On a certain sum of money, the compound interest for 2 years is Rs.304.5 and…
2025
On a certain sum of money, the compound interest for 2 years is Rs.304.5 and the simple interest for the same period of time is Rs.290. The rate of interest per annum:
- A.
9%
- B.
8%
- C.
11%
- D.
10%
Show answer & explanation
Correct answer: D
Concept: For a given sum and rate, the difference between the compound interest and the simple interest accumulated over 2 years equals the simple interest earned on the first year's own interest — that is, (CI − SI) for 2 years = SI for 1 year × (rate/100).
Application:
Simple interest for 2 years = Rs. 290, so simple interest for 1 year = 290/2 = Rs. 145.
Difference between compound interest (Rs. 304.5) and simple interest (Rs. 290) for 2 years = 304.5 − 290 = Rs. 14.5.
By the identity above, this difference equals the interest earned on the first year's simple interest at the unknown rate: 145 × (rate/100) = 14.5.
Solve: rate = (14.5 / 145) × 100 = 10%.
Cross-check: Since the simple interest for 1 year is Rs. 145 at a 10% rate, the principal = 145 / (10/100) = Rs. 1450. Compound interest for 2 years at 10% on Rs. 1450 = 1450 × [(1 + 10/100)2 − 1] = 1450 × 0.21 = Rs. 304.5, which matches the given compound interest and confirms the rate.