Say you have a dollar that doubles in value every day. How much money will you have after a month?
For most people, the answer is rather shocking: You will have more than $1 billion after 31 days of doubling.
Although the math is just basic arithmetic, many of us assume the final number will be far smaller, a blind spot known as exponential-growth bias. Simply put, exponential-growth bias is the tendency to neglect the effects of compound interest, which is what happens when earned interest is reinvested. Research shows that this bias matters: Households with a stronger bias tend to save less and borrow more. They have portfolios that include more short-term assets and an overall lower net worth.
In recent years, behavioral economists have come up with tests to measure an individual’s level of exponential-growth bias. Here’s a typical question:
Assume that you deposit $400 every month into a retirement savings account that earns a 10% yearly rate of interest. How much money do you think you will have in your account after 40 years (including interest earned)?
Ready for the answer? It’s about $2.5 million after 40 years. If you didn’t get it right, don’t worry; most people don’t. In fact, a clear majority make the exact same error. They multiply 400 x 12 x 40 x 1.1, which is equal to $211,200. Not a paltry amount, but it’s less than 10% of the actual total
(The correct calculation requires adding the earned interest for each year to the principal sum, and then calculating the interest for the next year based on that amount. While online calculators can make the process far easier, they do require that people first realize they need help.)
How did you do? If you were far off in your estimate, you may have exponential-growth bias and should be mindful of making two common mistakes when it comes to saving for retirement.
The first isn’t saving enough, as exponential-growth bias leads people to underestimate the benefits of long-term investing. Because such people think that their savings grow linearly, and not exponentially, they believe it is relatively easy to make up for lost time. That makes it easier to postpone saving.
This was demonstrated in a study by behavioral scientists Michael Liersch, at New York University at the time, and Craig McKenzie, of the University of California, San Diego, which asked subjects to consider two people, Alan and Bill, who are saving for retirement in 40 years.
Alan deposits $100 every month into his retirement account. Bill waits 20 years before depositing money into his account. Both accounts earn 10% interest every year, compounded annually. How much money would Bill need to deposit into his account each month to have the same amount of money as Alan when they both retire?
The majority of participants thought the answer was $200, or twice as much as Alan. The correct answer is $773 a month. The lesson is that making up for lost time tends to be much more difficult than people think.
Such financial confusion has a clear effect on savings. A recent paperby Gopi Shah Goda, deputy director of Stanford University’s Institute for Economic Policy Research, and her colleagues finds that those at highest risk for exponential-growth bias contribute significantly less to their retirement accounts, even after controlling for cognitive ability, financial literacy and many demographic factors.
The second financial mistake influenced by exponential-growth bias is taking on too much debt, as the bias leads people to underestimate the long-term cost of debt. According to research by Victor Stango, a professor at University of California-Davis, and Jonathan Zinman, a professor at Dartmouth College, exponential-growth bias increases the short-term debt-to-income ratio of households from 23% to 54%. Because people with the bias don’t understand how interest accumulates, they are more likely to take on expensive loans. The interest quickly adds up. On a $5,000 credit-card balance, for instance, a customer paying the 3% monthly minimum will spend $5,188 on interest alone. It will also take that customer more than 17 years to pay off the debt.
Taken together, these two tendencies—saving less and borrowing more—can severely undermine individuals’ financial security. The good news is that relatively simple interventions can reduce the impact of exponential-growth bias.
One easy fix is to do the math for people. Research suggests it doesn’t matter if people are given old-fashioned calculators—they still can’t solve questions involving compound growth. This suggests that, instead of just telling people their interest rate, we should tell them how much they could expect to have or owe in the future based on that rate.
For instance, Drs. Liersch and McKenzie showed that exposing employees at a Fortune 100 company to their future retirement-account balance if they continued to contribute (and their savings continued to earn 8% annually) led to a 14-percentage-point increase in those who said they wanted to save more. Similar effects were found when college students were given a simple chart showing the growth of their money over time.
Furthermore, research I conducted with Dan Goldstein of Microsoft Research and Hal Hershfield, a professor at the University of California, Los Angeles, has shown that exposing people to their projected monthly income in retirement (rather than a lump sum) can make people even more likely to boost their savings rate, at least when the lump sum is modest. This suggests that individuals understand dollar amounts better than interest rates, and that everyday dollar amounts are best of all.
The larger lesson is that the best way to convince people to save more is to help them understand the reality of compounding, which is the magic that happens to their money when they invest it and leave it alone.
Dr. Benartzi (@shlomobenartzi) is a professor and co-head of the behavioral decision-making group at UCLA Anderson School of Management and a frequent contributor to Journal Reports. You can reach him at email@example.com.