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Basic CI Formula Application

Introduction

Compound Interest (CI) is one of the most commonly asked topics in aptitude exams. It represents how money grows when interest is added not only on the original amount (principal) but also on the interest earned over time. Understanding the basic formula helps you solve any CI problem quickly and accurately.

Pattern: Basic CI Formula Application

Pattern

The key concept is: Compound Interest is calculated on both the principal and accumulated interest.

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

Where:
P = Principal amount, R = Rate of interest per annum, T = Time in years.

Step-by-Step Example

Question

Find the compound interest on ₹5,000 at 8% per annum for 3 years.

Solution

  1. Step 1: Identify the given values

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

  2. Step 2: Apply the formula for Amount

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

  3. Step 3: Compute the value

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

  4. Step 4: Find the Compound Interest

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

  5. Final Answer:

    Compound Interest = ₹1,298.50

  6. Quick Check:

    After 1 year → ₹5,400; after 2 years → ₹5,832; after 3 years → ₹6,298.50 ✅

Quick Variations

1. Sometimes you may be asked to find the Total Amount instead of CI (use A directly).

2. For different compounding frequencies (half-yearly, quarterly), divide R and T accordingly.

3. CI formula applies to any currency or percentage value - the concept remains the same.

Trick to Always Use

  • Step 1: Identify P, R, and T clearly from the question.
  • Step 2: Use A = P(1 + R/100)T for annual compounding.
  • Step 3: Subtract Principal from Amount to get CI.
  • Step 4: Cross-check by applying successive percentage increases for small T values.

Summary

Summary

In the Basic CI Formula Application pattern:

  • Amount = P(1 + R/100)T is the core formula.
  • Compound Interest = Amount - Principal.
  • Used for annual compounding unless stated otherwise.
  • Always double-check by successive year growth for short time periods.

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.

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