APR (Annual percentage rate)

Understanding exponential (percentage-based) growth can be easier with this neat formula. This formula helps you determine the Doubling Time, which is how long it takes for an initial quantity to double at a given percentage growth rate.

In simpler terms: If you borrow $100 at a 10% interest rate, this formula will tell you how long it will take for your debt to grow from $100 to $200 (assuming you make no payments). This same formula can also be applied to investments to see how long it will take for your investment to double.

Here’s how it works:

Take the number 70, divide it by the percentage growth rate per unit time, and you'll get the doubling time. Reference - Dr. Albert A. Bartlett (Professor Emeritus, Department of Physics)

Examples:

• 7% APR
  • 70 / 7 = 10
  • This means the quantity will double every 10 years.
• 10% APR
  • 70 / 10 = 7
  • For instance, if you borrow $100 at 10% interest, it will become $200 in 7 years.
• 20% APR
  • 70 / 20 = 3.5
  • This means the quantity will double every 3.5 years. For example, starting with $1,000 in debt at 20% APR:
    • Year 0: $1,000
    • Year 3.5: $2,000
    • Year 7: $4,000
    • Year 10.5: $8,000
    • Year 14: $16,000
    • Year 17.5: $32,000

This formula is very useful for understanding both the growth of debt and the growth of investments.