Compounding
In short
Compounding happens when what you gain is added to the base and then earns gains of its own. The classic example is interest on interest. The result is exponential growth: slow at first, then accelerating. The psychological problem is that our intuition treats it as linear growth. Research shows that people systematically underestimate exponential growth, sometimes enormously, and that this shapes their decisions about saving and debt.
What it says
How it works. McKenzie and Liersch (2011) give a simple example. You deposit $1,000 at the start of each year, at 7% interest compounded annually. After three years you have $3,440: the first $1,000 has grown to $1,225, the next to $1,145, the last to $1,070. The total is almost 15%, not 7%, above what you deposited, because each year you earn interest on the earlier interest too. After 40 years you have deposited $40,000 but have $213,610 in the account, more than five times as much.
Intuition linearizes. Wagenaar and Sagaria (1975) showed participants numerical series and graphs that grew exponentially and asked them to extrapolate. Growth was grossly underestimated. The authors write that it was not unusual for two-thirds of participants to give estimates below 10% of the correct value. The effect was larger the faster the growth. Neither special instructions about exponential growth nor daily experience with growth processes improved the estimates.
The cost in money. Stango and Zinman (2009) call the phenomenon exponential growth bias, the tendency to linearize an exponential function when judging it intuitively. They show that this tendency explains why people underestimate the interest rate on a loan and the future value of an investment. More-biased households borrow more, save less and use financial advice more, even after accounting for many other household characteristics. The authors write that their measure does not seem to be merely a stand-in for financial sophistication in general.
The cost of waiting. McKenzie and Liersch (2011) showed the same thing for long-term saving:
- Experiment 1. Students estimated how much they would accumulate by depositing $400 a month at 10% a year for 40 years. Typical answers grew linearly. After 40 years, the median estimate was below 10% of the correct value, more than $2 million short. On average, 90% of participants underestimated.
- Experiment 2. Alan saves $100 a month for 40 years. Bill starts 20 years later. More than half of participants thought Bill would need twice as much, $200 a month, to catch up. In reality he would need $773 a month, nearly eight times as much. Responses were practically the same among participants who showed they understood compound interest.
- Experiments 3–5. When shown directly how savings grow exponentially, both students and employees of a large company said they wanted to save more.
Example
McKenzie and Liersch’s example of Alan and Bill is the clearest. Both retire in 40 years, and interest is 10% a year. Alan puts aside $100 a month starting today. Bill waits 20 years. Intuitively, it seems Bill can make up for it by doubling the amount. In fact, Alan’s first 20 years had the most time to grow, and Bill would have to deposit nearly eight times as much each month to reach the same total.
How to apply it
The suggestions below extrapolate from the studies cited. The first two rest directly on them. The third is an analogy we propose.
- Don’t estimate in your head; calculate. Studies show that intuition systematically underestimates, and that merely understanding the formula did not help (McKenzie and Liersch, 2011). Use a compound interest calculator when comparing savings, a loan or an investment.
- Look at the curve, not today’s figure. In McKenzie and Liersch’s experiments, seeing how the amount grows over time made people want to save more. When you make a plan, draw or ask for the 20–40 year graph.
- Ask the same question about debt. Compounding works against you too. Stango and Zinman (2009) found that people who linearize more borrow more.
- Look for processes that build on themselves. An analogy, not a research finding: some things in life work partly like compound interest, for example a skill that helps you learn the next one faster. In such cases, starting early matters more than it seems.
Limits and nuances
- The studies are mostly about estimates. Wagenaar and Sagaria (1975) and McKenzie and Liersch (2011) used estimation tasks, and McKenzie and Liersch worked mostly with students. Stango and Zinman (2009) use observational data on households, so the links they found are associations, not causal effects shown by experiment.
- Intention is not behaviour. In the experiment with employees, McKenzie and Liersch measured how interested people were in saving more, not how much they actually saved afterwards.
- Returns are not guaranteed. The examples use a fixed rate (7%, 10%). Real investments have variable returns, inflation and costs. Compounding works on the real return, not the one in the example.
- Exponential growth does not last forever. Outside interest, few processes grow at a constant rate indefinitely. Extending the idea to habits or careers is a useful metaphor, not a law.
- It is not the same as “marginal gains”. The idea of marginal gains (many small improvements, in many areas at once) is related but different. Compounding is growth on growth over time. Marginal gains are small improvements added up. The popular formula “1% better every day, 37 times better in a year” (1.01 to the power of 365 ≈ 37.8) combines them, assuming that each improvement applies on top of all the earlier ones, without limit. It is a correct calculation built on an unproven assumption, not a research finding.
Sources
- Willem A. Wagenaar, Sabato D. Sagaria (1975). Misperception of exponential growth
- Victor Stango, Jonathan Zinman (2009). Exponential Growth Bias and Household Finance
- Craig R. M. McKenzie, Michael J. Liersch (2011). Misunderstanding Savings Growth: Implications for Retirement Savings Behavior
See also: Delayed gratification, First-order negative, second-order positive