RAS question
The difference between compound interest and simple interest on ₹8,000 for 2 years at 5% per annum is:
Correct answer: (B) ₹20.
The difference between compound interest and simple interest on Rs 8,000 for 2 years at 5% per annum is Rs 20.
Explanation
For 2 years, the gap between compound interest and simple interest is P x (R/100)^2. Substituting the given values gives 8000 x (5/100)^2 = 8000 x 0.0025 = Rs 20. The longer check gives the same result: simple interest is 8000 x 5 x 2 / 100 = Rs 800, while compound interest is 8000 x (1.05)^2 - 8000 = Rs 820. The Consumer Financial Protection Bureau explains the key idea behind this gap: compound interest counts interest on both the original money and the interest already earned. That extra interest-on-interest is why CI exceeds SI here by Rs 20.
Why the other options are wrong
- (A) Rs 40 doubles the actual 2-year gap; the formula P x (R/100)^2 gives Rs 20, not Rs 40.
- (C) Rs 25 would require 8000 x (R/100)^2 to equal 25, but at 5% the squared rate is 0.0025, giving Rs 20.
- (D) Rs 10 is only half of the verified gap, since CI is Rs 820 and SI is Rs 800.
Concept
This tests percentage-based interest, especially the standard 2-year shortcut for the difference between CI and SI. It recurs in RAS reasoning because it checks both formula recall and quick numerical substitution.