The APR: apples to apples

Now let’s discuss what was innovative about the APR back when it became a mandated disclosure, and why it’s so important in allowing you to shop for the best credit deal.

Before you ever heard of the APR, you knew about interest rates.   A lower interest rate is a better deal than a higher rate, right?  So why couldn’t you just compare interest rates and not worry about that APR stuff?

Well, it turns out that “interest rate” is not a precise legal term.  Over the centuries that our commercial system evolved,  different kinds of transactions got in the custom of calculating interest rates in different ways, which eventually got written into the laws that regulated different kinds of sellers and lenders.

The interest rate becomes especially slippery when applied to the most common form of consumer credit — making periodic, or installment, payments to retire a debt or pay off a sale.   To understand this, we will have to do some math.  Bear with me.

Let’s start from the deal we discussed in the last post:  I lend you $100 and you have to pay it back at the end of a year, with a simple interest rate of 6%.  Using the formula  I = P x R x T, where I is interest, P is principal, R is the interest rate, and T is the time expressed in years, you can see that if R is 6%, then I = $6. If you pay me back $106 at the end of the year, everyone would agree that you paid interest at a rate of 6%.

But what if, instead of repaying $106 at the end of the year,  I ask you to repay in monthly installments of $8.83, so that at the end of 12 months I have received my $106.   A bank might call that 6% add-on interest.  Is it the same transaction?  You know that it isn’t, because instead of getting the use of the whole $100 for a whole year, you are giving me part of it back month by month.  This may be advertised as 6% interest, but you can intuit that this is more expensive credit.  But how much more expensive?

Consider a further wrinkle.  What if a loan company offered to lend you $100 at 6% interest,  but deducted the interest up front so that you only got $94 in your hands which you then paid back in monthly installments of $7.83?  That is what used to be called “discount interest.”  As you can intuit, it is even more expensive than add-on interest.

The truest measure of interest is what is called actuarial interest.  This is the measure that takes into account how much you pay for credit relative to the amount of credit you have for the length of time you have it.  The interest rate for APR purposes is the actuarial interest rate.

If you know the rate, you can derive the dollar amount of interest by going step by step, applying the rate to the remaining unpaid principal balance in every payment period,  then adding up the interest paid over the whole life of the contract.   Deriving the rate from the dollar amount is more difficult.  And really, the disadvantage of using an actuarial rate is that no one can do the math in their head.  In the days before calculators and computers, you can see where merchants didn’t want to be bothered by computing interest rates in the most honest and meaningful way.  But nowadays, there is no excuse.

In case you are curious, in the example above, the 6% add-0n interest works out to an APR of 10.9%.  And the 6% discount interest for the same loan represents an APR of 12.2%.

Before the APR, if you wanted to shop for credit, you could consult a bank, a credit union, a small-loan company, and a car dealer.  They would quote you their interest rates, but it would be like trying to compare hotel rates in Toronto, New York, and Sydney without realizing that the “dollars” in question were three different currencies.   Thanks to the APR, everyone now can have an apples-to-apples comparison of finance costs,  no matter who is extending the credit.




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