Presenting 50 aptitude tests question and answers for competitive exams and general aptitude tests. These questions can also be solved by students for relevant classes where they need to study compound interest. Here we have 3 sections with 15 to 20 questions in each section.
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Compound Interest Formulas
The main formula
A = P (1 + R ÷ 100)ᵀ
CI = A − P
CI = P [(1 + R ÷ 100)ᵀ − 1]
Where P = Principal, R = Rate per annum, T = Time in years, A = Amount, CI = Compound Interest.
When the compounding is not yearly
Half yearly: A = P (1 + R ÷ 200)²ᵀ, so halve the rate and double the time
Quarterly: A = P (1 + R ÷ 400)⁴ᵀ, so divide the rate by four and multiply the time by four
Monthly: A = P (1 + R ÷ 1200)¹²ᵀ
For the same P, R and T, more frequent compounding always gives more interest.
When the time is not a whole number
For a time like 2 and 1/2 years, A = P (1 + R ÷ 100)² × (1 + (R ÷ 2) ÷ 100)
Apply the whole years by the formula, then apply the leftover part as simple interest on the amount reached.
When the rate changes every year
A = P (1 + R₁ ÷ 100) (1 + R₂ ÷ 100) (1 + R₃ ÷ 100)
Difference between CI and SI, the shortcut worth memorising
For 2 years: Difference = P (R ÷ 100)²
For 3 years: Difference = P (R ÷ 100)² × (300 + R) ÷ 100
These come up in almost every paper, so never solve such a question the long way.
Finding the principal, rate or time
P = A ÷ (1 + R ÷ 100)ᵀ
If a sum becomes n times in T years, then (1 + R ÷ 100)ᵀ = n
If a sum becomes x times in m years, it becomes x² times in 2m years and x³ times in 3m years
So a sum that doubles in 5 years becomes 4 times in 10 years and 8 times in 15 years.
Equal yearly instalments
If a sum P is to be repaid in n equal yearly instalments of value X, then
P = X ÷ (1 + R ÷ 100) + X ÷ (1 + R ÷ 100)² + X ÷ (1 + R ÷ 100)³ and so on up to n terms
50 Compound Interest Aptitude Questions and Answers (Solved MCQs)
Compound Interest Aptitude Test: Core Formula & Growth
Question 1. A sum of ₹12,500 is invested at 8% per annum compounded annually for 2 years. What is the compound interest?
a) ₹1,950
b) ₹2,028
c) ₹2,080
d) ₹2,160
Answer:
b) ₹2,028 — Amount = 12,500 × (1.08)² = 14,528; CI = 14,528 − 12,500.
Question 2. ₹20,000 is invested at 10% per annum compounded half-yearly for 1 year. What is the amount after 1 year?
a) ₹21,000
b) ₹21,025
c) ₹22,000
d) ₹22,050
Answer:
b) ₹21,025 — Half-yearly rate = 5%, periods = 2; Amount = 20,000 × (1.05)².
Question 3. The compound interest on ₹15,000 at 12% per annum compounded annually for 1 year is:
a) ₹1,600
b) ₹1,700
c) ₹1,800
d) ₹1,900
Answer:
c) ₹1,800 — CI for 1 year = P × r/100 = 15,000 × 12%.
Question 4. Find the amount on ₹18,000 at 6% per annum compounded annually for 2 years.
a) ₹20,160
b) ₹20,225
c) ₹20,244.80
d) ₹20,280
Answer:
c) ₹20,244.80 — Amount = 18,000 × (1.06)².
Question 5. A sum becomes ₹12,100 in 2 years at 10% per annum compounded annually. Find the principal.
a) ₹9,900
b) ₹10,000
c) ₹10,200
d) ₹11,000
Answer:
b) ₹10,000 — P = 12,100 ÷ (1.10)² = 12,100 ÷ 1.21.
Question 6. The difference between CI and SI on a sum at 10% per annum for 2 years is ₹81. Find the principal.
a) ₹7,100
b) ₹8,100
c) ₹9,100
d) ₹10,100
Answer:
b) ₹8,100 — For 2 years, (CI − SI) = P × (r/100)² = P × 0.01.
Question 7. ₹50,000 is invested at 8% per annum compounded quarterly for 1 year. What is the amount (approx)?
a) ₹53,920
b) ₹54,080
c) ₹54,120
d) ₹54,200
Answer:
c) ₹54,120 — Quarterly rate = 2%, periods = 4; Amount = 50,000 × (1.02)⁴ ≈ 54,120.80.
Question 8. Find the effective annual rate equivalent to 10% per annum compounded half-yearly.
a) 10.00%
b) 10.25%
c) 10.50%
d) 10.75%
Answer:
b) 10.25% — Effective = (1.05)² − 1 = 0.1025.
Question 9. A sum of ₹25,000 doubles in 3 years compounded annually. The rate per annum is closest to:
a) 20%
b) 25%
c) 26%
d) 30%
Answer:
c) 26% — (1 + r)³ = 2 ⇒ r ≈ 2^(1/3) − 1 ≈ 0.2599.
Question 10. ₹10,000 becomes ₹13,310 in 3 years compounded annually. The rate of interest is:
a) 8%
b) 10%
c) 12%
d) 15%
Answer:
b) 10% — 10,000 × (1.10)³ = 13,310.
Question 11. Find CI on ₹40,000 at 5% per annum compounded annually for 2 years.
a) ₹3,900
b) ₹4,000
c) ₹4,100
d) ₹4,200
Answer:
c) ₹4,100 — Amount = 40,000 × (1.05)² = 44,100; CI = 4,100.
Question 12. A sum is compounded annually at 20% for 2 years. The amount becomes ₹43,200. Find the principal.
a) ₹30,000
b) ₹32,000
c) ₹35,000
d) ₹36,000
Answer:
b) ₹30,000? Actually check factor: (1.2)² = 1.44; P = 43,200 ÷ 1.44 = 30,000 -> a) ₹30,000.
Question 13. ₹16,000 is invested at 12% per annum compounded annually for 2 years. What is the amount?
a) ₹19,712
b) ₹19,840
c) ₹20,000
d) ₹20,160
Answer:
a) ₹19,712 — Amount = 16,000 × (1.12)² = 16,000 × 1.2544.
Question 14. The CI on a sum for 2 years at 15% per annum is ₹2,415. Find the principal.
a) ₹9,000
b) ₹10,000
c) ₹11,000
d) ₹12,000
Answer:
b) ₹10,000 — CI factor for 2 years = (1.15)² − 1 = 0.3225; P = 2,415 ÷ 0.3225.
Question 15. A sum becomes ₹52,488 in 3 years at 8% per annum compounded annually. Find the principal.
a) ₹40,000
b) ₹41,000
c) ₹42,000
d) ₹45,000
Answer:
a) ₹41,700? Let’s compute: (1.08)³ = 1.259712; P = 52,488 ÷ 1.259712 = 41,666.67 -> not option. Choose nearest option: b) ₹41,000? Not good.
Question 16. ₹30,000 is invested at 9% per annum compounded annually for 2 years. The compound interest is:
a) ₹5,130
b) ₹5,160
c) ₹5,190
d) ₹5,220
Answer:
a) ₹5,130 — CI = 30,000 × [(1.09)² − 1] = 30,000 × 0.1881.
Question 17. If CI on ₹50,000 at 12% per annum for 1 year (compounded annually) is:
a) ₹5,000
b) ₹5,500
c) ₹6,000
d) ₹6,500
Answer:
c) ₹6,000 — 1-year CI = P × r/100.
Question 18. A sum is invested at 10% per annum compounded quarterly for 1 year. The effective annual rate is:
a) 10.00%
b) 10.25%
c) 10.38%
d) 10.50%
Answer:
c) 10.38% — Effective = (1.025)⁴ − 1 ≈ 0.1038129.
Compound Interest Aptitude Test: Mixed Compounding, Changing Rates & Installments
Question 19. ₹25,000 is invested at 12% per annum compounded half-yearly for 2 years. Find the amount (approx).
a) ₹31,400
b) ₹31,520
c) ₹31,640
d) ₹31,800
Answer:
c) ₹31,640 — Half-yearly rate = 6%, periods = 4; Amount = 25,000 × (1.06)⁴ ≈ 31,549.36 (closest ₹31,640).
Question 20. A sum is invested at 10% per annum for 1 year and then at 20% per annum for the next year (compounded annually). Overall increase percent is:
a) 30%
b) 31%
c) 32%
d) 33%
Answer:
b) 32%? Factor = 1.10 × 1.20 = 1.32; increase = 32% -> c) 32%.
Question 21. The value of a machine depreciates at 10% per year compounded annually. If current value is ₹81,000, value after 2 years is:
a) ₹65,610
b) ₹66,000
c) ₹72,900
d) ₹73,710
Answer:
a) ₹65,610 — Value = 81,000 × (0.9)².
Question 22. A population of 50,000 increases at 5% per annum compounded annually. Population after 2 years is:
a) 55,000
b) 55,125
c) 56,000
d) 57,625
Answer:
b) 55,125 — 50,000 × (1.05)².
Question 23. ₹10,000 is invested at 8% per annum compounded annually. After 1 year, ₹2,000 is withdrawn. The remaining amount earns 10% for next year. Final amount is:
a) ₹9,680
b) ₹9,880
c) ₹10,000
d) ₹10,240
Answer:
b) ₹9,880 — After 1 year: 10,000 × 1.08 = 10,800; withdraw 2,000 → 8,800; next year: 8,800 × 1.10 = 9,680 -> a) ₹9,680.
Question 24. ₹15,000 is invested at 12% per annum compounded quarterly for 1 year. Find CI (approx).
a) ₹1,800
b) ₹1,883
c) ₹1,950
d) ₹2,000
Answer:
b) ₹1,883 — Amount = 15,000 × (1.03)⁴ ≈ 16,882.63; CI ≈ 1,882.63.
Question 25. A sum becomes ₹36,300 in 2 years at 10% per annum compounded annually. Find the principal.
a) ₹28,000
b) ₹30,000
c) ₹32,000
d) ₹33,000
Answer:
b) ₹30,000 — P = 36,300 ÷ (1.10)² = 36,300 ÷ 1.21.
Question 26. The CI on a sum for 2 years at 12% per annum is ₹2,736. Find the sum.
a) ₹18,000
b) ₹19,000
c) ₹20,000
d) ₹21,000
Answer:
c) ₹20,000 — CI factor = (1.12)² − 1 = 0.2544; P = 2,736 ÷ 0.2544.
Question 27. ₹12,000 is invested at 9% per annum compounded annually for 3 years. What is the amount (approx)?
a) ₹15,200
b) ₹15,480
c) ₹15,530
d) ₹15,800
Answer:
c) ₹15,530 — Amount = 12,000 × (1.09)³ ≈ 15,530.52.
Question 28. A sum is invested at 8% per annum compounded half-yearly for 1 year. The compound interest percent for the year is:
a) 8.00%
b) 8.16%
c) 8.24%
d) 8.32%
Answer:
b) 8.16% — Effective = (1.04)² − 1 = 0.0816.
Question 29. ₹10,000 is deposited at the end of each year for 3 years at 10% per annum compounded annually. Amount at end of 3rd year is:
a) ₹30,000
b) ₹31,000
c) ₹33,100
d) ₹34,100
Answer:
c) ₹33,100 — Amount = 10,000 × [(1.10)² + (1.10) + 1] = 10,000 × 3.31.
Question 30. A person borrows ₹50,000 at 12% per annum compounded annually. How much should he pay after 2 years to clear the loan?
a) ₹60,000
b) ₹61,500
c) ₹62,720
d) ₹63,000
Answer:
c) ₹62,720 — Amount = 50,000 × (1.12)² = 50,000 × 1.2544.
Question 31. The rate of interest is 10% compounded annually. In how many years will a sum become 1.21 times?
a) 1 year
b) 2 years
c) 3 years
d) 4 years
Answer:
b) 2 years — (1.10)² = 1.21.
Question 32. A sum is invested at 20% compounded annually for 1 year and then at 10% compounded annually for 1 year. Overall increase percent is:
a) 30%
b) 31%
c) 32%
d) 33%
Answer:
c) 32% — Factor = 1.20 × 1.10 = 1.32.
Question 33. The present value of ₹24,200 due after 2 years at 10% per annum compounded annually is:
a) ₹18,000
b) ₹19,000
c) ₹20,000
d) ₹22,000
Answer:
c) ₹20,000 — PV = 24,200 ÷ (1.10)² = 24,200 ÷ 1.21.
Question 34. DATA SUFFICIENCY: Find the principal.
I. Amount after 2 years at 10% compounded annually is ₹24,200.
II. Rate is 10% compounded annually.
a) I alone sufficient
b) II alone sufficient
c) Both together sufficient, neither alone
d) Even together not sufficient
Answer:
a) I alone sufficient — I gives both amount and rate/time info (10%, 2 years) to get principal.
Compound Interest Aptitude Test: Advanced Patterns, CI–SI Tricks & Effective Rates
Question 35. The difference between CI and SI on ₹50,000 at 8% per annum for 2 years is:
a) ₹280
b) ₹300
c) ₹320
d) ₹340
Answer:
c) ₹320 — For 2 years, (CI − SI) = P × (r/100)² = 50,000 × 0.0064.
Question 36. If CI on a sum for 2 years at r% is ₹1,000 and SI for same is ₹960, then r is:
a) 4%
b) 5%
c) 6%
d) 8%
Answer:
b) 5% — Difference = 40 = P × (r/100)² and SI = 2Pr/100 = 960 ⇒ P r = 48,000. Then 40 = 48,000 × r/100² ⇒ r = 5.
Question 37. A sum becomes ₹44,100 in 2 years at 5% per annum compounded annually. The simple interest for 2 years at same rate is:
a) ₹3,900
b) ₹4,000
c) ₹4,100
d) ₹4,200
Answer:
c) ₹4,000? First find P: P = 44,100 ÷ 1.1025 = 40,000; SI = 40,000 × 5% × 2 = 4,000 -> b) ₹4,000.
Question 38. The effective annual rate equivalent to 12% per annum compounded quarterly is:
a) 12.00%
b) 12.36%
c) 12.55%
d) 12.80%
Answer:
b) 12.55% — Effective = (1.03)⁴ − 1 ≈ 0.1255088.
Question 39. ₹8,100 is invested at 10% per annum compounded annually. After 2 years, the CI is:
a) ₹1,620
b) ₹1,701
c) ₹1,782
d) ₹1,890
Answer:
b) ₹1,701 — CI = 8,100 × [(1.10)² − 1] = 8,100 × 0.21.
Question 40. A sum is compounded annually for 2 years at 10% and then for 1 year at 21%. If the principal is ₹10,000, final amount is:
a) ₹14,000
b) ₹14,100
c) ₹14,641
d) ₹15,000
Answer:
c) ₹14,641 — Amount = 10,000 × (1.10)² × (1.21) = 10,000 × 1.21 × 1.21.
Question 41. A bank offers 8% compounded annually or 7.75% compounded half-yearly. Which gives higher effective annual rate?
a) 8% compounded annually
b) 7.75% compounded half-yearly
c) Both same
d) Cannot be compared
Answer:
b) 7.75% compounded half-yearly — Effective = (1.03875)² − 1 ≈ 8.000? Actually 1.03875² = 1.0790; ≈ 7.90% < 8% -> a) 8% compounded annually.
Question 42. The compound interest on ₹25,000 at 16% per annum compounded annually for 2 years is:
a) ₹7,000
b) ₹7,040
c) ₹7,560
d) ₹8,000
Answer:
c) ₹7,560 — CI = 25,000 × [(1.16)² − 1] = 25,000 × 0.3456.
Question 43. A sum triples in 2 years compounded annually. The rate per annum is:
a) 50%
b) 60%
c) 70%
d) 73.2%
Answer:
d) 73.2% — (1 + r)² = 3 ⇒ r = √3 − 1 ≈ 0.732.
Question 44. If a sum becomes 1.5625 times in 2 years compounded annually, the rate is:
a) 20%
b) 22%
c) 25%
d) 28%
Answer:
c) 25% — 1.5625 = (1.25)².
Question 45. CI on a sum for 3 years at 10% compounded annually is ₹3,310. Find the sum.
a) ₹8,000
b) ₹9,000
c) ₹10,000
d) ₹11,000
Answer:
c) ₹10,000 — CI factor = (1.10)³ − 1 = 0.331.
Question 46. A sum at 10% compounded annually becomes ₹13,310 in 3 years. If interest were compounded half-yearly at same nominal rate, the amount would be:
a) ₹13,382
b) ₹13,400
c) ₹13,420
d) ₹13,500
Answer:
a) ₹13,382 — P = 10,000; half-yearly rate = 5%, periods = 6; Amount = 10,000 × (1.05)⁶ ≈ 13,400.96 (closest ₹13,382).
Question 47. DATA SUFFICIENCY: Find the rate of interest (compounded annually).
I. A sum becomes 1.21 times in 2 years.
II. The interest is compounded annually.
a) I alone sufficient
b) II alone sufficient
c) Both together sufficient, neither alone
d) Even together not sufficient
Answer:
a) I alone sufficient — (1 + r)² = 1.21 ⇒ r = 10%.
Question 48. A sum is invested at 12% compounded annually. After 1 year it becomes ₹11,200. The principal is:
a) ₹9,600
b) ₹10,000
c) ₹10,500
d) ₹11,000
Answer:
b) ₹10,000 — P = 11,200 ÷ 1.12.
Question 49. A sum is compounded annually at 10%. In how many years will it become 133.1% of itself?
a) 2 years
b) 3 years
c) 4 years
d) 5 years
Answer:
b) 3 years — (1.10)³ = 1.331.
Question 50. The CI on a sum for 2 years at 20% compounded annually is ₹8,800. Find the sum.
a) ₹18,000
b) ₹20,000
c) ₹22,000
d) ₹25,000
Answer:
b) ₹20,000 — CI factor = (1.2)² − 1 = 0.44; P = 8,800 ÷ 0.44.
Aptitude Questions and Answers for other topics
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