Practice Questions
Concept Explanation
For the same principal and rate, compound interest exceeds simple interest because CI earns interest on interest.
Key Formulas
- 2 years: Difference = P(R/100)^2
- 3 years: Difference = P(R/100)^2 × (3 + R/100)
Example
P = Rs. 10,000, R = 10%, 2 years. Difference = 10000 × (0.1)^2 = Rs. 100.
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Q1 EasyThe difference between CI and SI on Rs. 1200 for 1 year at 10% per annum compounded half-yearly is:ExplanationFormula: SI = (P × R × T)/100; for half-yearly CI, A = P(1 + R/200)^(2T). SI = (1200 × 10 × 1)/100 = Rs. 120. Half-yearly rate = 5% and periods = 2, so CI = 1200 × (1.05)^2 − 1200 = 1323 − 1200 = Rs. 123. Difference = CI − SI = 123 − 120 = Rs. 3. Hence the answer is Rs. 3.
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Q2 EasyThe difference between simple and compound interest on Rs. 6000 for 2 years at 5% is:ExplanationFormula for 2 years: CI − SI = P(R/100)^2. Difference = 6000 × (5/100)^2 = 6000 × 0.0025 = Rs. 15. Check: SI = (6000 × 5 × 2)/100 = Rs. 600; CI = 6000 × (1.05)^2 − 6000 = Rs. 615; 615 − 600 = Rs. 15. Hence the answer is Rs. 15.
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Q3 EasyDifference of CI and SI on Rs. 10000 for 2 years at 5%:ExplanationFormula for 2 years: CI − SI = P(R/100)^2. Difference = 10000 × (5/100)^2 = 10000 × 0.0025 = Rs. 25. Check: SI = Rs. 1,000; CI = 10000 × 1.1025 − 10000 = Rs. 1,025; difference = Rs. 25. Hence the answer is Rs. 25.
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Q4 EasyThe difference between compound interest and simple interest on Rs. 8,000 at 10% per annum for 2 years is:ExplanationFormula for 2 years: CI − SI = P(R/100)^2. Difference = 8000 × (10/100)^2 = 8000 × 0.01 = Rs. 80. Check: SI = Rs. 1,600; CI = 8000 × 1.21 − 8000 = Rs. 1,680; difference = Rs. 80. Hence the answer is Rs. 80.
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Q5 EasyThe difference between CI and SI on Rs. 4,000 for 2 years at 5% per annum is:ExplanationFormula for 2 years: CI − SI = P(R/100)^2. Difference = 4000 × (5/100)^2 = 4000 × 0.0025 = Rs. 10. Hence the answer is Rs. 10.
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Q6 MediumDifference between CI and SI on a sum at 10% for 2 years is Rs. 50. Sum:ExplanationFormula for 2 years: CI − SI = P(R/100)^2. So 50 = P × (10/100)^2 = P × 0.01 ⇒ P = 50 / 0.01 = Rs. 5,000. Check: SI = 1000, CI = 1050, difference = 50. Hence the sum is Rs. 5,000.
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Q7 MediumCI − SI on Rs. 16,000 at 5% per annum for 2 years equals:ExplanationFormula for 2 years: CI − SI = P(R/100)^2. Difference = 16000 × (5/100)^2 = 16000 × 0.0025 = Rs. 40. Hence the answer is Rs. 40.
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Q8 MediumThe difference between CI and SI on a certain sum at 12% per annum for 2 years is Rs. 72. The sum is:ExplanationFormula: CI − SI = P(R/100)^2. So 72 = P × (12/100)^2 = P × 0.0144 ⇒ P = 72 / 0.0144 = Rs. 5,000. Hence the sum is Rs. 5,000.
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Q9 MediumDifference between CI and SI on Rs. 5,000 at 20% per annum for 2 years is:ExplanationFormula for 2 years: CI − SI = P(R/100)^2. Difference = 5000 × (20/100)^2 = 5000 × 0.04 = Rs. 200. Check: SI = 2000; CI = 5000 × 1.44 − 5000 = 2200; difference = 200. Hence the answer is Rs. 200.
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Q10 MediumOn a sum of Rs. 25,000 at 10% for 2 years, CI exceeds SI by:ExplanationFormula for 2 years: CI − SI = P(R/100)^2. Difference = 25000 × 0.01 = Rs. 250. Hence the answer is Rs. 250.
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Q11 HardFind the difference between CI and SI on Rs. 10,000 at 10% per annum for 3 years (compounded annually).ExplanationFormula for 3 years: CI − SI = P(R/100)^2 × (3 + R/100). Difference = 10000 × (0.1)^2 × (3 + 0.1) = 100 × 3.1 = Rs. 310. Check: SI = 3000; A = 10000 × 1.331 = 13310 so CI = 3310; 3310 − 3000 = 310. Hence the answer is Rs. 310.
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Q12 HardIf the difference between CI and SI on a sum for 2 years at 8% per annum is Rs. 64, the principal is:ExplanationFormula: CI − SI = P(R/100)^2. 64 = P × (8/100)^2 = P × 0.0064 ⇒ P = 64 / 0.0064 = Rs. 10,000. Hence the principal is Rs. 10,000.
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Q13 HardCI − SI on Rs. 15,000 at 10% for 3 years (annually) is:ExplanationFormula for 3 years: CI − SI = P(R/100)^2 × (3 + R/100). Difference = 15000 × 0.01 × 3.1 = Rs. 465. Check: SI = 4500; A = 15000 × 1.331 = 19965 so CI = 4965; 4965 − 4500 = 465. Hence the answer is Rs. 465.
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Q14 HardDifference between CI and SI on Rs. 12,000 at 5% for 3 years is:ExplanationFormula for 3 years: CI − SI = P(R/100)^2 × (3 + R/100). Difference = 12000 × (0.05)^2 × (3 + 0.05) = 12000 × 0.0025 × 3.05 = 30 × 3.05 = Rs. 31.50. Hence the answer is Rs. 31.50.
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DS1 Easy
In a bank aptitude drill, candidates must find CI − SI for 2 years. What is the difference?
Statement IThe principal is Rs. 10,000 and the rate is 10% per annum.
Statement IIThe interest is calculated for exactly 2 years.
ExplanationFormula for 2 years: CI − SI = P(R/100)^2. Statement I gives P and R but not time. Statement II gives time but not P and R. Together: difference = 10000 × 0.01 = Rs. 100. Both are needed. Answer: C. -
DS2 Medium
For the principal. What is the principal?
Statement ICI − SI for 2 years at 10% per annum is Rs. 100.
Statement IIThe rate is 10% per annum and the time is 2 years.
ExplanationFormula: P = (CI − SI) / (R/100)^2. Statement I alone: P = 100 / 0.01 = Rs. 10,000. Statement II alone does not give the difference. Statement I alone is sufficient. Answer: A.
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DS3 Medium
What is the difference between compound interest and simple interest for 3 years?
Statement IPrincipal is Rs. 10,000 and rate is 10% per annum.
Statement IITime period is 3 years and compounding is annual.
ExplanationFormula for 3 years: CI − SI = P(R/100)^2 × (3 + R/100). Neither statement alone has all of P, R and T = 3. Together: difference = 10000 × 0.01 × 3.1 = Rs. 310. Both are needed. Answer: C. -
DS4 Hard
An HR quant quiz asks: is CI − SI greater than Rs. 200 for 2 years?
Statement IPrincipal is Rs. 25,000 at 10% per annum for 2 years.
Statement IIThe rate of interest is 10% per annum.
ExplanationStatement I alone: difference = 25000 × 0.01 = Rs. 250 > 200, so the answer is Yes. Statement II alone cannot decide without principal and time. Statement I alone is sufficient. Answer: A.