Category Archives: Financial Literacy

Capital One 360 Money Market OFFER500 $500 Incentive Bait-and-Switch

Recently I have been in dispute with Capital One regarding a promotional offer for opening and funding a Money Market account. Anyone who has read my website or Google searches my name knows that I am not one to back down when being ripped off by a large corporation. I have gone up against Amazon.com, Bank of America, MetroPCS, and others I can’t even recall, and I rarely lose. It is not that I am seeking being defrauded, but that in America, large corporations basically operate like it is the Wild West, reneging on contractually obligated terms with condescension, glee, and no fear of reprisal or even public opinion. I am seriously considering switching from Republican to Democrat and voting for Elizabeth Warren, as Trump has done nothing but enable the corporate fleecing of individual Americans by gutting the Consumer Financial Protection Bureau (CFPB) and many other laws and regulatory bodies.


I opened a Capital One 360 Money Market account # [redacted] on September 7, 2018 using promotion code OFFER500, and fulfilled the requirements of this offer with cumulative deposits as of October 15, 2018. Although the required 60 days have passed, Capital One contends I am ineligible for the $500 incentive due to not depositing $50,000 all at once. However, the terms of the offer were plainly written and do not require the deposits to be made all at once:

Here’s the full scoop on how to earn your $500 bonus: Open a 360 Money Market account and deposit at least $50,000 between 12:00 a.m. ET on September 1, 2018, and 11:59 p.m. ET on October 31, 2018. When you open your account, enter your promotional code—OFFER500. (Please do not share this code with others.) Deposits must be from another bank (transfers between Capital One accounts will not qualify).

My deposits were in excess of $50,000, came from external banks, and were completed on October 15, 2018. I am writing to request fulfillment of the $500 bonus per the offer terms.

Capital One has been nothing but rude and condescending to me. They say on the phone that I’m mistaken, that the terms haven’t changed and always said cycling is not allowed even though I demonstrated orally and in writing that this is false. They rebutted my CFPB complaint which was summarily closed, and I’ve already written up the small claims filing form and sent it to them two months ago but they told me on the phone to go ahead and try suing them. No offer of a consolation $200 like others got, and no offer to be eligible for another bonus in the future (prior account holders are barred from receiving a promotional incentive, even if they didn’t receive a promotional incentive for their prior account).

I am going to go with the Florida and Delaware attorney general complaints, BBB, et cetera before suing, as suing is a hassle with serving the summons on their registered agent and paying a large filing fee. I stated multiple times in letters and on the phone that I know they paid out the $500 bonus automatically to all customers up until September 21, 2018 who did the same sort of deposits that I did, but they wouldn’t admit to this or even address it.

Their attorney is wrong—they are in violation of laws on deceptive business practices and probably the Uniform Commercial Code too. If it was a business account that charges a fee based on deposit volume and you cycled deposits, they would still charge fees on the full totals of the deposits.

A key part of the terms is that it says $50,000 in “deposits must be from another bank” (plural). Also note that another offer, CELEBRATE (PDF), uses different terms “$500 bonus — you maintained a daily balance of $50,000 or more for the first 90 days following the Initial Funding Period.” But, both OFFER500 (PDF) and OFFER200 (PDF) do not require the 90 days balance nor mention of balance or withdrawals disqualifying one for the incentive. I brought this up on phone calls and in writing and they don’t even respond or address it.

My CFPB complaint was answered by an employee named Jonathan who signed and printed his response letter both with only his first name and would not give his last name on the phone. I then complained by email to Kleber Santos, President, Retail & Direct Bank at Capital One, who referred the issue back to Jonathan. Jonathan called me and was most patronizing and rude in explaining (incorrectly) that I misunderstood the terms and that Capital One will not be paying anything, and he told me to go ahead and try suing them when I brought up the possibility of a small claims lawsuit.

In the CFPB response letter, Jonathan lists all of my deposit and withdrawal activity and states:

As a result of this activity, your 360 Money Market balance didn’t reach at least $50,000.00, the balance requirement necessary for earning the $500.00 bonus. To successfully earn the $500.00 bonus and have it post within 60 days after completion, your 360 Money Market needed to be externally funded and have a total balance of at least $50,000.00 by October 31, 2018, at 11:59 PM ET.

As a result, we will not be honoring the posting of a $500.00 bonus to your 360 Money Market.


At every step in communicating by phone and in writing to Capital One and the CFPB I have explained the mismatch in terms, including attaching a PDF file each time of the terms as displayed when I opened the account which do not contain the language about the balance of the account needing to reach $50,000.00 at any single point in time. As the terms were in actuality written, there is only a requirement that deposits between September 1, 2018 and October 31, 2018 sum to $50,000.00 or more and come from external banks. The terms had no mention of intervening withdrawals not being allowed. Capital One will not address this nor will they address that they were in fact paying out bonuses to all customers up until September 21, 2018, and made no attempt to retroactively debit the bonus from these customers.


Why “Crapital” One is a fitting moniker

Online, Capital One is derogatorily referred to as Crapital One, and this is well deserved. Capital One loves suing its customers in small claims court—they sued more than 500,000 individual customers per year in 2008, 2009, and 2010 for debts much smaller than most credit card issues would sue for. It is no wonder they are not afraid of being sued, as they obviously have an expansive network of attorneys and paralegals to handle suing individual customers en masse. In small claims court, they are almost universally the plantiff rather than the defendant. This is in diametric opposition to common perceptions of small claims court being a venue for consumers to seek financial justice against large corporations. The Center for Responsible Lending has challenged Capital One in an amicus brief to a federal appeals court regarding Capital One’s “misleading overdraft fee practice” to deduct the maximum amount from customers’ deposit accounts. It should not be a surprise that an overdrawn Capital One account, even by just a few dollars, will invariably cascade into hundreds of dollars in overdraft fees that Capital One is happy to sue their customers in small claims court for.

Capital One should be avoided. ING Direct was a fine bank before Capital One acquired them, rebranded as Capital One 360, and changed the modus operandi to ripping customers off rather than helping them. If you, too, are a victim of Capital One, I suggest emailing their executives, and complaining, both publicly and in private, through regulatory agencies, the court, social media, personal websites, et cetera. Not only do they systematically prey on subprime customers in an organized fashion—they brazenly act in bad faith against detail-oriented, rule-following customers like myself.

The simple solution would be for them to honor their terms as written for past customers and adjust the terms for future customers. But no—Capital One continues their bait-and-switch scheme even after the backlash they are experiencing on the OFFER500 debacle. They continue to offer a similar promotion, OFFER200, which substitutes a $200 bonus for $10,000 in deposits with otherwise identical terms:

https://www.capitalone.com/offer200/ (PDF)

Here’s the full scoop on how to earn your $200 bonus: Open a 360 Money Market account and deposit at least $10,000 between 12:00 a.m. ET on between December 12, 2018, and 11:59 p.m. ET on March 31, 2019. When you open your account, enter your promotional code—OFFER200. (Please do not share this code with others.) Deposits must be from another bank (transfers between Capital One accounts will not qualify). If you have or had an open savings product with Capital One after January 1, 2016, you’re ineligible for the bonus. This offer cannot be combined with any other Capital One Bank or Capital One 360 new account opening offer. Bonus is only valid for one account.

When will I actually get my bonus? Capital One will deposit the $200 bonus into your account within 60 days after completing the above conditions. If your account is in default, closed, or suspended, or otherwise not in good standing, you will not receive the bonus.

They could easily stipulate that the account must attain a $10,000 balance during the promotion period. Their employees and executives erroneously purport that the terms say that, which they do not. As written, one who does not have $10,000 on-hand should be able to receive the bonus by making deposits from another bank and withdrawals to another bank (e.g., “cycling”) of smaller amounts which in aggregate sum to $10,000 or more of deposits during the promotion period. Although the terms say “transfers between Capital One accounts will not qualify,” they do not say that transfers between Capital One accounts and external banks do not qualify. Moreover, they were paying out such bonuses programmatically and automatically to customers who cycled deposits up until September 21, 2018, when someone in marketing or loss prevention must have noticed they could be saving quite a bit of money by not doing this. But, where is the requisite change in terms? Nowhere to be found, even in Capital One’s new promotions, which makes this nothing less than a bait-and-switch. Theirs is a deceptive and misleading business practice in violation of contractually obliged terms—terms which Capital One could easily adjust and currently are quite concise and clear—in opposition to their contentions to the contrary. Shameful.

Combating Investing Profiteers and Their Propaganda Against Low-Cost Investing

No one knew better than Jack Bogle (1929–2019) that the interests of the financial industry are diametrically opposed to the interests of the common person. Low-cost index-tracking funds now comprise about 20% of the market for U.S. stock mutual funds, and this share continues to grow. However, Americans’ financial and investing literacy remains low, and those seeking out information are overwhelmed by propaganda from profiteers, which makes it hard to discern the truth.

John Paulson, a wealthy profiteer in the hedge fund industry, surprisingly shared some truth in a recent Bloomberg Opinion column:

“The other thing I love about this business, when I say why I went into this business, is the fee structure,” he [Paulson] added, detailing how much he could make in charging a 1 per cent management fee and 20 per cent performance fee on different levels of assets.

“The more money you manage, the greater the fees,” he said. “Now ultimately we managed over $30bn, and there were years our returns were well in excess of 20 per cent, so to get to those levels, the fees just pour out of the sky.”

The column author (Matt Levine) continues, elaborating on how Paulson profited even while screwing over his investors:

Also if you start losing money you don’t have to give the fees back: “The 63-year-old money manager said that almost 75 to 80 per cent of the money managed by Paulson & Co was now his own capital, reflecting years of disappointing returns that have driven outside investors away”—though also reflecting earlier years of huge returns and huge fees that allowed him to have billions of dollars of his own money in his fund—and “he would consider turning his firm Paulson & Co into a family office ‘in the next year or two.'”

Hedge funds aren’t even open to the ordinary investor; you must be an accredited investor with at least a $1 million net worth excluding one’s home, or income over $200,000 in the past few years. Supposedly, hedge funds are where “smart money” goes; accredited investors are sometimes referred to as “sophisticated” investors, such as in Australian law. This is ironic, because it is foolish to pay 1% per year of portfolio value plus 20% of gains, when active investors are demonstrably incompetent. Above, we see that Paulson had a few good years early on causing foolish investors to pour into his fund, followed by many years of terrible returns that led them to pull out. All along, he collected about 1% per year in management fees plus about 20% of investors’ gains during good years, while losing nothing in bad years. This is highway robbery.

Vanguard, the company Jack Bogle founded, fought profiteering on multiple fronts. They fought against “load fees,” which are sales commissions for stockbrokers that come as a percentage of invested assets. Up until the 1970s, no-load mutual funds were almost unheard of, and it was common for brokers to get as much as 5% right off the top—if you put in $10,000, only $9,500 got invested and they kept $500, immediately kneecapping your returns. Now, investments with load fees are the abnormality. And, although Vanguard has always offered actively managed funds, they pioneered index-tracking funds with much lower fees. Tracking an index, such as the S&P 500, has shown to be consistently better than active management. Most fund managers produce returns that are lower than an index fund. When you add sky-high fees on top of this, you are guaranteed to lose money. Conway (2014) writes in a Barron’s article:

How hard it is to predict who will do well. This isn’t part of the latest S&P study, but the index maker’s previous work on the subject suggests there’s no statistically significant persistence among funds in the highest-performing groups. There’s no new evidence suggesting that’s changed.

When you look at your 401(k) plan, you will almost certainly see investment options that don’t belong there. There are almost assuredly funds in there that charge fees of 1% per year or more, and sometimes a low-cost index fund, with an annual fee of about 0.05%, isn’t even available. The profiteers’ reach is deep, and it extends even to our teachers who are scammed by 403(b) annuity plans, in cahoots with lawmakers and administrators who partner with profiteering companies to only put bad investment options on the table.

Online, the propaganda against low-cost investing is widespread. The industry reaps massive profits while creating little value, not unlike the tobacco companies. They have a lot to lose. This is why there are daily propoganda pieces in the news saying things like “if everyone invested in index funds, it would be a catastrophe” and stuffing Wikipedia pages with propaganda such as “many investors also find it difficult to beat the performance of the S&P 500 Index due to their lack of experience/skill in investing” and purporting that unsuccessful active managers are actually “closet indexers,” justifying high fees while failing to deliver the product (active management) that purportedly produces profits.

In truth, active management is a nothingburger. You pay high fees and get lower returns than an index fund. It’s sort of like going to a bank and paying $200 to arrange to be mugged in the parking lot.

Even without sales commissions, financial advisors and other financial professionals still have plenty of ways to profiteer. They do this via an annual or quarterly fee assessed against “assets under management” that you have made them custodian of, which is usually around 1% per year. Framing this as 1% per year actually does a disservice to the investor, however. The stock market only returns about 10% per year as a long-term average, before inflation which is roughly 3%. One percent of 10% is actually a 10% fee, and if adjusting for inflation, a 14% fee. Would you pay a real estate agent 14%?

On top of this, the investments financial advisors place you in, even if index funds, likely do not have the 0.05% or even lower annual fees that are offered by Vanguard, Fidelity, Charles Schwab, and others. You might see your money in a fund that is substantially similar yet has a 0.5% annual fee, with your advisor receiving a cut from the affiliated company. If you can expect a long-term average of 7% in real returns before fees, then 1.5% of fund and advisor fees gobbles up 21.4% of these returns. Each and every year.

The FINRA foundation’s recent study of Millennial investors found that Millennials are actually eager to work face-to-face with financial professionals rather than do-it-yourself investing or using a robo-advisor. Also, Millennials had no idea that you need substantial assets to work with a financial advisor, and they expected an advisor to take a whopping 5% of assets under management as a fee each year. Such lack of knowledge is kryptonite to achieving financial independence. Even a high income cannot compensate. “A fool and his money are soon parted,” as the saying goes. In this industry, it is not helpful that wolves masquerade as sheep and sheep do not even notice they are being eaten.

The common American does not have access to a hedge fund or even a financial advisor, yet they still have a 401(k) plan available, chock full of bad investment options. There might only be one low-cost index fund available in their 401(k) fund menu, or even none at all. About half of Americans do not invest in stocks at all, and if they do, they don’t know that buying and holding the whole market is the best strategy. This fact is both counterintuitive and pilloried by propagandists in the financial media. To combat profiteering and propaganda by vested interests in the financial industry, financial education is key, but must be coupled with outlawing and derriding profiteering practices. A good place to start is with 403(b) plans for public school teachers. Teachers lack financial knowledge, shape the next generation’s knowledge, and are besieged with low pay, awful pension plans that no one ever gets a pension from, cringeworthy annuities masquerading as investment options, and sales representatives that stake out school cafeterias to cajole them into financial ruination. Therefore, for my forthcoming Education Ph.D. dissertation at University of Central Florida, An Investigation of Investing and Retirement Knowledge Among Preservice Teachers, I am surveying the next generation of teachers to provide (a) evidence to support reforms both nationally and locally and (b) instructional design recommendations for financial education programs.

This article was also posted on Tippyfi.

Thoughts on Big Three Question #2 used to assess financial literacy: Inflation

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

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:

Inflation Question by Educational Attainment

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 Three was “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.

Decisions and Outcomes

Decisions and outcomes are not necessarily related. One can make a good decision that results in a bad outcome, but this does not mean the decision itself was bad. This can be represented by a simple table:

Good OutcomeBad Outcome
Good Decision
Bad Decision

Here are a few examples that come to mind:

Decision Table

We know that investing a lump sum now is better than dollar-cost averaging your way into stocks or timing the market by attempting to “buy the dip” (e.g., Williams & Bacon, 1993; Panyagometh & Zhu, 2016). Although lump-sum investing is the preferable decision, there is a nontrivial probability of an inferior outcome as compared to investing at a later time. If a bad outcome occurs, it is more salient than had a good outcome of equal magnitude occurred. However, this should basically be chalked up to bad luck. A bad outcome does not mean a bad decision was made.

Separating decisions from outcomes goes against our nature. It is contrary to human psychology. In her 2018 book, Thinking in Bets, poker champion Annie Duke calls the human prediction to judge decisions by the resultant outcomes “resulting.” Resulting is akin to confusing causation for correlation in science.

Making a bet where the odds are in your favor is a good decision, even if you lose. With more and more such bets, a result commensurate with the prudence of the decision approaches inevitability. In the stock market, you can think of each trading day as a bet, with these bets stacking up over time. Below, probabilities from Bloomberg data, compiled by Vanguard, show the probability of positive returns for S&P 500 investment time frames within the selected dates (1/04/1988 to 2/16/2018).

S&P 500 investment during 1/04/1988–2/16/2018Probability of positive return
One day.54
One week.58
One month.64
One year.83
Ten years.91

Although start and end points matter, the pattern has been shown to hold even over the duration of the stock market’s history, including the Great Depression. Above, we see the probabilities of positive returns averaged across all day, week, month, year, and 10-year periods within a 30-year range. A 54% chance of positive returns on any particular day increases to a 91% chance of positive returns during any particular 10-year period within the 30-year period sampled.

Of course, this data nevertheless shows a 9% chance of losing money in a 10-year span. However, if you are unlucky enough to have invested the bulk of your money at an unfortunate time, this does not mean your decision was bad—just that you happened to have a bad outcome. It takes longer than 10 years for the probability of positive returns to approach inevitability—more like 30 years. Time will tell whether the recent market peak on September 20, 2018 will require months, years, or more than a decade to overcome.

The financial industry is built on confounding decisions with outcomes. A hedge fund manager is said to be “hot,” endowed with stock-picking genius, if his speculations pay off in a given year. Even for investors who were lucky enough to pick him, their decision was certainly bad; picking a low-cost index-tracking mutual fund and sticking with it for many years is a better decision. The speculator’s success is based on chance and luck, not skill. The speculator’s decisions are always bad, although their outcomes may be good, for a time. Eventually, good luck will inevitably run out, leading to underperformance of the index-tracking mutual fund, or worse, a spectacular capital wipeout à la Enron or Bernie Madoff.

We must all take a step back to carefully consider whether a good outcome was actually the result of a good decision, and whether a bad outcome resulted from a bad decision, or from a good decision that should be repeated despite a bad outcome occurring this particular time. On the whole, as a series of good decisions lengthens, good outcomes become inevitable, and as a series of bad decisions lengthens, bad outcomes become inevitable. In making such determinations, our psychology and the limited information available may work against us.

This article was also posted on Tippyfi.

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 www.meta-financial.com):

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.”
True
False
Do not know
Refuse to answer