Compound Interest – Find the annual rate from successive-year interests: If the compound interest of a certain sum for two successive years is ₹ 225 and ₹ 238.50 respectively, what is the annual rate of interest?

Introduction / Context:
Under compound interest, the interest earned in the second year equals the first year’s interest grown by one more year at the same rate, because the second year accrues interest on both the principal and the first-year interest. This relationship allows us to extract the rate directly from the ratio of successive-year interests.

Given Data / Assumptions:

• First-year CI = 225
• Second-year CI = 238.50
• Constant annual rate r

Concept / Approach:
For annual compounding, Interest in Year 2 = Interest in Year 1 * (1 + r/100). Therefore (1 + r/100) = 238.50 / 225. Solve for r by subtracting 1 and converting to percent.

Step-by-Step Solution:
Compute ratio: 238.50 / 225 = 1.06Thus 1 + r/100 = 1.06 ⇒ r/100 = 0.06Therefore r = 6%

Verification / Alternative check:
If r = 6%, any first-year interest I grows to I * 1.06 in Year 2, which fits 225 → 238.50 exactly. No principal value is required to confirm the rate.

Why Other Options Are Wrong:
5%, 7.5%, 10%, or 4% would produce ratios 1.05, 1.075, 1.10, or 1.04—not equal to 1.06 observed from the data.

Common Pitfalls:
Equating the difference (238.50 − 225) to the rate times principal is incorrect; the relationship is multiplicative from one year’s interest to the next under compounding.

Final Answer:
6%