Annual & Half-Yearly Calculations (CI / Amount)
SSC GD Exam Preparation - Quantitative Aptitude
This chapter teaches how to compute Compound Interest (CI) when interest is added annually or half-yearly.
🔹 1. Annual (Yearly) Compounding
Interest is added once every year.
Formula:
A = P(1 + R/100)T
Where:
P = Principal
R = Rate (%) per annum
T = Time (in years)
Example:
Find CI on ₹2000 at 10% for 2 years (annual).
A = 2000(1.10)² = 2000 × 1.21 = ₹2420
CI = 2420 − 2000 = ₹420
🔹 2. Half-Yearly Compounding
Interest is compounded two times in a year.
Adjustments:
| Element | Annual | Half-Yearly |
|---|---|---|
| Rate | R | R/2 |
| Time | T | 2T |
Formula:
A = P(1 + R/200)2T
Example:
Find CI on ₹2000 at 10% for 1 year (half-yearly).
• Rate = 10/2 = 5%
• Time = 2 periods
A = 2000(1.05)² = 2000 × 1.1025 = ₹2205
CI = 2205 − 2000 = ₹205
👉 CI (half-yearly) > CI (annual) because compounding happens more times.
🔹 3. Comparison Table
| Basis | Annual Compounding | Half-Yearly Compounding |
|---|---|---|
| Interest added | Once per year | Twice per year |
| Growth speed | Slower | Faster |
| Interest amount | Less | More |
| Formula | A = P(1 + R/100)T | A = P(1 + R/200)2T |
🔹 4. Quick Trick (Shortcut)
For 1 year CI (Half-Yearly)
CI = SI + (SI × R) / 200
Example:
P = 5000, R = 12%, T = 1
SI = 600
Extra = SI×R/200 = 600×12/200 = 36
CI = 600 + 36 = 636
🧠 Practice Section: 15 Questions (With Answers)
Each Q followed by its Answer (SSC style). Click on "View Answer" to check your understanding.
Q1. Find amount on ₹5000 at 10% for 2 years (annual).
View Answer
A = 5000 × 1.21 = ₹6050
Q2. CI for above question.
View Answer
CI = 6050 − 5000 = ₹1050
Q3. Find CI on ₹4000 at 8% for 2 years (half-yearly).
View Answer
Rate = 4%, Time = 4 periods, A = 4000 × (1.04)⁴ = ₹4864.86, CI ≈ ₹864.86
Q4. A = ? when P=3000, R=6%, T=3 years (annual).
View Answer
A = 3000 × (1.06)³ = ₹3573.05
Q5. CI for above question.
View Answer
CI = 3573.05 − 3000 = ₹573.05
Q6. CI on ₹1000 at 20% for 1 year (half-yearly).
View Answer
Rate = 10%, Time = 2, A = 1000 × (1.10)² = ₹1210, CI = ₹210
Q7. Amount on ₹8000 at 5% for 3 years (annual).
View Answer
A = 8000 × (1.05)³ = ₹9261
Q8. Find CI difference between annual & half-yearly for 10% on ₹5000 (1 year).
View Answer
Annual CI = 500, Half-yearly CI = 525, Difference = ₹25
Q9. Half-yearly amount for ₹6000 at 12% for 1 year.
View Answer
Rate = 6%, Time = 2, A = 6000 × (1.06)² = ₹6732
Q10. CI on ₹2500 at 4% for 2 years (annual).
View Answer
A = 2500 × 1.0816 = ₹2704, CI = ₹204
Q11. CI on ₹1500 at 8% for 6 months (half-yearly).
View Answer
One half-year only → Rate = 4%, A = 1500 × 1.04 = ₹1560, CI = ₹60
Q12. Annual CI on ₹10000 at 5% for 1 year.
View Answer
A = 10000 × 1.05 = ₹10500, CI = ₹500
Q13. Half-yearly CI on ₹10000 at 5% for 1 year.
View Answer
Rate = 2.5%, Time = 2, A = 10000(1.025)² = ₹10506.25, CI = ₹506.25
Q14. Find CI on ₹2000 for 2 years at 10% (half-yearly).
View Answer
Rate = 5%, Time = 4, A = 2000(1.05)⁴ = ₹2431.01, CI ≈ ₹431.01
Q15. Which is bigger — annual CI or half-yearly CI?
View Answer
Half-Yearly CI is always higher.
✅ SSC GD Exam Strategy
🟢 Remember rate and time adjustments for half-yearly compounding
🟢 Practice quick calculations for different compounding periods
🟢 Master the shortcut formula for 1-year half-yearly CI
🟢 Understand that more frequent compounding = higher interest
🟢 Time yourself - aim for 45-60 seconds per compounding question
You've completed Annual & Half-Yearly Calculations!
SSC GD Tip: Understanding different compounding periods is crucial for solving compound interest problems efficiently. Remember that half-yearly compounding gives higher returns than annual compounding due to more frequent interest calculations. Practice the rate and time adjustments (R/2 and 2T for half-yearly) until they become second nature. The shortcut formula for 1-year half-yearly CI can save valuable time in exams. Regular practice with previous year SSC GD questions will build your speed and accuracy in solving these problems.
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