## How to be financially literate

Here’s a little test. You buy a new £1,000 computer, but you need to take on some debt to finance it. You have two options: pay in 12 instalments, £100 a month for a year; or borrow at an interest rate of 20 per cent and pay back £1,200 at the end of the year. Which is the better offer?* Or are they both the same?

Take your time. Annamaria Lusardi, an Italian economics professor now based at Dartmouth College in the United States, has been asking a lot of people this question. Only seven per cent of Americans get the answer right. Even simpler multiple choice questions about interest rates and minimum payments on credit cards baffle the majority of people.

*Read the whole column here. The answer is below…*

*Borrowing at 20 per cent is a much better offer. Either way, you pay back £1200 in total, but the monthly instalments require you to start paying back the loan almost immediately. The implicit interest rate of the monthly instalment deal is closer to 30 per cent than 20 per cent. That’s a very large difference.*

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^{th}of November, 2010 • Other Writing • Comments off
## 23 Comments

Richard Bruns says:Where can I get the lesson plan for the ‘rules of thumb’ class mentioned in the article? I’d like to see if I can incorporate it into the introductory Econ class I teach.

16^{th}of November, 2010eric says:Tim would you mind taking me through how you got the implicit interest rate for the installment option (closer to 30). great article and thank you for your time.

16best, Eric

^{th}of November, 2010praxis22 says:Perhaps I just don’t understand the word implicit, nor would I buy anything on credit, so this is kind of moot, however.

1000+20% = 1200

1000+35% = 1350 (from @einspain)

Yet you pay 1200, “either way” so what are the assumptions about the credit card? Where does the extra 150 go?

16^{th}of November, 2010Tim Harford says:@praxis22 – In paying by installments you begin paying back almost immediately. You borrowed £1000 and after 6 months you’ve paid back £600. Yet somehow you still pay a total of £200 interest over the year. This means the interest rate is way higher than 20 per cent.

16^{th}of November, 2010praxis22 says:@Tim, While I accept the premise that paying by installments cost more, (because of the target demographic, catalogue clubs, high street HP are offered to those who are often denied credit, as opposed to those with stable incomes who are eligable for a credit card at a better “revolving” rate.) I still don’t see the “truth” of it, so to speak.

I can understand that with a credit card you pay interest only on the outstanding balance, so if you paid 100 off you credit card balance every month the cumulative interest would drop, as you paid down the principle. This is why there are penalties for early repayment on some fixed term loans I presume.

But the statement is pharsed that you pay 1200 regardless over the course of a y

ear. While if you do the math long form, the card @20% means you repay only 1103.5 (rounding up) This is approx 10.5% interest over the term, presuming 1.666666

667% interest per month (20% ÷ 12)

Otherwise “either way” it just doesn’t make sense. 1200 == 1200 Or perhaps I’m m

16issing something?

^{th}of November, 2010Patrick Burns says:Unlike other commenters, your mathematical point makes sense to me. But you are implicitly assuming rationality that might not exist. Paying monthly could be the preferred course rather than getting to the end of the year with the money spent on other things.

16^{th}of November, 2010James Annan says:Another way to look at it is to realise that the second person is borrowing 1000 for the whole year, but the first is only borrowing it for one month, and then 900 for another month, etc…so although they both pay 200 extra, one loan was much larger on average over the interval of the loan. In order to have the full use of 1000 for a year, the first person would have to take out more loans throughout the year, each of which would incur additional interest.

17^{th}of November, 2010Popup says:Praxis, you’re missing a fundamental aspect of ‘financial literacy’. – “Money today” is worth more than “money tomorrow”.

17Paying £1200 spread out over the next 12 months is more expensive than paying the whole sum in 12 months time.

^{th}of November, 2010Nils says:The problem are semantics:

“or borrow at an interest rate of 20 per cent and pay back £1,200 at the end of the year.”

I understood this like I would have to pay 20% of $1000 every month and then in addition to that $1200 after 12 months. That would, obviously, have been worse.

17^{th}of November, 2010Nils says:In addition to that: What do I care about implicit interest rates?

The real question is: What kind of benefit do I gain from having money available during that year? If the answer is ‘none’, then it doesn’t matter what I do.

If, however, I can buy something nice (and due to inflation perhaps cheaper) today, because I only have to pay back in a year, then having then paying back later makes sense.

Another reason would be a some way to invest the money during the year and thus gain some small interest rate.

Point is: For most people those options are almost the same. Paying back later is slightly better.

17^{th}of November, 2010Mike McCarthy says:Perhaps I’m looking at this too simplisticly but the question asks ‘which is the best offer’. To my (and it seems many other) eyes the ‘best offer’ is the one which offers the lowest total interest payments. Since in both examples the interest paid is £200 I can see why many people would shrug thier shoulders and say there was no diference. Of course I understand now that there is a difference, but in the example chosen this is academic and I’m not sure it’s the best way to assess the financial literacy, or otherwise, of the general public.

17^{th}of November, 2010PJ White says:I think you’re absolutely right that people need rules of thumb. Trouble is, the one you end with – don’t pay for a computer by instalments – would be quickly latched onto by providers of financial products…and quickly rendered out of date.

That points to the basic problem with the original test – it’s rather artificial. It doesn’t address the real financial choices that people are likely to face. So isn’t that helpful.

I just wrote about this on a youthmoney education website I do. Hope it’s within etiquette to leave a link. http://www.youthmoney.com/2010/11/17/rules-of-thumb-better-than-tricky-tests/

17^{th}of November, 2010Mo says:@praxis22: you’re right that you pay the same 1200 regardless in both cases. But in one case you’ve borrowed 1000 for a whole year; in the other case, you only borrowed 1000 for a month, then you borrowed 900 for a month, then 800, and so on. So effectively it’s 1000 + 20% = 1200 in one case, but [less] + [more%] = 1200 in the other.

17(I don’t know how to do the calculation to work out what those figures are, but the principle is there.)

^{th}of November, 2010Fake Name says:I am also a little confused by the example.

Is it better to pay the total amount at the end of the year rather than in monthly installments because instead of forking over GBP 100 over every month, you can put it in a fixed deposit (12 months for the first GBP 100, 11 months for the second GBP 100 and so on) and thereby earn some interest from it? Is this lost interest some sort of opportunity cost when you pay in monthly installments?

18^{th}of November, 2010Ruben says:Eric, I’m a bit rusty on this but I believe this is how it goes:

You can calculate the net present value by discounting each installment by 1,66% (that’s 20% interest divided by 12 months); that would be 100/1.0166+100/1.0166^2+…100/1.66^12. This gives a value of £1079,51, which represents the actual price of the computer if you were to buy it now.

Note this is almost £80,- higher! So you’re actually coughing up an additional £80 today to pay in monthly installments.

The implicit interest rate of almost 30% is found when we add the interest rate (20%) of the other option: 1079,51*1,2=1295,41, that is 29,51%

This can be attributed to the time value of money: an amount money that you have now is worth more than that same amount of money you’ll get in the future.

18^{th}of November, 2010eric says:my question is just how you get the “closer to 30.” With the installment option I get a number arond 40%…any chance you could clarify your “closer to 30%”

18^{th}of November, 2010Indigo S. says:I understand that, theoretically, I am better off hanging on to my money for as long as possible. In real life, though, I would probably opt for the instalment plan, on the grounds that I’m not sure I would do anything profitable with the money in the intervening year anyway… and if I were to end up frittering it away on other consumer goods, I would not be able to make the lump sum repayment at the end of the year.

18^{th}of November, 2010Jennie France says:How about saving until you can pay cash? Hello?

18^{th}of November, 2010praxis22 says:@popup I kept staring at it and thinking “inflation/money illusion” but I presumed there was something deeper to it than that. Meaning, something that would make sense to a financial illiterate.

Even though I understand the principle I was more looking at it from Nils’ point of view, “where is the benefit” and it appears from a reply I got back from Tim, that the benefit is you can then use the money saved to pay off other debt.

This is of course moot, if like me, you have no debt, don’t run a CC balance, and don’t buy in instalments, but hey ho…

19^{th}of November, 2010Steven Slezak says:I think we need to approach this from a different angle. If you borrow $1000 and pay back $1200 at the end of the year, you can see the interest rate is 20% per year. But if you pay back at a rate of $100 per month for 12 months — the same dollar amount — the rate is actually around 2.9% per month, or roughly 35% per year. Since 35% is much higher than 20%, a single payment of $1200 makes sense. Even though 12 payments of $100 each is the same amount, the cost of the money is much, much higher.

20If you borrowed the money at 20% with monthly payments, the payment would be $92.63 per month.

So what would you rather pay — $100 a month or $92.63 per month?

The higher amount is 20% compounded annually. The lower amount is 20% annual rate compounded monthly.

The difference is not the total amount paid but the rate and the number of payments per year.

^{th}of November, 2010Steven Slezak says:Here is the rule of thumb study: http://www.cepr.org/meets/wkcn/7/784/papers/FischerFinal.pdf

20^{th}of November, 2010Penny says:Agreed with Indigo S. Most people are in a position where their income is monthly or more frequent, there is little to gain by paying off later. My ISA allowance is maxed out and I’m not so obsessed with free things I want a hypothetical good deal on a loan that leaves me in exactly the same position in a year’s time…when actually I’ll just feel richer for the year, spend money on silly things and have trouble paying it off.

If the exact question was “which is the better offer?” then the pay monthly option is not necessarily a wrong answer, they have only misunderstood if it was more explicitly “which has the lower interest rate?”.

22^{nd}of November, 2010dan says:Tim, I have a related question. Lets say a business does $100K/month in revenue and earns a 10% profit each month. At the end of 1 year the total revenue would be $1.2 million and profit would be 10% or $120K. However, since the 10% is earned each month the “implicit” return would be much higher than 10%. Is this correct?

5^{th}of December, 2010