Thoughts on Big Three Question #1 used to assess financial literacy: Savings account interest

Regarding assessment of financial literacy, in both the United States and abroad, the “Big Three” multiple-choice questions written by Lusardi and Mitchell are typically used. Findings show that somewhere around 50% or even more people do not answer all three questions correctly, which is evidence of a widespread lack of financial literacy. This varies by sub-groups—for example, those with more education tend to do better. Overall, all groups of people do much worse than we would expect or hope, however.

The Big Three questions balance accuracy of interpretation and conciseness, but nevertheless, and not unexpectedly, there may be issues of understanding related to wording, choices, and arithmetic, rather than substance. Furthermore, as a construct, financial literacy is interrelated with and difficult to disentangle from basic mathematical skills in manipulating numbers and percentages, which might be called arithmetic skills, numeracy, or quantitative literacy. In fact, recent research (e.g., Cole, Paulson, & Shastry, 2016) is showing that taking mathematics courses may improve financial literacy more than taking personal finance courses!

Here, I will discuss the first of the Big Three questions. There are several similar questions that have appeared in the recent S&P Global FinLit Survey and elsewhere that I might also discuss in a future article, after I discuss the Big Three Questions 2 and 3 in other future articles.

Big Three Questions

1. Suppose you had $100 in a savings account and the interest rate was 2% per year. After 5 years, how much do you think you would have in the account if you left the money to grow?
More than $102
Exactly $102
Less than $102
Do not know
Refuse to answer

With this question, we are talking about nominal future dollars rather than real future dollars, although it is not explicitly stated. The major world currencies are fiat money, meaning they are not redeemable with the government or banks for land, precious metals, or other commodities. Central banks that issue currencies, such as the U.S. Federal Reserve and European Central Bank, aim to achieve a gradual devaluation in the purchasing power of the issued currency over time, which is termed “inflation.” The Federal Reserve adjusts monetary policy while presently aiming for about 2% inflation per year, through measures such as adjusting the federal funds rate (“interest rate”) via market actions and paying banks that amount of interest for keeping reserves on deposit with the Fed, and quantitative easing (QE) by which the Fed uses the fiat money and credit it creates to purchase public and private debt. In response to the 2008 financial crisis, the Fed dropped interest rates to 0%, and only began increasing rates about 1.00% in mid-2017.

In considering this question, historical context is relevant. Prior to 2008, there were times when it would be common for U.S. savings accounts to pay much more interest per year than 2%; sometimes even 5% or higher. During 2009–2017, receiving 2% interest on a savings account would have been absurdly high. Given the Fed’s low interest rates, checking and savings accounts that paid 2% during this timeframe likely did so as part of promotional gimmicks with special requirements, such as using a debit card 10 times per month or only receiving the interest rate on balances of up to $5,000. In 2018, the Fed has finally started substantially increasing rates, so as of November 2018 it is now common to find savings accounts offering 2% interest per year.

The United States still uses paper money and coin extensively. One can withdraw cash from their bank account easily, and many banks will allow customers to order $100 boxes of nickels or $500 boxes of quarters with no fee (nickels have the highest metal value of circulating U.S. coinage, besides copper cents from 1982 and prior). Therefore, it is not advisable for the Fed to reduce interest rates below 0%, because it would result in individuals and firms stuffing cash and coin into vaults or mattresses to avoid loss of principal. QE is an additional lever to stimulate the economy when the interest rate lever is already fully depressed (rates at 0%).

Returning to the question at hand, assuming (and this is an important assumption) that the reader knows we are talking about nominal rather than real dollars, the question is absurdly easy. Even if the interest was only compounded once, at the end of the five year period, the nominal account balance would be $110, which is far above $102. The correct answer is “more than $102.”

Given that the question indicates the “interest rate was 2% per year,” this implies that interest is compounded at least once per year (annually). If compounded annually, the balances at the end of each year would be as follows:
Year 0: $100.00
Year 1: $102.00
Year 2: $104.04 (note here that we pick up 4¢ thanks to compounding of the $2.00 of interest earned in the prior year; compounding continues in future years)
Year 3: $106.12
Year 4: $108.24
Year 5: $110.41

As we see above, the effect of compounding five times (once each year) instead of only one time at the end of the five-year period is an additional 41¢ in nominal interest earnings. Therefore, one could change $102 to $110 in the answer choices and “more than $110” would still be correct like “more than $102” is. As it stands, assuming the reader knows we are discussing nominal dollars, the question does not even require an understanding of compounding returns.

When we discuss “interest rate” on a “per year” basis, this infers annual percentage yield (APY) rather than annual percentage rate (APR). Although interest can be compounded once per year, it can also be compounded each quarter (four times per year), each month (12 times per year), each day (365 times per year), or hypothetically it can even be compounded “continuously,” at every instant down to infinitesimal durations (i.e., even more frequently than each nanosecond). As we approach continuous compounding we approach the Pert equation, Pe^(rt) where P is principal (i.e., $100.00), e is the transcendental mathematical constant of approximately 2.718, r is the interest rate (i.e., 2%), and t is time (i.e., 5 years). If we were to continuously compound $100.00 at a rate of 2.00% for 5 years, the result would be $110.52, which is 11¢ higher than annual compounding, as shown below (computation thanks to

Pert equation

Therefore, depending on frequency of compounding, ranging from one calculation at the end of five years to infinite compounding throughout the duration of five years, at a rate of 2.00%, the account winds up with a minimum of $110.00 after five years and a maximum of $110.52.

Savings accounts typically compound monthly or quarterly and advertise APY, which is slightly higher than APR. Credit cards typically compound daily and advertise APR, which is significantly lower than APY. On my financial education website I have put forth an APR to APY calculator that shows the difference; a credit card that has a 24.99% APR compounded daily actually earns 28.38% APY in interest for the credit card issuer. Naturally, financial institutions advertise APR or APY depending on what looks better to the consumer, unless compelled otherwise, and they compound likewise. Therefore, although credit cards could compound interest once each statement, they compound each day to make more money for the issuer, and although savings accounts could compound each day, banks like to compound monthly or even quarterly to reduce the amount of money they pay out in interest.

It is safe to say that most people do not have a good understanding of the difference between APR and APY, because they do not even understand basic percentage arithmetic involving only two calculations. A majority of people likely do not even understand the difference between “percent more” and “percent off.” For instance, if a coupon takes $5 off a $15 purchase resulting in paying $10 instead of $15, both of these statements are correct:
You saved 33.3% (one-third)
You got 50% more for your money

Moreover, questions frequently appear on standardized tests such as: “If a tree grows 5% per year, how much has it grown after 2 years?” The answer due to compounding is 10.25%, but many erroneously answer 10.00%, showing a lack of understanding of compounding, or potentially a mis-reading of the question.

Regarding the “do not know” and “refuse to answer” choices: Because there are only three legitimate choices, including “do not know” helps prevent guessing, but some respondents may select it when they actually have an inkling of the correct answer—particularly females, who tend to have less confidence in their ability to accurately answer the question. Not many people select “refuse to answer,” and I do not see the rationale to include this choice at all, besides consistency as compared with other questions on a financial questionnaire (such as the National Financial Capability Study) that ask participants personal questions about their finances that they may not want to answer.

I will discuss the other two Big Three questions in future articles:

2. Imagine that the interest rate on your savings account was 1% per year and inflation was 2% per year. After 1 year, how much would you be able to buy with the money in this account?
More than today
Exactly the same
Less than today
Do not know
Refuse to answer

3. Please tell me whether this statement is true or false. “Buying a single company’s stock usually provides a safer return than a stock mutual fund.”
Do not know
Refuse to answer

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