values: (1 + r/100) = 2880 / 2400. Step 4: Simplify the ratio 2880 / 2400 = 1.2. Step 5: Hence, 1 + r/100 = 1.2. Step 6: Subtract 1 from both sides to get r/100 = 1.2 − 1 = 0.2. Step 7: Multiply by 100 to get r = 0.2 * 100 = 20 percent per annum. Step 8: Thus, the annual rate of compound interest is 20 percent.

Verification / Alternative check:
We can verify by assuming the principal P and checking both amounts. Suppose P is some value; after 1 year, A₁ = P * 1.2 = 2400, so P = 2400 / 1.2 = 2000. After 2 years, A₂ = 2000 * (1.2)^2 = 2000 * 1.44 = 2880, which matches the given amount. This confirms that both the data and calculated rate r = 20 percent are internally consistent.

Why Other Options Are Wrong:
At 15 % (factor 1.15), the second year amount would be 2400 * 1.15 = 2760, not 2880. At 10 % (factor 1.10), A₂ would be 2400 * 1.10 = 2640, again incorrect. At 12 % (factor 1.12), A₂ would be 2400 * 1.12 = 2688. At 25 % (factor 1.25), the amount would jump to 2400 * 1.25 = 3000. None of these match the given A₂ except the factor 1.2 corresponding to 20 percent per annum.

Common Pitfalls:
One common mistake is to treat the difference between 2880 and 2400 as simple interest for one year and base the rate on the original principal instead of on the amount. Others wrongly assume that the increase of Rs. 480 over Rs. 2400 is 48 percent rather than correctly computing 480/2400 = 0.2, that is 20 percent. Remembering that under compound interest with yearly compounding, consecutive amounts differ by the factor (1 + r/100) is essential.

Final Answer:
The annual rate of compound interest implied by the given amounts is 20 % per annum.