Ram earns ₹600 as simple interest over two years. If the same principal were…
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Ram earns ₹600 as simple interest over two years. If the same principal were invested at the same annual rate, the compound interest for two years would be ₹630. What is the annual rate of interest?
Answer: D. 10% — ConceptFor the same principal P and annual rate r%, the simple interest for two years is 2Pr/100. Over two years, the excess of compound interest over simple…
- A.
5%
- B.
20%
- C.
30%
- D.
10%
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Show answer & explanation
Correct answer: D
Concept
For the same principal P and annual rate r%, the simple interest for two years is 2Pr/100.
Over two years, the excess of compound interest over simple interest is the interest earned in the second year on the first year's interest.
Application
Let the interest for one year be I = Pr/100. Since the simple interest for two years is ₹600, 2I = 600, so I = ₹300.
The excess of compound interest over simple interest is ₹630 − ₹600 = ₹30.
This ₹30 is interest at r% on the first year's interest of ₹300: 30 = 300r/100.
Solving gives r = 10.
Cross-check
At 10%, the interest on ₹300 for the second year is ₹300 × 10/100 = ₹30. Thus the compound interest is ₹600 + ₹30 = ₹630, confirming that the annual rate is 10%.