Continuing from the savings account interest question, here I will talk about Question #2 of the “Big Three” financial literacy questions created by Annamaria Lusardi and Olivia S. Mitchell.

The prior question asked about the resultant nominal account balance of a savings account after five years earning 2% per year of interest. The second question is similar but introduces the construct of inflation and assesses understanding of erosion of savings via inflation.

**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

More than today

Exactly the same

Less than today

Do not know

Refuse to answer

The prior question was correctly answered by 75% of respondents to the 2015 National Financial Capability Study, but the above question was only correctly answered by 60% of respondents. If we break down respondents by educational attainment, their responses were as follows:

The green (left) bars represent correctly answering the question as “less than today.” The yellow bars represent selecting “Do not know,” and the red bars represent selecting “More than today” or “Exactly the same,” both of which are incorrect. “Refuse to answer” respondents are excluded in the above statistics, and I have used the nationally representative weights provided by the FINRA foundation. The above figure is from my 2017 poster presentation on financial capability and educational attainment.

As we see, more educated respondents get the answer right more often. Although many highly educated respondents select a wrong answer, they are much less likely to select “Do not know” than those with less education.

There are many hidden assumptions in this question which can be confusing for the reader. We must assume inflation refers not to expansion of the money supply but rather to increases in prices of consumer goods. The question deals with generalities rather than specifics; the reader must assume we are talking about goods on average, rather than a particular sector. If we are talking about 16 GB USB flash drives, one would probably be able to buy more of them in a year because technology prices tend to decline, but other goods go up in price. The reader must also assume we are talking about national averages, because prices may fluctuate contrary to overall inflation in certain regions.

Respondents who understand this question are likely able to divine the difference between nominal dollars and real purchasing power. Nominally, the account balance increases from $100.00 to $101.00. This is true whether the 1.00% interest rate is an annual percentage yield (APY) or an annual percentage rate (APR) compounded quarterly or monthly. Even monthly compounding would fail to increase the resultant nominal balance to $101.01 (assuming favorable rounding errors do not occur), as $101.0046 would be rounded down to the nearest cent.

With inflation being 2.00%, this means it takes, on average, 2.00% more dollars to buy the same items a year later. For “Exactly the same” to be the correct answer, the final nominal account balance would have to be $102.00, not $101.00. This means that it took 1.96% less dollars to buy the same goods at Year 0 than Year 1, or 2.00% more dollars to buy the same goods at Year 1 than Year 0. (Incidentally, many people are baffled when I tell them about this quirk of percentages. Examples: If the stock market drops 20%, it has to go up 25% to get back where it was. At Michaels [*sic*] arts and crafts store, forgetting to use your 50% off coupon means you paid 100% more than you would have had you remembered.)

“How much would you be able to buy” begs a response: “of what?” The question prompt does not provide this, and it couldn’t without being unwieldy. Nonetheless, a respondent could pick “More than today” and be technically correct if they make an undesired assumption about “of what?” If we are talking about quarters, one would be able to go to the bank and get 404 of them after a year, as compared with 400 at the start. A smart aleck could argue the “wrong” answer is actually right, and we must rely on the metaphorical spirit of the law rather than letter of the law to interpret the question appropriately.

In the scenario, real returns, which adjust for inflation, are about –1% in this year, because the nominal return of 1% was overwhelmed by inflation which exceeded the return, at 2%. Specifically, real returns would be ($101.00 / $102.00) – 1, which is .9902 – 1, which is –.0098. Multiplying by 100 to get a percentage, this is –.98%. Therefore, “Less than today” is the correct response with the unlucky individual in the question prompt having lost 0.98% of their real purchasing power. The Internal Revenue Service disregards inflation and would expect income tax to be paid on the $1.00 of increase in your savings account balance, and they actually classify interest income as “unearned” income. These two facts taken together are rather insulting.

In the end, you can buy 4 more quarters, 10 more dimes, 20 more nickels, or 100 more cents. Your account balance increased $1.00 and you owe anywhere from zero to 37¢ to the IRS, and possibly up to 15¢ of state income tax (in California if your income is over $1 million for the year). However, your purchasing power has declined by almost 0.98%.

In truth, the Big Three financial literacy questions are not magical. Although their widespread use has shown us the sorry state of financial literacy both in the United States and abroad, the questions are susceptible to biases such as framing and interpretation, and to an extent they confound financial literacy with linguistic knowledge, mathematical knowledge, and/or knowledge of financial practices and institutions. Regarding framing in particular, Stolper and Walter (2017, p. 596) state:

Another shortcoming of test-based measures of financial literacy is their sensitivity to framing. Specifically, Lusardi and Mitchell (2011a, b) and van Rooij et al. (2011b) document that the answers of survey participants differ significantly based on the wording of the test questions. In fact, the percentage of correct answers doubled in the latter study when the wording for the third question of the

Big Threewas “buying company stock usually provides a safer return than a stock mutual fund” as compared to phrasing the question reversely, i.e. “buying a stock mutual fund usually provides a safer return than a company stock“. Hence, Lusardi and Mitchell (2014) conclude that some answers classified as “correct” might instead reflect simple guessing of respondents and highlight that measurement error might be an issue when eliciting financial ability based on test questions.

In a future post, I will discuss the final Big Three question on a single stock versus a stock mutual fund, including Stolper and Walter’s criticism of the question’s susceptibility to framing effects.