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Basic CI Formula Application

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Introduction

Compound Interest (CI) aptitude exams में सबसे ज़्यादा पूछे जाने वाले topics में से एक है। यह बताता है कि पैसा कैसे बढ़ता है जब ब्याज न सिर्फ़ original amount (principal) पर, बल्कि समय-समय पर जुड़े हुए interest पर भी लगाया जाता है। Basic formula समझने से आप किसी भी CI problem को जल्दी और accurately solve कर सकते हैं।

Pattern: Basic CI Formula Application

Pattern: Basic CI Formula Application

मुख्य concept यह है: Compound Interest principal और accumulated interest - दोनों पर लगता है।

Main formulas:
Amount (A) = P × (1 + R/100)T
Compound Interest (CI) = A - P

जहाँ:
P = Principal amount, R = प्रति वर्ष ब्याज दर, T = समय (सालों में)।

Step-by-Step Example

Question

₹5,000 पर 8% प्रति वर्ष की दर से 3 साल के लिए compound interest निकालें।

Solution

  1. Step 1: Given values पहचानें

    Principal (P) = ₹5,000, Rate (R) = 8%, Time (T) = 3 years.

  2. Step 2: Amount का formula लगाएँ

    A = P × (1 + R/100)T
    = 5,000 × (1 + 8/100)3
    = 5,000 × (1.08)3

  3. Step 3: Value calculate करें

    (1.08)3 = 1.2597
    A = 5,000 × 1.2597 = ₹6,298.50

  4. Step 4: Compound Interest निकालें

    CI = A - P = 6,298.50 - 5,000 = ₹1,298.50

  5. Final Answer:

    Compound Interest = ₹1,298.50

  6. Quick Check:

    1 साल बाद → ₹5,400; 2 साल बाद → ₹5,832; 3 साल बाद → ₹6,298.50 ✅

Quick Variations

1. कभी-कभी आपको Total Amount निकालने को कहा जाता है - ऐसे में सीधे A निकालें।

2. अगर compounding half-yearly या quarterly हो तो R और T को उसी हिसाब से adjust करें।

3. CI किसी भी currency या percentage पर लागू होता है - concept हमेशा same रहता है।

Trick to Always Use

  • Step 1: Question से P, R और T सही से पहचानें।
  • Step 2: Annual compounding के लिए A = P(1 + R/100)T formula लगाएँ।
  • Step 3: Amount में से Principal घटाकर CI निकालें।
  • Step 4: छोटे T के लिए successive percentage increase से cross-check कर लें।

Summary

Basic CI Formula Application pattern में:

  • Amount = P(1 + R/100)T मुख्य formula है।
  • Compound Interest = Amount - Principal।
  • जब तक कुछ और न कहा जाए, annual compounding ही मानें।
  • Short time period वाले questions में तेजी से check करने के लिए successive year growth देखें।

Practice

(1/5)
1. Find the compound interest on ₹8,000 at 10% per annum for 2 years.
easy
A. ₹1,680.00
B. ₹1,600.00
C. ₹1,700.00
D. ₹1,800.00

Solution

  1. Step 1: Identify given values

    P = ₹8,000, R = 10% p.a., T = 2 years.

  2. Step 2: Apply formula for Amount

    A = P × (1 + R/100)^T = 8,000 × (1 + 10/100)^2 = 8,000 × (1.1)^2.

  3. Step 3: Compute

    (1.1)^2 = 1.21 → A = 8,000 × 1.21 = ₹9,680.00.

  4. Final Answer:

    CI = A - P = 9,680.00 - 8,000.00 = ₹1,680.00 → Option A.

  5. Quick Check:

    Year 1 interest = 10% of 8,000 = 800; principal for year 2 = 8,800; year 2 interest = 10% of 8,800 = 880; total interest = 800 + 880 = ₹1,680.00 ✅
Hint: Compute A = P(1 + R/100)^T, then subtract P to get CI.
Common Mistakes: Using SI formula (P×R×T/100) instead of compounding year-by-year.
2. What will be the compound interest on ₹10,000 at 5% per annum for 2 years?
easy
A. ₹1,050.00
B. ₹1,025.00
C. ₹1,000.00
D. ₹1,100.00

Solution

  1. Step 1: Identify given values

    P = ₹10,000, R = 5% p.a., T = 2 years.

  2. Step 2: Apply CI formula

    A = 10,000 × (1 + 5/100)^2 = 10,000 × (1.05)^2.

  3. Step 3: Compute

    (1.05)^2 = 1.1025 → A = 10,000 × 1.1025 = ₹11,025.00.

  4. Final Answer:

    CI = A - P = 11,025.00 - 10,000.00 = ₹1,025.00 → Option B.

  5. Quick Check:

    10,000 → 10,500 (after 1 year) → 11,025 (after 2 years) → CI = 11,025 - 10,000 = ₹1,025.00 ✅
Hint: Raise (1 + R/100) to T first, then multiply by P for A.
Common Mistakes: Rounding intermediate values too early; leads to small errors.
3. Find the compound interest on ₹6,000 at 12% per annum for 2 years.
easy
A. ₹1,440.20
B. ₹1,500.60
C. ₹1,526.40
D. ₹1,520.80

Solution

  1. Step 1: Identify given values

    P = ₹6,000, R = 12% p.a., T = 2 years.

  2. Step 2: Apply CI formula

    A = 6,000 × (1 + 12/100)^2 = 6,000 × (1.12)^2.

  3. Step 3: Compute

    (1.12)^2 = 1.2544 → A = 6,000 × 1.2544 = ₹7,526.40 → CI = 7,526.40 - 6,000.00 = ₹1,526.40.

  4. Final Answer:

    Compound Interest = ₹1,526.40 → Option C.

  5. Quick Check:

    Year 1 interest = 12% of 6,000 = 720 → principal becomes 6,720; Year 2 interest = 12% of 6,720 = 806.40; total interest = 720 + 806.40 = ₹1,526.40 ✅
Hint: Compute year-by-year interest if powers are hard; add yearly interests to confirm.
Common Mistakes: Forgetting to include the first year's interest when calculating the second year's base.
4. Find the compound interest on ₹15,000 at 9% per annum for 3 years.
medium
A. ₹4,425.44
B. ₹4,185.44
C. ₹4,167.44
D. ₹4,050.44

Solution

  1. Step 1: Identify given values

    P = ₹15,000, R = 9% p.a., T = 3 years.

  2. Step 2: Apply CI formula

    A = 15,000 × (1 + 9/100)^3 = 15,000 × (1.09)^3.

  3. Step 3: Compute

    (1.09)^2 = 1.1881; (1.09)^3 = 1.1881 × 1.09 = 1.295029 → A = 15,000 × 1.295029 ≈ ₹19,425.44 → CI = 19,425.44 - 15,000.00 = ₹4,425.44.

  4. Final Answer:

    Compound Interest = ₹4,425.44 → Option A.

  5. Quick Check:

    Year-wise: 15,000 → 16,350.00 → 17,811.50 → 19,425.44; CI = 19,425.44 - 15,000 = ₹4,425.44 ✅
Hint: Use (1 + R/100)^3 values remembered or compute sequentially: multiply by (1 + R/100) three times.
Common Mistakes: Using truncated values for (1 + R/100)^3 too early, causing small rounding errors.
5. The compound interest on ₹20,000 at 10% per annum for 3 years will be approximately:
medium
A. ₹6,100.00
B. ₹6,200.00
C. ₹6,300.00
D. ₹6,620.00

Solution

  1. Step 1: Identify given values

    P = ₹20,000, R = 10% p.a., T = 3 years.

  2. Step 2: Apply formula for Amount

    A = 20,000 × (1 + 10/100)^3 = 20,000 × (1.1)^3.

  3. Step 3: Compute

    (1.1)^2 = 1.21; (1.1)^3 = 1.331 → A = 20,000 × 1.331 = ₹26,620.00 → CI = 26,620.00 - 20,000.00 = ₹6,620.00.

  4. Final Answer:

    Compound Interest = ₹6,620.00 → Option D.

  5. Quick Check:

    Successive amounts: 20,000 → 22,000 → 24,200 → 26,620; CI = 26,620 - 20,000 = ₹6,620.00 ✅
Hint: Use successive multiplication by (1 + R/100) for each year to avoid power calculations if needed.
Common Mistakes: Using simple interest formula or stopping compounding one year early.