# The Rule of 72 and the Power of the Double (aka Compounding)

## Dec 1, 2022

Use these quick calculations to determine your savings at a future date… • Existing savings balance
• Investment rate of return (expected)
• Long-term inflation rate (estimated)
• #years your savings can grow

In this post, I’ll walk you through an example.

In doing so, I’ll introduce you to the Rule of 72, how to calculate real rate of return, how doubling simplifies the compounding calculation and sensitivity analysis (as a bonus).

We’ll use these values:

• Existing savings: \$1.75M
• Investment rate of return: 12%
• Inflation rate: 4%
• #years to grow: 45 years

## The Rule of 72

The Rule of 72 is a “back of the envelope” approximation used to estimate the years required to double an amount of money at a given rate of return.

The rule: 72 / “rate of return” = “# years to double”.

Using my #s: 72 / 12 = 6 years to double.

That sounds great. But six years isn’t realistic.

We need to adjust the 12% rate, which is a nominal rate.

## Calculating Real Rate of Return

The real rate of return is the annual percentage of profit earned on an investment, adjusted for inflation. The real return rate indicates money’s actual purchasing power over time.

Nominal means that a dollar now is worth a dollar later (years later)…

Given the inflation of late, we can understand why this isn’t realistic. A dollar six years from now won’t buy as much.

So, to account for inflation, we need to use the “real” rate of return. We take the “rate of return” from above and subtract the inflation rate.

For nearly 40 years, inflation hovered near 2%. Right now, it is around 8%.

Many experts believe it will settle around 4% over the long term.

72 / (12 nominal rate - 4 inflation rate) or 72 / 8 = 9 years to double.

Therefore…

The Tactical Asset Allocation (TAA) model I follow doubles my money in real purchasing power every 9 years, assuming a 4% inflation rate.

## Power of the Double

The compounded return is the rate of return of an investment over a cumulative series of time. Doubling is a single case of the compound return equation: An initial investment is multiplied by 2 raised to the power of the number of doubles. Such as: \$1,000 investment x (2)^5 doubles.

I’m 46 years old, almost 47. I’m also an optimist and expect to live to at least 92.

In that case, I expect to get another:

92 - 47 = 45 years of life.

45 / 9 years to double = 5 more doubles.

Starting with savings of \$1.75M:

\$1.75M x 2 x 2 x 2 x 2 x 2 = \$56M in real terms, at age 92.

I’ll take it.

## Pressure-Testing the Outcome

Sensitivity analysis determines how different values of an independent variable affect a particular dependent variable under a given set of assumptions.

In this case, I’ll vary the real rate of return to see its impact on my savings growth.

But first…

What is absolutely necessary to make the \$56M outcome possible?

• I need at least a 12% annual return (nominal). This is where my Fast Follow Investor.com TAA strategy comes in.
• I need at most a 4% long-term inflation rate. I must count on the Federal Reserve to help control this!

What happens if my 8% real return drops to 6%?

Perhaps my nominal return comes in at 11% with a long-term inflation rate of 5% (11-5 = 6).

Adjusting the real return from 8% to 6% increases a 9-year double to a 12-year double.

45 / 12 = 3.75 doubles.

3.75 doubles reduce my savings at age 92 from \$56M to \$23.5M.

It’s certainly less, but I’ll still take it.

## So, in Summary

• Investment return minus inflation rate = real return
• 72 / real return = # years to double
• Remaining years of life / # years to double = # of doubles
• Existing savings x 2^(# of doubles) gives you your savings target, in real dollars 