Illiteracy rules
I hope you won’t mind me setting a little test of financial literacy. You buy a new £1,000 computer and borrow money to pay for it. You have a choice: either (a) pay 12 monthly instalments of £100; or (b) borrow money at an APR of 20 per cent, meaning you pay back £1,200 at the end of the year. Which offer is better – or are they (c) identical? (The answer is at the end of this column.)
If you don’t get it right, don’t worry: 93 per cent of Americans don’t either, according to Annamaria Lusardi, an economics professor and director of the Financial Literacy Center. (Financial illiteracy is also widespread internationally, she adds.) Far more obvious financial questions baffle the majority of people. And if you think the question is academic – and would like a hint at the answer – just ask yourself why companies are so keen to let you pay in instalments.
The sophistication of financial products has increased dramatically; the sophistication of consumers has not. “Knowledge hasn’t caught up with the real world,” says Lusardi. “The important word is ‘literacy’. You can’t live in society without being able to read and write, and now you can’t live without being able to read and write financially.”
The obvious answer is financial education. But it has been tried and doesn’t seem to work terribly well. According to a survey published by Lewis Mandell of the University of Washington, financial education seems to have no impact on formal measures of financial literacy, although, puzzlingly, it does seem to improve financial decisions a little later in life.
For this reason, financial education sceptics such as law professor Lauren Wills argue that the whole project to boost financial literacy is misconceived and actively harmful. (My analogy: why not improve medical outcomes by teaching people to practise surgery on family members?) Wills would prefer regulators to simplify the financial landscape – presumably with a combination of bans and regulatory “nudges” – and simply abandon the financial education project entirely.
Professor Lusardi disagrees. While the track record of financial education is not encouraging, she says “the evidence that is available now tells us very little” about whether it would work if done right. Classes are often offered by poorly trained teachers, she says, or courses for employees might be a single lunchtime chat about pensions.
“A one-hour seminar is not going to work, for sure,” she says. In short, perhaps the reason that financial education doesn’t seem to work is that nobody has tried it properly.
The Financial Literacy Center is trying more creative approaches. One promising technique is to use video testimony from workplace peers; another tactic, in partnership with a not-for-profit organisation, D2D, is to develop computer games that incorporate some financial concepts. Lusardi says initial results are promising and full randomised trials are in progress.
I sympathise with both sides of this debate. I simply don’t believe that financial education is impossible, or more trouble than it is worth. But without some intelligent regulation to preserve transparency and protect consumers – at the very least, from the most egregious abuses – I fear that the ability of educators to clarify how finance works will be outpaced by the ability of credit-card marketers and subprime mortgage peddlers to muddy the waters again. The financial educators should do better, but the financial regulators may have to meet them halfway.
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The answer is (b). The instalment payments hide a deceptively high interest rate. Because capital is being repaid almost immediately but total interest is still £200, the true interest rate is much higher than 20 per cent. Reader Ian Nicol informs me that Excel uses the formula (RATE(1*12,–100,1000)*12) to calculate interest rate, in this case more than 35 per cent.
Also published at ft.com.
11 Comments
Igor says:
I am not sure the answer to your question is so simple. You asked which offer was better, not which offer charged lower interest rate.
It might be easier for consumers to come up with 100 pounds each month then to come up with 1200 all at once. Of course you could argue that the consumer could invest those 100 pounds and be better off at the end of the year, but would it be worth the effort? Or you could say that simply leaving the money on your checking account was still better than paying the monthly installments, but the temptation to spend that money might be too great for some consumers.
Do you think there are sane individuals who could read your answer and still say that (b) is the better choice?
26th of February, 2011Tim Harford says:
A loyal reader writes:
“You borrow £1000 for 1 year.
You make 12 amortized payments of £100 at the end of each month such that you owe zero at the end of the year.
As per Excel formula Rate = 2.923% per month. But this is a rate expressed with monthly compounding.
So AER is NOT 2.923% x 12 which is where your reader gets his 35%. He has forgotten to compound 12 times.
AER = (1.02923^12 – 1) * 100 = 41.3%.
35% is the rate expressed with monthly compounding. So you cannot compare it directly with paying back £1200 at the end of the year with AER = 20%.
You are less likely to make mistakes like this if you use continously compounded interest rates based on natural logs … but that is another story.”
I find it amusing, of course, that in a column about financial literacy I hadn’t managed to figure this out for myself. Note, by the way, that the question doesn’t ask for a specific calculation – just for multiple choice. And 7 per cent is a pretty low hit rate for a three-way multiple choice question.
26th of February, 2011Victoria Tomlinson says:
Glad to see these other comments – I too have been struggling with this (while gardening)!
Surely working out the interest rates is making it academic (in this particular question)? The problem with interest rates is when the punter ends up paying out more overall than they thought they were doing or could afford to do.
In this case, the consumer would cough up £1200 for a computer over a year, either way. Isn’t that what matters? And as Igor says it’s then just a matter of what is the most manageable way of paying that.
The big issue in terms of financial management is when one of the options would have meant paying another £200 or even £500 over the year without realising that was the deal they were being offered?
Tim has to be right that we need financial education – I was driving a bunch of 19 year old girls at university the other day, and they were all saying that the only financial education has come from parents – they couldn’t believe how little they had learnt at school and how much they needed to understand.
26th of February, 2011Mark Crompton says:
Another area of illiteracy is risk. Advisers like tro ask clients to grade their taste for risk. We know they favour risk because if their clients don’t want risk they can put their money on deposit or with NSI without paying an adviser. But is there a benefit to going higher risk? If as they advise higher risk means possibility of higher return at risk of losses, the only difference is that the returns have a higher range. It will average at the midpoint, which could easily be zero but is hard to calculate, as what is the midpoint between an unknowable top end and a lose everything bottom end? While the low risk inflation tracker probably has a range of at most 3%, all above zero. So on average the high risk investments are likely to return less.
26th of February, 2011mwstory says:
I had a similar reaction to the first comment above.
26th of February, 2011Lots of people with poor impulse control use seemingly illogical financial products to regulate their spending, eg Christmas savings clubs, so the best deal financially might not suit a particuar consumer.
An extreme example I heard about recently was someone withdrawing cash on on their credit card (with the fees and interest charges that result), taking the card home, returning to the shops and spending only cash. She reasoned that the hefty fees charged would actually be a saving compared to the overspend she would have suffered had she had the temptation of the card in her purse.
Sam L. says:
My initial thought with the installment vs. lump sum payment was to consider the time value of money. The net present value of $1200 payment in one year is less than the value of the earlier payments, so while the $$’s are the same, the one that forces you to pay sooner has a higher time value.
I know NPV is much more valuable to businesses making long term financial choices than it is to individuals, but there is still something to be said for considering the fact that money received in the future has a lower value than money received today, which is part of what makes the installment plans a better deal for the company, and a poor deal for you.
26th of February, 2011Paul says:
Wouldn’t it be easier to calculate the cost of each option today? $1200 in a year is 1200/a today where a is the actualization rate (meaning your preference for money today opposite to money in the future).
If You have a nice investment opportunity with a high Return on investment but that is valid only today then paying in instalments might be the better option.
26th of February, 2011Attila says:
This question has me stumped (possibly a proof for the lack of financial education? :-)). If we take the question as stated in the first paragraph (ie. pay 12×100 or 1×1200) and we abstract away other factors (such as inflation or the comparative difficulty of coming up with smaller vs. larger sums), wouldn’t the answer be (c)? (“the same”)
Could someone please enlighten me?
28th of February, 2011Hans van der Drift says:
When I read this I was thinking about it from the financiers point of view rather than the consumer. I doubt the Financier would want to wait for 12 months to get their money, the risk is 100% till payment date, but with the monthly payments its reduced every month.
So what monthly payment would need to be charged to be equivalent to 20%? £92.63
But this is a another question. How can you structure the repayments to be better for the financier? How about Double the payments and get a £50 quick payment Discount? Rate = 53.35%
Hans
1st of March, 2011Tim Harford says:
Re: comment number 2, Ian Nicol responds: “I just looked at the comments and the difference is that my calculation is for simple interest (APR) usually used for loans. The other is for compound interest (AER) which is usually used for savings. The calculations are correct but their use is incorrect.”
1st of March, 2011Miss Nomer says:
It looks like the variety of responses to this issue demonstrates that some degree of financial education would be beneficial.
Regarding the test itself:
1) It’s not meant to be a test that takes into account psychological matters (such as what you’d do if you had £100 in your bank account today that you didn’t need to pay to someone until much later) or considers all the different financial situations that you could be in. Such matters raise valid issues, but these are different issues to the one the question addresses.
2) You don’t need to use a spreadsheet or a calculator or get bogged down in calculations to determine interest rates or worry about the differences between APR and AER to answer the question.
Here’s one straightforward way to look at it (there are undoubtedly others).
Think of the question like this; you have to pay £1,200 to someone. In a) you pay £100 in January, £100 in February and so on until the final payment of £100 in December. In b) you simply pay £1,200 in December. Which is the better deal for you?
Consider making payments as in approach a), but, instead of paying a £100 instalment in January, you could pop it in a building society account or similar. In February you could do the same. Carry on doing this all year and by December you’ll have the £1,200 that you’ve put into your building society account, plus some interest. You can use this to pay the £1,200 that you owe, and keep the interest for something else. So you’re better off keeping the money through the year and paying what you owe at the end. i.e. Approach b) is better for you.
Sorry I wasn’t more succinct: hopefully I was clear.
Please excuse me now, I’m just off to practise some keyhole surgery as my brother’s appendix is presenting early signs of swelling and I fear that I’ll be performing an appendectomy before the week is out.
1st of March, 2011