Practice Questions
Concept Explanation
Compound Interest (CI) is interest on principal plus accumulated interest. When compounded annually, interest is added once per year.
Key Formulas
- A = P(1 + R/100)^T
- CI = A − P
Example
P = Rs. 10,000, R = 10%, T = 2 years. A = 10000 × 1.1^2 = Rs. 12,100. CI = Rs. 2,100.
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Q1 EasyAn amount of Rs. 1,00,000 is invested for 2 years at 10% CI compounded annually. The amount is:ExplanationA = P(1 + R/100)^T = 100000 × (1.1)^2 = 100000 × 1.21 = Rs. 1,21,000. Answer: B.
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Q2 EasyAmount when P = Rs. 5000, r = 10%, t = 2 years, CI annually is:ExplanationA = 5000 × (1.1)^2 = 5000 × 1.21 = Rs. 6,050. Answer: C.
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Q3 EasyCI on Rs. 10,000 at 10% per annum for 2 years compounded annually is:ExplanationA = 10000 × (1.1)^2 = Rs. 12,100. CI = 12100 − 10000 = Rs. 2,100. Answer: B.
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Q4 EasyFind the amount on Rs. 8,000 at 5% for 2 years compounded annually.ExplanationA = 8000 × (1.05)^2 = 8000 × 1.1025 = Rs. 8,820. Answer: B.
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Q5 EasyCI on Rs. 16,000 at 5% for 2 years compounded annually is:ExplanationA = 16000 × (1.05)^2 = 16000 × 1.1025 = Rs. 17,640. CI = 17640 − 16000 = Rs. 1,640. Answer: B.
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Q6 MediumThe compound interest on Rs. 30,000 at 7% per annum is Rs. 4347. The period (in years) is:ExplanationAmount = 30000 + 4347 = Rs. 34,347. Check A = P(1 + R/100)^T. For T = 2: 30000 × (1.07)^2 = 30000 × 1.1449 = Rs. 34,347. CI = 34347 − 30000 = Rs. 4,347. So the period is 2 years. Answer: B.
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Q7 MediumCI on Rs. 7500 for 2 years at 8% p.a. compounded annually is:ExplanationA = 7500 × (1.08)^2 = 7500 × 1.1664 = Rs. 8,748. CI = 8748 − 7500 = Rs. 1,248. Answer: C.
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Q8 MediumCI on Rs. 5,000 at 20% per annum for 2 years compounded annually is:ExplanationA = 5000 × (1.2)^2 = 5000 × 1.44 = Rs. 7,200. CI = 7200 − 5000 = Rs. 2,200. Answer: C.
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Q9 MediumAmount on Rs. 12,000 at 10% for 3 years compounded annually is:ExplanationA = 12000 × (1.1)^3 = 12000 × 1.331 = Rs. 15,972. Answer: C.
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Q10 MediumCI on Rs. 20,000 at 10% for 2 years compounded annually is:ExplanationA = 20000 × 1.21 = Rs. 24,200. CI = 24200 − 20000 = Rs. 4,200. Answer: C.
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Q11 HardThe difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 4% per annum is Re. 1. The sum (in Rs.) is:ExplanationFor 2 years, CI − SI = P(R/100)^2. So 1 = P(4/100)^2 = P × 0.0016 ⇒ P = 1/0.0016 = Rs. 625. Answer: B.
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Q12 HardThe compound interest on a certain sum for 2 years at 10% per annum is Rs. 525. The simple interest on the same sum for double the time at half the rate percent per annum is:ExplanationCI = P[(1.1)^2 − 1] = P × 0.21 = 525 ⇒ P = 525/0.21 = Rs. 2,500. Double time = 4 years; half rate = 5%. SI = (2500 × 5 × 4)/100 = Rs. 500. Answer: B.
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Q13 HardAmount on Rs. 15,000 at 8% for 2 years compounded annually is:ExplanationA = 15000 × (1.08)^2 = 15000 × 1.1664 = Rs. 17,496. Answer: B.
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Q14 HardIf the difference between CI and SI on a sum for 2 years at 5% p.a. compounded annually is Rs. 25, the sum is:ExplanationCI − SI = P(R/100)^2 ⇒ 25 = P(0.05)^2 = 0.0025P ⇒ P = 25/0.0025 = Rs. 10,000. Answer: C.
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DS1 Easy
What is the amount after 2 years?
Statement IPrincipal is Rs. 1,00,000.
Statement IIRate is 10% compounded annually.
ExplanationTime is given in the question (2 years). Statement I lacks rate; Statement II lacks principal. Together: A = 100000 × (1.1)^2 = Rs. 1,21,000. Answer: C. -
DS2 Medium
What is the compound interest (annual compounding)?
Statement IP = Rs. 7,500 at 8% for 2 years compounded annually.
Statement IICI − SI for 2 years at 8% on this principal is Rs. 48.
ExplanationStatement I: A = 7500 × (1.08)^2 = Rs. 8,748; CI = Rs. 1,248. Statement II: P(0.08)^2 = 48 ⇒ P = Rs. 7,500; SI = (7500 × 8 × 2)/100 = Rs. 1,200; CI = 1200 + 48 = Rs. 1,248. Either alone is sufficient. Answer: D.
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DS3 Medium
Is the period 2 years?
Statement ICI on Rs. 30,000 at 7% p.a. is Rs. 4,347.
Statement IIPrincipal is Rs. 30,000 and the amount at 7% compounded annually is Rs. 34,347.
ExplanationStatement I: 30000 × (1.07)^2 − 30000 = 4347, so T = 2. Statement II: 34347/30000 = 1.1449 = (1.07)^2, so T = 2. Either alone is sufficient. Answer: D. -
DS4 Hard
What is the principal?
Statement ICI on the sum for 2 years at 10% p.a. compounded annually is Rs. 525.
Statement IISI on the same sum for 4 years at 5% p.a. is Rs. 500.
ExplanationStatement I: P × 0.21 = 525 ⇒ P = Rs. 2,500. Statement II: (P × 5 × 4)/100 = 500 ⇒ P = Rs. 2,500. Either statement alone is sufficient. Answer: D.