The simple interest on a sum of money for 3 years at 20/3% per annum is ₹6750.…
2025
The simple interest on a sum of money for 3 years at 20/3% per annum is ₹6750. What will be the compound interest on the same sum at the same rate for the same period, compounded annually?
Answer: A. Rs. 7210 — Simple Interest (SI) and Compound Interest (CI) follow two different formulas for the same principal, rate, and time. SI grows linearly: SI = (P × R × T)/100.…
- A.
Rs. 7210
- B.
Rs. 6655
- C.
Rs. 4496
- D.
Rs. 8125
Attempted by 4 students.
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Correct answer: A
Simple Interest (SI) and Compound Interest (CI) follow two different formulas for the same principal, rate, and time. SI grows linearly: SI = (P × R × T)/100. CI grows multiplicatively: the compounded amount is A = P × (1 + R/100)T, and CI = A − P. When only SI is given, the principal must first be recovered from the SI formula before switching to the compound-growth formula.
Recover the principal from SI: 6750 = P × (20/3) × 3 / 100 = P × 20/100 = P/5, so P = 6750 × 5 = ₹33,750.
Apply the compounding formula for the same rate and time: A = P × (1 + R/100)3 = 33750 × (1 + 20/300)3 = 33750 × (16/15)3.
Evaluate the growth factor: (16/15)3 = 4096/3375, so A = 33750 × 4096/3375 = 10 × 4096 = ₹40,960.
Compute the compound interest: CI = A − P = 40960 − 33750 = ₹7,210.
Cross-check: the same growth factor can be verified via the binomial expansion (1 + 1/15)3 = 1 + 3(1/15) + 3(1/15)2 + (1/15)3 ≈ 1.21363, and 33,750 × 1.21363 ≈ ₹40,960 — confirming the compound interest of ₹7,210.