Compound Interest – Solved Problems with Explanation
Compound Interest is an important concept in finance and competitive mathematics. Unlike Simple Interest, interest is calculated on both the principal and the accumulated interest from previous periods.
This article provides multiple solved problems on Compound Interest with detailed, step-by-step explanations to help students master the topic.
Compound Interest Formula
Amount (A) = P × (1 + R/100)T
Compound Interest (CI) = Amount − Principal
- P = Principal
- R = Rate of interest per annum
- T = Time in years
Solved Compound Interest Problems
Problem 1: Find the compound interest on ₹10,000 at 10% per annum for 2 years.
Solution:
P = ₹10,000, R = 10%, T = 2 years
A = 10000 × (1 + 10/100)² = 10000 × (1.1)² = 10000 × 1.21 = ₹12,100
CI = A − P = 12,100 − 10,000 = ₹2,100
Compound Interest = ₹2,100
Problem 2: Find the amount after 3 years if ₹8,000 is compounded annually at 5%.
Solution:
A = 8000 × (1.05)³ = 8000 × 1.1576 = ₹9,261 (approx.)
Amount ≈ ₹9,261
Problem 3: Calculate the CI on ₹5,000 for 2 years at 8% per annum.
Solution:
A = 5000 × (1.08)² = 5000 × 1.1664 = ₹5,832
CI = 5832 − 5000 = ₹832
Compound Interest = ₹832
Problem 4: Find the principal if the amount becomes ₹13,310 in 3 years at 10% CI.
Solution:
A = ₹13,310, R = 10%, T = 3
P = A ÷ (1.1)³ = 13310 ÷ 1.331 = ₹10,000
Principal = ₹10,000
Problem 5: Find the CI on ₹16,000 at 10% per annum compounded half-yearly for 1 year.
Solution:
Rate per half-year = 10% ÷ 2 = 5% Time = 2 half-years
A = 16000 × (1.05)² = 16000 × 1.1025 = ₹17,640
CI = 17,640 − 16,000 = ₹1,640
Compound Interest = ₹1,640
Problem 6: Find the difference between CI and SI on ₹20,000 at 10% for 2 years.
Solution:
SI = (20000 × 10 × 2) ÷ 100 = ₹4,000
CI = 20000 × (1.1)² − 20000 = 24200 − 20000 = ₹4,200
Difference = 4,200 − 4,000 = ₹200
Difference = ₹200
Problem 7: At what rate will ₹4,000 become ₹4,840 in 2 years (CI)?
Solution:
A/P = 4840 ÷ 4000 = 1.21
(1 + R/100)² = 1.21 1 + R/100 = 1.1 R = 10%
Rate = 10% per annum
Problem 8: Find the CI earned if ₹6,250 becomes ₹7,562.50 in 2 years.
Solution:
CI = Amount − Principal = 7,562.50 − 6,250 = ₹1,312.50
Compound Interest = ₹1,312.50
Exam Tips
✔ Always identify compounding period
✔ Convert rate and time accordingly
✔ Use (1 + R/100)² shortcut for 2 years
Common Mistakes
- Forgetting to adjust rate for half-yearly compounding
- Mixing SI and CI formulas
- Calculation errors with powers
- Incorrect difference calculation
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