EconixaECONOMICS FUNDAMENTALS

Interactive calculator

Rule of 72 Calculator

The rule of 72 is a quick approximation: years to double ~ 72 / growth rate. At 6% growth, doubling takes about 12 years. Enter any growth or interest rate to get the estimated doubling time — and see how close the approximation is to the exact logarithm. In this release this page is powered by the closest available interactive widget; a dedicated widget for this topic is planned.

Spending Multiplier Calculator

k = 1 ÷ (1 − MPC), then ΔY = k × ΔG

Multiplier k = 5.000
Total GDP change ΔY = 500.00
Steps
  1. Marginal propensity to save: MPS = 1 − MPC = 1 − 0.80 = 0.20
  2. Multiplier: k = 1 ÷ MPS = 1 ÷ 0.20 = 5.000
  3. Total change: ΔY = k × ΔG = 5.000 × 100.00 = 500.00
  4. Round by round (each round respent at rate MPC): R1 = 100.00 → R2 = 80.00 → R3 = 64.00 → R4 = 51.20 → R5 = 40.96 → … converging to 500.00.
Why it works

The first round adds ΔG to GDP. A share MPC of that income is respent, adding MPC × ΔG, then MPC² × ΔG, and so on. This geometric series sums to ΔG × (1 + MPC + MPC² + …) = ΔG ÷ (1 − MPC).

How to use it

  1. Enter the annual growth or interest rate.

  2. Read the estimated years to double.

  3. Compare with the exact doubling time shown.

What you will learn

  • Apply the rule of 72.
  • Explain why it is an approximation.
  • Use it for quick mental estimates.