There is a 40% increase in an amount in 5 years at simple interest. Using the same annual rate, what will be the compound interest (in rupees) on Rs 25,000 after 3 years?

Introduction / Context:
This question links simple interest and compound interest by using the same annual rate of interest in two separate contexts. First, a 40% increase over 5 years at simple interest is given. From that, you must infer the yearly rate. Then you apply this rate to compute the compound interest on a new principal over 3 years.

Given Data / Assumptions:

• At simple interest, an amount increases by 40% in 5 years.
• We must find the equivalent annual rate r%.
• Principal for the compound interest part is Rs 25,000.
• Time period for compound interest = 3 years.
• Interest is compounded annually for the second part.

Concept / Approach:
Under simple interest, a 40% increase over 5 years implies that the total interest is 40% of the principal across the full period. Thus, the simple interest rate per year is 40 / 5 = 8%. Once we have r = 8%, we compute the compound interest using CI = P * [(1 + r/100)^3 - 1] on Rs 25,000 for 3 years.

Step-by-Step Solution:
Step 1: From simple interest data: Total increase = 40% in 5 years implies r = 40 / 5 = 8% per annum. Step 2: Use compound interest formula for P = 25,000, r = 8%, n = 3 years. Step 3: Compute compound factor: 1 + r/100 = 1 + 8/100 = 1.08. Step 4: Raise the factor to the 3rd power: 1.08^3 = 1.08 * 1.08 * 1.08 = 1.259712. Step 5: Compute the amount: A = 25,000 * 1.259712 = 31,492.8 (rupees). Step 6: Compound interest: CI = A - P = 31,492.8 - 25,000 = Rs 6,492.8.
Verification / Alternative check:
You can also compute the interest year by year: Year 1 interest = 25,000 * 8% = 2,000, amount = 27,000. Year 2 interest = 27,000 * 8% = 2,160, amount = 29,160. Year 3 interest = 29,160 * 8% = 2,332.8, final amount = 31,492.8, so CI = 6,492.8.
Why Other Options Are Wrong:
Rs 12,985.6 and Rs 16,232 are too large, as they would correspond to much higher rates or longer periods. Rs 9,739.2 is larger than the actual CI and does not match the detailed step-by-step calculation.
Common Pitfalls:
Many students forget that the 40% increase is over 5 years, not per year, and incorrectly take r as 40% instead of 8%. Others mistakenly compute simple interest again for 3 years instead of using the compound interest formula, missing the interest-on-interest effect.
Final Answer:
The compound interest on Rs 25,000 after 3 years at this rate is Rs 6,492.8.