APR in May

From Jeff Schwarz: “While researching home equity loans for my mom, I noticed that banks advertise percentage rates for the loan and a different, higher number, for the Annual Percentage Rate. What is that? And what’s the difference (please don’t answer ‘About half a percent.’).”

There are a lot of ways of calculating interest, especially as it can be compounded annually (8% on $1,000 is $80 interest) or quarterly ($82.43) or monthly ($83) or daily ($83.28) or even “continuously” ($83.29). And most financial institutions use a 360-day year, but some might want to use 365 days. And in the old days, there were even more games that could be played to keep you from understanding – and being able to meaningfully compare – interest rates, whether you were borrowing or putting money in a savings account.

The Truth in Lending Act changed all that. I forget exactly what the rules are for calculating the Annual Percentage Rate, but the nice thing is: That’s not the point. The point is that you can rest assured it’s calculated the same way by everyone, so that you can confidently compare the APR.

Not clear on compounding? Well, the first part is easy: 8% compounded annually is clearly $80 on $1,000. But quarterly means you’d get $20 the first quarter and then earn 8% on $1,020 – not just $1,000 – in the second quarter, and thus earn $20.40. So the third quarter you’re earning interest on $1,040.40 – $20.81. Get it? And daily compounding gives you (or the lender) even a little more juice.

And while we’re on the general topic:

From Phil Martino: “I read one of your articles many years ago and have never forgotten it. It was the one about if you borrowed $1000 from a friend and paid him back at $100/month for 12 months, how much interest did you pay? I have asked dozens of people over the years that question. Like you said, a lot of intelligent people say 20%. It is a lesson I’ll remember for life. Thanks.”

Not quite clear why this has proved particularly helpful to Phil, except that it may have won him some barroom bets. The answer of course (drinks on me!) is that if you paid the full $1200 all at once at the end of the loan – returning the $1,000 and paying $200 interest for the right to have used $1,000 for a year – then you did indeed pay 20% interest. But the fact is, you borrowed $1,000 for just one month. Then, having repaid $100 (some of which was interest, some principle), you borrowed less than $1,000 – and less still each month that followed. So you paid $200 to borrow, on average, less than $1,000 for the year. In this case, the interest rate works out to about 35%.

Hard to calculate on your fingers and toes? Indeed. And that’s why the Truth in Lending Act and APR are so useful.