Simple Interest & Compound Interest – Hard Level Questions – UGC NET Paper 1

Q1): Find the compound interest on ₹8,000 at 10% p.a. for 2 years, compounded half-yearly.
A) ₹1,680.00
B) ₹1,724.05
C) ₹1,760.00
D) ₹1,800.00

Answer: B) ₹1,724.05

Explanation:

  • Step 1: Half-yearly ⇒ rate per half-year = 10%/2 = 5%, periods = 2×2 = 4
  • Step 2: Formula: A = P(1 + r/100)^n
  • Step 3: Symbols: P = 8000, r = 5 (per half-year), n = 4
  • Step 4: A = 8000(1.05)^4 = 8000 × 1.21550625 = 9724.05
  • Final: CI = A − P = 9724.05 − 8000 = 1724.05, so option B is correct

Q2): Find the amount on ₹10,000 at 8% p.a. for 2 years, compounded quarterly (approx.).
A) ₹11,680.00
B) ₹11,716.59
C) ₹11,728.00
D) ₹11,760.00

Answer: B) ₹11,716.59

Explanation:

  • Step 1: Quarterly ⇒ rate per quarter = 8%/4 = 2%, periods = 2×4 = 8
  • Step 2: Formula: A = P(1 + r/100)^n
  • Step 3: Symbols: P = 10000, r = 2 (per quarter), n = 8
  • Step 4: A = 10000(1.02)^8 ≈ 10000 × 1.171659381 = 11716.59
  • Final: Amount ≈ ₹11,716.59, so option B is correct

Q3): A nominal rate is 12% p.a. compounded quarterly. The effective annual rate is:
A) 12.00%
B) 12.36%
C) 12.55%
D) 12.80%

Answer: C) 12.55%

Explanation:

  • Step 1: Quarterly ⇒ rate per quarter = 12%/4 = 3%, periods = 4
  • Step 2: Formula: Effective rate = (1 + r/100)^n − 1
  • Step 3: Symbols: r = 3 (per quarter), n = 4
  • Step 4: Effective rate = (1.03)^4 − 1 = 1.12550881 − 1 = 0.12550881
  • Final: Effective rate ≈ 12.55%, so option C is correct

Q4): The compound interest on a sum at 12% p.a. for 2 years (annual compounding) is ₹3,816. The principal is:
A) ₹12,000
B) ₹14,000
C) ₹15,000
D) ₹16,000

Answer: C) ₹15,000

Explanation:

  • Step 1: Formula: CI = P[(1 + R/100)^T − 1]
  • Step 2: Symbols: P = principal, R = 12, T = 2
  • Step 3: (1.12)^2 = 1.2544 ⇒ CI = P(1.2544 − 1) = 0.2544P
  • Step 4: 3816 = 0.2544P ⇒ P = 3816 / 0.2544 = 15000
  • Final: Principal = ₹15,000, so option C is correct

Q5): ₹10,000 becomes ₹13,225 in 2 years at compound interest (annual). The rate is:
A) 12%
B) 15%
C) 16%
D) 18%

Answer: B) 15%

Explanation:

  • Step 1: Formula: A = P(1 + R/100)^2
  • Step 2: Symbols: A = 13225, P = 10000, R = ?
  • Step 3: A/P = 13225/10000 = 1.3225 ⇒ (1 + R/100)^2 = 1.3225
  • Step 4: √1.3225 = 1.15 ⇒ 1 + R/100 = 1.15 ⇒ R = 15
  • Final: Rate = 15% p.a., so option B is correct

Q6): Find (CI − SI) on ₹20,000 at 5% p.a. for 3 years.
A) ₹150.00
B) ₹152.50
C) ₹156.25
D) ₹160.00

Answer: B) ₹152.50

Explanation:

  • Step 1: SI formula: SI = (P × R × T) / 100
  • Step 2: SI = (20000 × 5 × 3) / 100 = 3000
  • Step 3: CI amount: A = 20000(1.05)^3 = 20000 × 1.157625 = 23152.50
  • Step 4: CI = A − P = 23152.50 − 20000 = 3152.50
  • Final: CI − SI = 3152.50 − 3000 = 152.50, so option B is correct

Q7): Extra interest earned in 1 year on ₹20,000 at 12% p.a. when compounded half-yearly instead of annually is:
A) ₹60
B) ₹72
C) ₹84
D) ₹96

Answer: B) ₹72

Explanation:

  • Step 1: Annual interest (1 year): 20000 × 12/100 = 2400
  • Step 2: Half-yearly ⇒ 6% each half-year, 2 periods
  • Step 3: Amount factor = (1.06)^2 = 1.1236 ⇒ interest = 20000(1.1236 − 1) = 2472
  • Step 4: Extra interest = 2472 − 2400 = 72
  • Final: Extra = ₹72, so option B is correct

Q8): ₹10,000 is invested for 2 years. Option 1: 10% p.a. compounded annually. Option 2: 9.5% p.a. compounded half-yearly. Option 1 exceeds Option 2 by (approx.):
A) ₹50.29
B) ₹60.29
C) ₹70.29
D) ₹80.29

Answer: B) ₹60.29

Explanation:

  • Step 1: Option 1 amount = 10000(1.10)^2 = 12100
  • Step 2: Option 2: half-yearly ⇒ 9.5%/2 = 4.75% per half-year, periods = 4
  • Step 3: Option 2 amount = 10000(1.0475)^4 ≈ 12039.71
  • Step 4: Difference = 12100 − 12039.71 = 60.29 (approx.)
  • Final: Option 1 exceeds by about ₹60.29, so option B is correct

Q9): ₹8,000 becomes ₹9,261 in 3 years at compound interest (annual). The rate is:
A) 4%
B) 5%
C) 6%
D) 7%

Answer: B) 5%

Explanation:

  • Step 1: Formula: A = P(1 + R/100)^3
  • Step 2: Symbols: A = 9261, P = 8000, R = ?
  • Step 3: A/P = 9261/8000 = 1.157625 ⇒ (1 + R/100)^3 = 1.157625
  • Step 4: 1.157625 = (1.05)^3 ⇒ 1 + R/100 = 1.05 ⇒ R = 5
  • Final: Rate = 5% p.a., so option B is correct

Q10): ₹10,000 becomes ₹17,280 at 20% p.a. compound interest (annual). The time is:
A) 2 years
B) 3 years
C) 4 years
D) 5 years

Answer: B) 3 years

Explanation:

  • Step 1: Formula: A = P(1 + R/100)^T
  • Step 2: Symbols: A/P = 17280/10000 = 1.728, R = 20
  • Step 3: 1 + R/100 = 1.20, so we need (1.20)^T = 1.728
  • Step 4: (1.20)^3 = 1.728
  • Final: T = 3 years, so option B is correct

Q11): ₹10,000 is invested at CI with yearly rates 8%, 10%, and 12% for 3 years. The compound interest is:
A) ₹3,250.60
B) ₹3,305.60
C) ₹3,360.00
D) ₹3,405.60

Answer: B) ₹3,305.60

Explanation:

  • Step 1: Different yearly rates ⇒ A = P(1+r1)(1+r2)(1+r3)
  • Step 2: Symbols: P = 10000, r1 = 0.08, r2 = 0.10, r3 = 0.12
  • Step 3: A = 10000 × 1.08 × 1.10 × 1.12 = 10000 × 1.33056 = 13305.60
  • Step 4: CI = A − P = 13305.60 − 10000
  • Final: CI = ₹3,305.60, so option B is correct

Q12): Find the amount on ₹20,000 at 10% p.a. for 2 years 6 months (annual compounding).
A) ₹25,000
B) ₹25,210
C) ₹25,410
D) ₹25,620

Answer: C) ₹25,410

Explanation:

  • Step 1: For fractional time: compound for full years, then SI on the amount for remaining time
  • Step 2: After 2 years: A₂ = 20000(1.10)^2 = 20000 × 1.21 = 24200
  • Step 3: Remaining 6 months = 0.5 year ⇒ SI on 24200 = (24200 × 10 × 0.5)/100
  • Step 4: Extra interest = 1210 ⇒ Final amount = 24200 + 1210 = 25410
  • Final: Amount = ₹25,410, so option C is correct

Q13): On ₹10,000 at 8% p.a. for 1 year, quarterly compounding gives how much MORE interest than half-yearly compounding (approx.)?
A) ₹6.32
B) ₹8.32
C) ₹10.32
D) ₹12.32

Answer: B) ₹8.32

Explanation:

  • Step 1: Half-yearly ⇒ 4% per half-year, 2 periods ⇒ A₁ = 10000(1.04)^2 = 10816
  • Step 2: Half-yearly interest = 10816 − 10000 = 816
  • Step 3: Quarterly ⇒ 2% per quarter, 4 periods ⇒ A₂ = 10000(1.02)^4 = 10824.3216
  • Step 4: Quarterly interest = 824.3216; difference = 824.3216 − 816 = 8.3216
  • Final: Extra ≈ ₹8.32, so option B is correct

Q14): At 10% p.a. compounded half-yearly, the amount after 2 years is ₹12,155.06. The principal is (approx.):
A) ₹9,500
B) ₹10,000
C) ₹10,500
D) ₹11,000

Answer: B) ₹10,000

Explanation:

  • Step 1: Half-yearly ⇒ rate per half-year = 10%/2 = 5%, periods = 4
  • Step 2: Formula: A = P(1 + r/100)^n
  • Step 3: A = P(1.05)^4 = P × 1.21550625
  • Step 4: P = 12155.06 / 1.21550625 ≈ 10000
  • Final: Principal ≈ ₹10,000, so option B is correct

Q15): ₹10,000 becomes ₹10,824.32 in 1 year when interest is compounded quarterly. The nominal annual rate is:
A) 6%
B) 7%
C) 8%
D) 9%

Answer: C) 8%

Explanation:

  • Step 1: Quarterly compounding ⇒ A = P(1 + R/400)^4
  • Step 2: Symbols: P = 10000, A = 10824.32, R = nominal annual rate
  • Step 3: A/P = 10824.32/10000 = 1.082432 ⇒ (1 + R/400)^4 ≈ 1.082432
  • Step 4: 1.082432 = (1.02)^4 ⇒ 1 + R/400 = 1.02 ⇒ R/400 = 0.02 ⇒ R = 8
  • Final: Nominal rate = 8% p.a., so option C is correct

Q16): The compound interest on a sum at 5% p.a. for 3 years is ₹1,261. The principal is:
A) ₹7,000
B) ₹8,000
C) ₹9,000
D) ₹10,000

Answer: B) ₹8,000

Explanation:

  • Step 1: Formula: CI = P[(1 + R/100)^T − 1]
  • Step 2: Symbols: R = 5, T = 3 ⇒ (1.05)^3 = 1.157625
  • Step 3: CI = P(1.157625 − 1) = P × 0.157625
  • Step 4: 1261 = 0.157625P ⇒ P = 1261 / 0.157625 = 8000
  • Final: Principal = ₹8,000, so option B is correct

Q17): Under compound interest (annual), find the interest earned in the 3rd year on ₹10,000 at 10% p.a.
A) ₹1,000
B) ₹1,100
C) ₹1,210
D) ₹1,331

Answer: C) ₹1,210

Explanation:

  • Step 1: In CI, “interest of a year” = rate × amount at start of that year
  • Step 2: Amount after 2 years = 10000(1.10)^2 = 12100
  • Step 3: 3rd year interest = 10% of 12100 = (12100 × 10)/100
  • Step 4: 12100 × 0.10 = 1210
  • Final: Interest in 3rd year = ₹1,210, so option C is correct

Q18): CI for 1 year is ₹1,000 and CI for 2 years is ₹2,100 on the same principal at the same rate (annual compounding). The rate is:
A) 8%
B) 9%
C) 10%
D) 12%

Answer: C) 10%

Explanation:

  • Step 1: Let CI₁ = interest in 1st year = P×R/100 = 1000
  • Step 2: CI₂ (2 years) = P(2R/100 + R²/10000) = CI₁(2 + R/100)
  • Step 3: Given CI₂/CI₁ = 2100/1000 = 2.1
  • Step 4: 2.1 = 2 + R/100 ⇒ R/100 = 0.1 ⇒ R = 10
  • Final: Rate = 10% p.a., so option C is correct

Q19): Under compound interest (annual), the amount after 2 years is ₹22,050 and after 3 years is ₹23,152.50. The rate is:
A) 4%
B) 5%
C) 6%
D) 7%

Answer: B) 5%

Explanation:

  • Step 1: In CI, A₃ = A₂(1 + R/100)
  • Step 2: So, (1 + R/100) = A₃ / A₂ = 23152.50 / 22050
  • Step 3: 23152.50 / 22050 = 1.05
  • Step 4: 1 + R/100 = 1.05 ⇒ R/100 = 0.05 ⇒ R = 5
  • Final: Rate = 5% p.a., so option B is correct

Q20): For the same principal and same rate, SI for 3 years equals CI for 2 years (annual compounding). The rate is:
A) 50%
B) 75%
C) 100%
D) 125%

Answer: C) 100%

Explanation:

  • Step 1: SI (3 years): SI = (P × R × 3) / 100
  • Step 2: CI (2 years): CI = P[(1 + R/100)^2 − 1] = P(2R/100 + R²/10000)
  • Step 3: Set equal and cancel P: 3R/100 = 2R/100 + R²/10000
  • Step 4: R/100 = R²/10000 ⇒ multiply by 10000: 100R = R² ⇒ R = 100 (R ≠ 0)
  • Final: Rate = 100% p.a., so option C is correct

This Tutorial is Related to: Ci Vs Si, Effective Rate, Fractional Years, Half-Yearly Compounding, Hard Level, Interest In Nth Year, Present Value, Quarterly Compounding, Si Ci Mcqs, Simple Interest &Amp; Compound Interest, Simple Interest &Amp; Compound Interest Questions, Ugc Net Paper 1, Unit 5, Varying Rates

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