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Cumulative / Growth Rate DI

Introduction

In Cumulative / Growth Rate Data Interpretation (DI), data is presented across multiple years or time intervals, and your task is to calculate total growth, average growth, or the Compound Annual Growth Rate (CAGR). This pattern is crucial for understanding how values evolve over time, such as company revenue, population, or production output.

Pattern: Cumulative / Growth Rate DI

Pattern

The key idea is to compare initial and final values across years and compute either total or annualized growth.

  • Total Growth (%) = ((Final - Initial) ÷ Initial) × 100
  • Average Growth per Year = Total Growth ÷ Number of Years
  • CAGR = [(Final ÷ Initial)1/n - 1] × 100, where n is the number of years

Step-by-Step Example

Question

The table below shows the annual revenue (in ₹ crore) of a company from 2020 to 2023. Find the compound annual growth rate (CAGR) of revenue during this period.

YearRevenue (₹ crore)
2020200
2021230
2022250
2023270

Solution

  1. Step 1: Identify initial and final values:

    Initial (2020) = ₹200 crore; Final (2023) = ₹270 crore; n = 3 years.

  2. Step 2: Apply CAGR formula:

    CAGR = [(270 ÷ 200)1/3 - 1] × 100 = (1.351/3 - 1) × 100 ≈ (1.104 - 1) × 100 = 10.4%.

  3. Step 3: Interpret the result:

    The company’s revenue grew at an average rate of 10.4% per year between 2020 and 2023.

  4. Final Answer:

    CAGR = 10.4% per annum

  5. Quick Check:

    Using 10.4% growth: 200 × (1.104)3 = 200 × 1.35 = 270 ✅

Quick Variations

1. Calculate overall percentage growth between two years.

2. Compare CAGR of two companies or regions.

3. Predict a future value given constant annual growth.

4. Identify which entity has the highest cumulative growth rate.

Trick to Always Use

  • Step 1: Identify base year, final year, and number of years.
  • Step 2: Use the CAGR formula if growth is compounding over multiple years.
  • Step 3: Round the final result to 2 decimal places for neatness.

Summary

Summary

In the Cumulative / Growth Rate DI pattern:

  • Use Total Growth (%) = ((Final - Initial) ÷ Initial) × 100 for overall change.
  • Use CAGR = [(Final ÷ Initial)1/n - 1] × 100 for annualized growth.
  • Identify the correct time span (n) and check your final year carefully.
  • Always cross-verify with a reverse calculation for quick validation.

Practice

(1/5)
1.

Company A - Revenue Growth (₹ crore)

The table below shows Company A’s revenue over two years. Find the total percentage growth from 2020 to 2023.

YearRevenue (₹ crore)
2020400
2023520
easy
A. 30%
B. 25%
C. 20%
D. 35%

Solution

  1. Step 1: Identify base and final values:

    Initial = ₹400 crore; Final = ₹520 crore.

  2. Step 2: Apply total growth formula:

    Growth% = ((520 - 400) ÷ 400) × 100 = (120 ÷ 400) × 100 = .

  3. Final Answer:

    30% → Option A.

  4. Quick Check:

    400 × 1.3 = 520 ✅

Hint: Subtract base from final, divide by base, and multiply by 100.
Common Mistakes: Using 2023 as base instead of 2020.
2.

City Population Growth (lakh)

The line chart shows population growth from 2016 to 2020. Find the average annual growth rate (simple growth per year).

YearPopulation (lakh)
201612
202015
easy
A. 6.25%
B. 7%
C. 7.5%
D. 8%

Solution

  1. Step 1: Compute total growth:

    Growth = 15 - 12 = 3; Total growth% = (3 ÷ 12) × 100 = 25%.

  2. Step 2: Divide by number of years:

    Years = 4 → Average = 25 ÷ 4 = .

  3. Final Answer:

    6.25% → Option A.

  4. Quick Check:

    6.25 × 4 = 25 ✅

Hint: Total growth ÷ number of years = annual growth.
Common Mistakes: Using CAGR instead of simple average growth.
3.

Firm X - Profit CAGR (₹ crore)

The bar graph shows Firm X’s profit growth. Find CAGR between 2018 and 2021.

YearProfit (₹ crore)
201810
202113.31
easy
A. 8%
B. 10%
C. 12%
D. 11%

Solution

  1. Step 1: Identify data:

    Initial = 10, Final = 13.31, n = 3.

  2. Step 2: Apply CAGR formula:

    CAGR = [(13.31 ÷ 10)1/3 - 1] × 100 = (1.3311/3 - 1) × 100 = (1.10 - 1) × 100 = .

  3. Final Answer:

    10% → Option B.

  4. Quick Check:

    10 × (1.10)3 = 13.31 ✅

Hint: Use CAGR when compounding over multiple years.
Common Mistakes: Using total growth ÷ years instead of CAGR formula.
4.

Exports Growth by Product (₹ crore)

The table shows export data for two products in two years. Which had the higher percentage growth?

Product20192022
P800960
Q600750
medium
A. Product P
B. Both equal
C. Product Q
D. Cannot determine

Solution

  1. Step 1: Calculate percentage growth:

    P: ((960 - 800) ÷ 800) × 100 = 20%.
    Q: ((750 - 600) ÷ 600) × 100 = 25%.

  2. Step 2: Compare:

    Q grew by 25%, higher than P (20%).

  3. Final Answer:

    → Option C.

  4. Quick Check:

    600 × 1.25 = 750 ✅

Hint: Compare growth% not absolute increase.
Common Mistakes: Judging by absolute numbers instead of percentages.
5.

Manufacturing Output Projection (₹ lakh)

The chart shows expected annual growth at 8% for a company starting at ₹250 lakh in 2019. Estimate its output after 3 years.

YearGrowth Rate
2019Base: ₹250 lakh
20228% p.a. compounded
medium
A. ₹310 lakh
B. ₹315 lakh
C. ₹315.8 lakh
D. ₹314.9 lakh

Solution

  1. Step 1: Use compound formula:

    Future Value = Present × (1 + r)n = 250 × (1.08)3.

  2. Step 2: Compute:

    (1.08)3 = 1.259712 → 250 × 1.259712 = ≈ ₹314.9 lakh.

  3. Final Answer:

    ₹314.9 lakh → Option D.

  4. Quick Check:

    8% compounded over 3 years ≈ 25.97% overall → 250 × 1.2597 ≈ 314.9 ✅

Hint: Use compound growth formula: Present × (1 + r)^n.
Common Mistakes: Adding simple 8% × 3 instead of compounding.

Mock Test

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