With every gain joins the sum that produces the next gain, so the growth is not a straight line. To find out whether people really take that in, a study paid a representative American sample to estimate growth of that kind across a span of years. By how much did they miss?
They guessed low, and badly. Seven percent a year for twenty years does not add 140 percent to a sum, it multiplies it by about 3.87. In the paid task the bias was substantial, and roughly one third of the sample answered as though compounding barely existed at all. The authors called the error .
Plain addition is the right model when the same amount arrives every year. Compound interest adds the same percentage to a base that keeps changing, and the two diverge slowly and then violently. Seven percent a year for twenty years multiplies a sum by about 3.87, and says something closer to 2.4.
Levy and Tasoff measured the gap with money on the table, which matters: without an incentive a wrong answer can always be waved away as carelessness rather than error. They ran the task on a sample built to represent the United States, so the result is not a quirk of undergraduates.
Fitting each person to a model of perceived compounding, they found substantial bias overall, and roughly a third of the sample at the extreme where compounding is essentially ignored. Higher bias also went with lower asset accumulation across the sample, which is suggestive and falls short of causal.
The part that should worry anyone designing advice is what failed to help. A simple , a picture of the curve, left the estimates where they were. The distance from an arithmetic question to a pension choice is also still open, and the direction of the error is not: when people are wrong about compounding, they are wrong downward.
wat. In compound interest the gain starts earning a gain of its own, and that is the layer the mind leaves out.
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The same mistake shrinks a savings account that grows and a debt that swells, so it bends exactly the decisions that run for decades.
How do we know?
Levy and Tasoff built a paid measure of the bias, ran it on a sample representative of the United States, and fitted each person’s answers to a model of how much compounding they perceive.
What is still unknown
An arithmetic question is not a real financial decision. The link the authors report between a person’s bias and their lower asset accumulation is an association, and not on its own proof that one produced the other.
Learn something?
Where to next
When does a lesson about money actually change behavior?saving
Why did the people who paid full price show up to more plays?bias
What happened when the Dunning-Kruger effect was run on random data?bias