If the compound interest on a certain sum of money for 3 years at 10% per…
2024
If the compound interest on a certain sum of money for 3 years at 10% per annum is Rs. 1655, what would be the simple interest on the same sum, at the same rate, for the same period?
Answer: B. Rs. 1500 — Concept: For a principal P invested at rate R% per annum for T years, the compound interest is CI = P × [(1 + R/100)T − 1], while the simple interest for the…
- A.
Rs. 1650
- B.
Rs. 1500
- C.
Rs. 1550
- D.
Rs. 1600
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Correct answer: B
Concept:
For a principal P invested at rate R% per annum for T years, the compound interest is CI = P × [(1 + R/100)T − 1], while the simple interest for the same principal, rate, and time is SI = (P × R × T) / 100. Because these are governed by different formulas, whenever a problem gives CI and asks for SI (or vice versa), the principal must first be recovered from the given interest before switching formulas.
Application:
Write the compound-interest equation for the given data: 1655 = P × [(1 + 10/100)3 − 1].
Evaluate the growth factor: (1.1)3 = 1.331, so 1655 = P × 0.331.
Solve for the principal: P = 1655 ÷ 0.331 = Rs. 5000.
Apply the simple-interest formula to the same principal, rate, and time: SI = (5000 × 10 × 3) ÷ 100 = Rs. 1500.
Cross-check:
With P = Rs. 5000, the amount after 3 years is 5000 × 1.331 = Rs. 6655, so the compound interest is 6655 − 5000 = Rs. 1655 — exactly matching the value given in the question, confirming the principal (and hence the simple interest) is correct.