How to Calculate Compound Growth
Compound growth equals the starting value times (1 + g) raised to the number of periods: End value = Start × (1 + g)ⁿ.
The Compound Growth formula
Calculator
Enter a starting value, a growth rate and a number of periods to compound it forward year by year.
Real GDP, population or income at the beginning of the period.
Entered as a percent. The calculator converts it to the growth factor 1 + g.
How many times the value compounds, usually years.
Growing $500 at 4% for 5 periods leaves $608.33.
- Growth factor
- 1.216653
- Value under simple growth
- $600
- Extra from compounding
- $8.33
- Total growth over the period
- 21.67%
- Periods to double (rule of 70)
- 17.5
- Direction
- Compounding up
One plus the growth rate, raised to the number of periods.
What you would get applying the rate to the original value every period instead.
Compounding adds $8.33 over simple growth because each period builds on the last.
Seventy divided by the growth rate in percent, which needs a positive rate.
How to calculate Compound Growth, step by step
- 1Write down the starting value. The level of real GDP, population, or income at the beginning of the period.
- 2Convert the growth rate to a decimal. Divide the percent by 100, so 4% becomes 0.04, then add 1 to get the growth factor.
- 3Raise the factor to the number of periods. Compute (1 + g)ⁿ, where n counts how many periods the value compounds for.
- 4Multiply by the starting value. End value = Start × (1 + g)ⁿ, which exceeds simple growth because each period grows on top of the last.
- 5Reverse it to find the rate. Given the start and end values, average growth = (End ÷ Start) raised to the power (1 ÷ n), minus 1.
Worked example: Compound Growth
Real GDP starts at $500 billion and grows 4% per year for 5 years. Convert the rate: g = 0.04, so the growth factor is 1.04. Raise it: 1.04⁵ = 1.216653. Multiply: 500 × 1.216653 = $608.33 billion. Simple growth of 4% × 5 = 20% would give only $600 billion, so compounding adds $8.33 billion.
Compound Growth questions
How is compound growth different from simple growth?
Simple growth applies the rate to the original value every period, while compound growth applies it to the new, larger value each period. Over many periods compounding produces a noticeably bigger total.
How long does a value take to double?
Use the rule of 70: divide 70 by the annual growth rate in percent. At 4% per year a value doubles in about 70 ÷ 4 = 17.5 years.
How do you work backwards to the growth rate?
Divide the end value by the start value, raise that to the power 1 ÷ n, and subtract 1. For $500 billion growing to $608.33 billion over 5 years the result is 0.04, or 4%.
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