On a certain principal, the simple interest for two years is Rs 2800 and the compound interest for two years is Rs 2996. What is the annual rate of interest?

Introduction / Context:
This question directly compares simple interest and compound interest on the same principal over the same time period. The difference between the two interests over two years provides a way to calculate the interest on interest, which then helps you to find the annual rate of interest.

Given Data / Assumptions:

• Simple interest (SI) for 2 years = Rs 2800.
• Compound interest (CI) for 2 years = Rs 2996.
• Same principal P and same annual rate r are used in both cases.
• Interest is compounded annually for CI.
• Time period n = 2 years.

Concept / Approach:
For 2 years, the difference between CI and SI arises only from the interest earned on the first year's interest during the second year. That extra amount is equal to the interest on the simple interest of one year. Using SI = P * r * 2 / 100 and CI - SI = interest on first year's interest, we can set up equations to find both P and r. However, we only need r, so we can eliminate P using algebra.

Step-by-Step Solution:
Step 1: Let the annual rate be r% and the principal be P. Step 2: Simple interest for 2 years: SI = P * r * 2 / 100 = 2800, so P * r = 2800 * 100 / 2 = 140000. Step 3: Difference between CI and SI: CI - SI = 2996 - 2800 = 196. Step 4: For 2 years, this difference equals interest on the first year's interest: Difference = (P * r / 100) * r / 100 = P * r^2 / 10000. Step 5: Using P * r = 140000, we have: P * r^2 / 10000 = (140000 * r) / 10000 = 14r. Step 6: So 14r = 196, giving r = 196 / 14 = 14.
Verification / Alternative check:
Take r = 14%. Then from P * r = 140000, we get P = 140000 / 14 = 10000. Compute SI: SI = 10000 * 14 * 2 / 100 = Rs 2800. Compute CI: A = 10000 * (1.14)^2 = 10000 * 1.2996 = 12996, so CI = 12996 - 10000 = Rs 2996. Both match the given values.
Why Other Options Are Wrong:
7 percent or 21 percent do not satisfy both the SI value and the CI difference simultaneously. 28 percent is far too high and would produce very large interest amounts, inconsistent with the given data.
Common Pitfalls:
Students often confuse the relation between CI and SI and forget that the difference over 2 years comes only from interest on interest in the second year. Misapplying CI formulas or not carefully handling the algebra frequently leads to incorrect rates.
Final Answer:
The annual rate of interest is 14 percent.