The difference between the compound interest and the simple interest accrued…
2024
The difference between the compound interest and the simple interest accrued on an amount of Rs. 18,000 in 2 years was Rs. 405. What was the rate of interest p.c.p.a.?
- A.
14%
- B.
16%
- C.
12.5%
- D.
15%
Show answer & explanation
Correct answer: D
Concept: For a sum invested for 2 years, the difference between compound interest (CI) and simple interest (SI) follows a fixed identity: Difference = P × (R/100)², where P is the principal and R is the annual rate percent. This extra amount arises because compounding applies interest-on-interest only from the second year onward.
Given: Principal P = Rs. 18,000, Time = 2 years, Difference between CI and SI = Rs. 405.
Substitute into the identity: 405 = 18,000 × (R/100)2
Divide both sides by 18,000: (R/100)2 = 405 / 18,000 = 9/400
Take the square root of both sides: R/100 = 3/20
Solve for R: R = (3/20) × 100 = 15
Cross-check: at R = 15%, SI for 2 years = (18,000 × 15 × 2)/100 = Rs. 5,400. CI for 2 years = 18,000 × [(1.15)2 − 1] = 18,000 × 0.3225 = Rs. 5,805. The difference 5,805 − 5,400 = Rs. 405, exactly matching the given data.
Therefore, the rate of interest is 15% p.c.p.a.