What it means
The difference between simple and compound growth is what happens to each year's return. Under simple interest the return is calculated on the starting sum every year, so growth is a straight line.
Under compounding the return is calculated on the balance as it stands, so each year starts from a slightly higher base and the curve steepens. Time is the dominant variable, far more than the rate.
Doubling the return rate helps, but doubling the number of years usually helps much more, because the later years are the ones working on the largest balance. This is why financial advisers press so hard on starting early: the first decade of contributions typically produces less than the last decade of growth.
Frequency matters too, though less than people assume. Interest can compound annually, quarterly, monthly or daily, and more frequent compounding produces a slightly higher effective rate than the headline nominal rate suggests.
The annual equivalent rate exists precisely so that products with different compounding frequencies can be compared honestly. Compounding is not confined to interest.
Reinvested dividends, retained profits reinvested in a business, recurring revenue that grows on top of a retained base and even the improvement rate of an operational process all behave the same way. A 2% weekly improvement and a 2% weekly decline diverge dramatically over a year for identical mathematical reasons.
The mirror image is where compounding does the most damage to households and companies. Credit card balances, unpaid tax and rolled-up interest on deferred loans all grow on the same curve, which is why a small balance ignored for long enough becomes a large one.
Understanding the mechanism is what makes the case for paying down high-rate debt before chasing investment returns.
In practice
Real-world examples
Example 1
An employee starts contributing $400 a month to a pension at 25 rather than 35. Assuming the same average return, the ten extra years of compounding leave her retirement pot far larger than a colleague who contributes the same monthly amount for a decade less.
Example 2
A profitable engineering firm retains all its earnings for six years and reinvests them in machinery and staff. Because each year's profit is earned on a larger asset base than the last, revenue growth accelerates even though the growth rate stays broadly constant.
Example 3
A household carries $6,000 on a credit card at 22% a year and makes only minimum payments. Interest is charged on a balance that barely falls, so after three years the amount owed has grown despite payments being made every month.
Think of it
Compounding is like rolling a snowball down a snowy hill. It starts small, but as it rolls, it picks up more snow, getting larger and faster with every single rotation.
Formula
Calculation
Future value = present value x (1 + rate)^number of periods.
Take $10,000 invested at 8% a year for 10 years with all returns reinvested. After year one the balance is $10,000 x 1.08 = $10,800. After year two it is $10,800 x 1.08 = $11,664, and after year three it is $11,664 x 1.08 = $12,597.12.
Carried through all ten years, the calculation is $10,000 x 1.08^10. Since 1.08^10 = 2.15892, the future value is $10,000 x 2.15892 = $21,589.25.
Simple interest at the same rate would have paid $800 a year for ten years, giving $10,000 + $8,000 = $18,000. The extra $21,589.25 - $18,000 = $3,589.25 is the value created purely by returns earning returns.Case study
Seen in the real world
In this illustrative and fictional example, the founders of Ashcombe Tools faced a choice each year: take profits out as dividends or reinvest them. For the first four years they took most of the profit out, reasoning that $180,000 a year was worth more in hand than in the business.
A new finance director modelled both paths over ten years. Reinvesting profit into capacity had historically produced a return of roughly 14% inside the business, while the founders' alternative savings were earning around 4%, and compounded over a decade that gap became the difference between a business worth a few million and one worth considerably more.
The founders changed policy, retaining two thirds of profit for six years before returning to larger distributions. The company later described the decision as the least exciting and most valuable one it ever made, since nothing about the business changed except where the profit went.
Watch out
Common mistakes
- Confusing simple and compound interest and assuming a 10% return over five years simply means 50%, which understates the real figure.
- Comparing two savings or loan products by their headline rates when they compound at different frequencies and therefore have different effective rates.
- Focusing on chasing a slightly higher rate while ignoring the far larger effect of starting earlier or leaving the money invested longer.
Questions
People also ask
What is the rule of 72?
Dividing 72 by the annual percentage return gives a rough number of years for money to double, so 8% takes about nine years.
Does compounding still help if returns are volatile?
Yes, but volatility reduces the compounded outcome relative to a steady average, which is why a smooth 7% beats an alternating 20% gain and 6% loss over long periods.
How does compounding apply to debt?
Identically, but against you; unpaid interest is added to the balance and then attracts interest itself, so balances grow faster the longer they are left.