Canada's Finance Minister Jim Flaherty proposes a task force to make recommendations toward improving financial literacy [National Post May 21]. An editorial in the National Post [May 23] strongly emphasizes the need for improved financial literacy. So lets do a short mid term exam.
Imagine a lender with a pool of outstanding loans of $300 each repaid at $369 14 days later. Imagine the lender is so efficient that the loan pool is always fully loaned out.
Question 1. What is the gross annualized rate of return on the loan pool. This would yield its gross revenue from which it would have to deduct all of its operating costs including bad debts, cost of capital, and all other expenses. Is the answer a)23%, b)600%, or c)21,653%?
Question 2. What is the annualized rate of interest cost to the borrowers who from time to time have loans from that pool? Is the answer a)23%, b)600% or c)21,653%?
25 marks if you made the same choice for both questions. You correctly realized that the annualized interest cost to the borrower is the same as the annualized interest rate that the lender earns. Your answer to question 2 should therefore be the same as your answer to question 1.
Another 75 marks if you chose c for both.
On this scale of grading the financial press, the Federal Government, and the Province of BC receive a score of 25% for choosing b for both questions. That is how they describe the payday loan on which this example is based.
The correct answer is c) or 21,653% and a financial tutorial follows. But first note how this explains a headline in the National Post May 19 "Payday Lenders Keen on Canada".
I have no quarrel with the payday loan industry except for transparency and disclosure. Undoubtedly they have high costs and expenses. However they are understandably unwilling to express their lending terms in the normal form for borrowing and lending transactions i.e. the equivalent annualized rate.
I do have a quarrel with the financial press and with government agencies who both failed the mid term exam and are seemingly reluctant to confess the deficiencies in their own financial literacy. They have done little to encourage transparency with respect to the cost of borrowing in general and payday loans in particular.
You will probably read more bafflegab about such loans being short term and non renewable. Think of it as get on the bus Gus. If you hop on a bus traveling 20km/hr and hop off after only 5 minutes or after a few kilometers you were still traveling at 20km/hr as long as you were on the bus.
Now for the tutorial.
1. Take a pocket financial calculator.
2. Enter -300 as PV for present value, negative because firm pays out cash.
3. Enter 369 as FV for future value.
4. Enter n as 1 for 1 period.
5. Request calculate i. result is 23% which is the % for the period which is 2 weeks.
6. Enter n=26 to say continue at this rate for 26 periods to equal 1 year.
7. Request calculate FV and the result is 65,261. If you gasp in astonishment then welcome to the power of compound interest.
8. Enter n=1. For now the calculator is holding in memory a PV=300 and a FV=65261.
9. Request calculate i. result is 21653% This is the equilibrating interest rate which describes the annual rate of interest reflected in a present value of 300 and a future value of 65,261 over a 1 year time horizon under the terms of the loan. This is the correct "annualized rate of interest".
For those of you who do not have a financial calculator you can use most spreadsheets such as Excel with its built in formulas and arrive at the same conclusion.
For those with only a pocket calculator it is somewhat tedious but here are the steps.
The formula to work with is PV(1+i)**26= FV
The 1+i is 1.23 as the rate per 2 week period is .23 (23%) and the expression must be raised to the 26th power for the 26 such periods in the year.
Enter 1.23 and save it to memory.
Now enter 300 multiply it by the saved 1.23.
The first time you do this you naturally get 369. Now hit multiply and memory recall and = and you get 453.87. Continue doing that for another 24 tedious times and you end up with 65,261 which is the future value.
Now use the same formula with the known PV and known FV and a time period of 1 for one year. It looks like
300(1+i)1=65261
Simplify to
(1+i)=217.53
i=216.53 which is the decimal equivalent of 21653%. Remember 50% is equal to .5 so you must move the decimal right 2 places when moving from a decimal equivalent to a percent.
I would be delighted to serve on the Finance Ministers proposed "task force on financial literacy, which would issue recommendations toward a national strategy toward improving Canadians' understanding of broader financial matters". However it scarcely needs a likely high cost task force tackling a convoluted assignment of "toward", "improving", "understanding", "broader", "matters". Just jump to one obvious conclusion "teach the use of financial calculators in high school".
