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Compound Interest — Questions and Answers

Compound Interest adds each period's interest back to the principal, so the base itself grows. Two facts carry most exam questions: the amount formula A = P(1 + R/100)ⁿ, and the standard difference between CI and SI, which is P(R/100)² for two years and P(R/100)²(3 + R/100) for three years. Half-yearly or quarterly compounding simply halves or quarters the rate while doubling or quadrupling the number of periods.

26 solved questionsArithmetic AptitudeFree · no signup

Compound Interest— Concepts, Formulas & Shortcuts

  • Amount A = P(1 + R/100)ⁿ; CI = A − P.
  • Half-yearly: rate becomes R/2 and periods become 2n. Quarterly: R/4 and 4n.
  • CI − SI for 2 years = P(R/100)².
  • CI − SI for 3 years = P(R/100)²(3 + R/100).
  • If a sum becomes n times in t years at CI, it becomes n^k times in kt years.
  • For small rates, CI for 2 years ≈ 2R + R²/100 percent of the principal.

Compound Interest Practice Questions with Answers

Attempt each question first, then open the explanation. All 26 questions below are free to read and require no signup.

  1. Q1.The compound interest on ₹10,000 at 10% per annum for 2 years is:

    Easy
    • A₹2,000
    • B₹2,100
    • C₹2,200
    • D₹2,210
    +Show Answer & Explanation

    Answer: B. ₹2,100

    Explanation: A = 10000 × 1.1² = ₹12,100. CI = 12100 − 10000 = ₹2,100.

    Compound Interest question 1 of 26

  2. Q2.The difference between compound and simple interest on ₹8,000 at 5% per annum for 2 years is:

    Moderate
    • A₹16
    • B₹20
    • C₹24
    • D₹25
    +Show Answer & Explanation

    Answer: B. ₹20

    Explanation: Difference = P(R/100)² = 8000 × (0.05)² = 8000 × 0.0025 = ₹20.

    Compound Interest question 2 of 26

  3. Q3.₹1,000 invested at 20% per annum compounded half-yearly amounts in 1 year to:

    Moderate
    • A₹1,200
    • B₹1,210
    • C₹1,220
    • D₹1,240
    +Show Answer & Explanation

    Answer: B. ₹1,210

    Explanation: Half-yearly: 10% for 2 periods → 1000 × 1.1² = ₹1,210.

    Compound Interest question 3 of 26

  4. Q4.A sum of money doubles itself in 4 years at compound interest. In how many years will it become 8 times?

    Moderate
    • A8 years
    • B10 years
    • C12 years
    • D16 years
    +Show Answer & Explanation

    Answer: C. 12 years

    Explanation: 8 = 2³, and each doubling takes 4 years, so 3 doublings = 12 years.

    Compound Interest question 4 of 26

  5. Q5.The compound interest on ₹4,000 at 10% per annum for 2 years is:

    Easy
    • A₹800
    • B₹820
    • C₹840
    • D₹880
    +Show Answer & Explanation

    Answer: C. ₹840

    Explanation: A = 4000 × 1.21 = ₹4,840 → CI = ₹840.

    Compound Interest question 5 of 26

  6. Q6.At what rate per cent per annum will ₹1,200 amount to ₹1,348.32 in 2 years at compound interest?

    Difficult
    • A5%
    • B6%
    • C6.5%
    • D7%
    +Show Answer & Explanation

    Answer: B. 6%

    Explanation: 1348.32/1200 = 1.1236 = (1.06)², so the rate is 6%.

    Compound Interest question 6 of 26

  7. Q7.The difference between CI and SI on a sum at 10% per annum for 2 years is ₹631. The sum is:

    Moderate
    • A₹31,550
    • B₹63,100
    • C₹63,000
    • D₹65,000
    +Show Answer & Explanation

    Answer: B. ₹63,100

    Explanation: P(R/100)² = 631 → P × 0.01 = 631 → P = ₹63,100.

    Compound Interest question 7 of 26

  8. Q8.₹25,000 invested at 12% per annum compound interest for 3 years amounts to approximately:

    Moderate
    • A₹34,000
    • B₹35,123
    • C₹36,000
    • D₹37,500
    +Show Answer & Explanation

    Answer: B. ₹35,123

    Explanation: A = 25000 × (1.12)³ = 25000 × 1.404928 ≈ ₹35,123.

    Compound Interest question 8 of 26

  9. Q9.The amount on ₹5,000 at 10% per annum compounded annually for 2 years is:

    Easy
    • A₹5,500
    • B₹6,000
    • C₹6,050
    • D₹6,100
    +Show Answer & Explanation

    Answer: C. ₹6,050

    Explanation: A = 5000 × 1.1² = 5000 × 1.21 = ₹6,050.

    Compound Interest question 9 of 26

  10. Q10.The compound interest on ₹2,000 at 5% per annum for 2 years is:

    Easy
    • A₹200
    • B₹205
    • C₹210
    • D₹220
    +Show Answer & Explanation

    Answer: B. ₹205

    Explanation: A = 2000 × 1.05² = 2000 × 1.1025 = ₹2,205 → CI = ₹205.

    Compound Interest question 10 of 26

  11. Q11.The difference between CI and SI on ₹10,000 at 4% per annum for 2 years is:

    Moderate
    • A₹8
    • B₹16
    • C₹20
    • D₹24
    +Show Answer & Explanation

    Answer: B. ₹16

    Explanation: Difference = P(R/100)² = 10000 × 0.0016 = ₹16.

    Compound Interest question 11 of 26

  12. Q12.A sum becomes ₹1,331 in 3 years at 10% per annum compound interest. The sum is:

    Moderate
    • A₹1,000
    • B₹1,100
    • C₹1,200
    • D₹1,250
    +Show Answer & Explanation

    Answer: A. ₹1,000

    Explanation: P × 1.1³ = 1331 → P × 1.331 = 1331 → P = ₹1,000.

    Compound Interest question 12 of 26

  13. Q13.₹8,000 at 10% per annum compounded half-yearly for 1 year amounts to:

    Moderate
    • A₹8,800
    • B₹8,820
    • C₹8,840
    • D₹9,000
    +Show Answer & Explanation

    Answer: B. ₹8,820

    Explanation: Half-yearly: 5% for 2 periods → 8000 × 1.05² = 8000 × 1.1025 = ₹8,820.

    Compound Interest question 13 of 26

  14. Q14.A sum of money triples in 6 years at compound interest. In how many years will it become 9 times?

    Moderate
    • A9 years
    • B12 years
    • C15 years
    • D18 years
    +Show Answer & Explanation

    Answer: B. 12 years

    Explanation: 9 = 3², and each tripling takes 6 years, so two triplings = 12 years.

    Compound Interest question 14 of 26

  15. Q15.The compound interest on ₹6,250 at 8% per annum for 2 years is:

    Moderate
    • A₹1,000
    • B₹1,040
    • C₹1,080
    • D₹1,120
    +Show Answer & Explanation

    Answer: B. ₹1,040

    Explanation: A = 6250 × 1.08² = 6250 × 1.1664 = ₹7,290 → CI = ₹1,040.

    Compound Interest question 15 of 26

  16. Q16.If the CI on a sum for 2 years at 5% is ₹410, the simple interest for the same period is:

    Difficult
    • A₹380
    • B₹390
    • C₹400
    • D₹405
    +Show Answer & Explanation

    Answer: C. ₹400

    Explanation: CI − SI = P(0.05)² and CI = P(1.05² − 1) = 0.1025P = 410 → P = ₹4,000. SI = 4000 × 5 × 2/100 = ₹400.

    Compound Interest question 16 of 26

  17. Q17.The population of a town is 10,000 and grows at 10% per annum. After 2 years it will be:

    Easy
    • A11,000
    • B12,000
    • C12,100
    • D12,500
    +Show Answer & Explanation

    Answer: C. 12,100

    Explanation: Population growth compounds like CI: 10,000 × 1.1² = 10,000 × 1.21 = 12,100 people.

    Compound Interest question 17 of 26

  18. Q18.A machine costing ₹20,000 depreciates at 10% per annum. Its value after 2 years is:

    Moderate
    • A₹16,000
    • B₹16,200
    • C₹16,800
    • D₹18,000
    +Show Answer & Explanation

    Answer: B. ₹16,200

    Explanation: Depreciation uses (1 − R/100)ⁿ: 20000 × 0.9² = 20000 × 0.81 = ₹16,200.

    Compound Interest question 18 of 26

  19. Q19.The amount on ₹2,000 at 5% per annum compounded annually for 2 years is:

    Easy
    • A₹2,100
    • B₹2,200
    • C₹2,205
    • D₹2,250
    +Show Answer & Explanation

    Answer: C. ₹2,205

    Explanation: 2000 × 1.05² = 2000 × 1.1025 = ₹2,205.

    Compound Interest question 19 of 26

  20. Q20.The compound interest on ₹8,000 at 10% per annum for 2 years is:

    Easy
    • A₹1,600
    • B₹1,680
    • C₹1,720
    • D₹1,800
    +Show Answer & Explanation

    Answer: B. ₹1,680

    Explanation: A = 8000 × 1.21 = ₹9,680 → CI = ₹1,680.

    Compound Interest question 20 of 26

  21. Q21.A sum doubles in 3 years at compound interest. In how many years will it become 4 times?

    Moderate
    • A6 years
    • B9 years
    • C12 years
    • D15 years
    +Show Answer & Explanation

    Answer: A. 6 years

    Explanation: 4 = 2², and each doubling takes 3 years → 6 years.

    Compound Interest question 21 of 26

  22. Q22.The difference between CI and SI on ₹4,000 at 10% per annum for 2 years is:

    Moderate
    • A₹20
    • B₹40
    • C₹60
    • D₹80
    +Show Answer & Explanation

    Answer: B. ₹40

    Explanation: Difference = P(R/100)² = 4000 × 0.01 = ₹40.

    Compound Interest question 22 of 26

  23. Q23.₹6,000 at 20% per annum compounded half-yearly for 1 year amounts to:

    Moderate
    • A₹7,200
    • B₹7,260
    • C₹7,320
    • D₹7,400
    +Show Answer & Explanation

    Answer: B. ₹7,260

    Explanation: Half-yearly: 10% for 2 periods → 6000 × 1.21 = ₹7,260.

    Compound Interest question 23 of 26

  24. Q24.A sum amounts to ₹9,261 in 3 years at 5% compound interest. The sum is:

    Difficult
    • A₹7,500
    • B₹8,000
    • C₹8,500
    • D₹9,000
    +Show Answer & Explanation

    Answer: B. ₹8,000

    Explanation: P × 1.05³ = 9261 → P × 1.157625 = 9261 → P = ₹8,000.

    Compound Interest question 24 of 26

  25. Q25.The value of a car worth ₹5,00,000 depreciating at 20% per annum after 2 years is:

    Moderate
    • A₹3,00,000
    • B₹3,20,000
    • C₹3,50,000
    • D₹4,00,000
    +Show Answer & Explanation

    Answer: B. ₹3,20,000

    Explanation: 500000 × 0.8² = 500000 × 0.64 = ₹3,20,000.

    Compound Interest question 25 of 26

  26. Q26.The compound interest on ₹1,500 at 8% per annum for 2 years is:

    Moderate
    • A₹240
    • B₹249.60
    • C₹256
    • D₹264
    +Show Answer & Explanation

    Answer: B. ₹249.60

    Explanation: A = 1500 × 1.08² = 1500 × 1.1664 = ₹1,749.60 → CI = ₹249.60.

    Compound Interest question 26 of 26

Compound Interest — Frequently Asked Questions

What is the difference between simple and compound interest?+

Simple interest is computed only on the original principal, so it is constant each year. Compound interest is computed on principal plus accumulated interest, so it grows each year. Over two years, the gap is exactly P(R/100)².

How does half-yearly compounding change the calculation?+

Use half the annual rate and twice the number of years. ₹1,000 at 20% p.a. compounded half-yearly for 1 year means 10% for 2 periods → ₹1,210.

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