## Monday, June 9, 2008

### Real Interest Rates

You’d think that a 6% interest rate means that you’d be charged \$6 in interest on a \$100 loan after one year, but this isn’t true. You’d actually be charged more. The difference has to do with compounding periods. It’s not hard to calculate the real interest rate being charged, but for some reason, banks aren’t required to tell the truth about interest rates.

For loans in the US and non-mortgage loans in Canada, interest is compounded monthly. For most mortgages in Canada, interest is compounded twice a year. I’ll explain Canadian mortgages first because they are a little easier to follow.

If you get a 6% mortgage in Canada, it is really 3% interest every 6 months. This means that without any payments, your outstanding debt is multiplied by 1.03 after 6 months. After a year, it has been multiplied by

1.03 x 1.03 = 1.0609.

This means that the real yearly interest rate being changed is 6.09%, not 6%. So, what? The difference looks small. Well, over the life of a 25-year \$200,000 mortgage, you’d pay an extra \$3100 in interest because of this small difference.

In the US, things are even worse. A published mortgage rate of 6% per year really means 0.5% per month. After a year, this compounds out to 6.17%. Over the life of a 25-year \$200,000 mortgage, you’d pay an extra \$5800 in interest because of this difference.

These examples are based on the current low interest rates. What if mortgage rates were at 12%? Over the life of a 25-year \$200,000 mortgage, Canadians would pay an extra \$14,000 and Americans an extra \$27,000 because of the extra compounding.

Monthly compounding is used in both countries for most non-mortgage loans. If you maintain a \$10,000 balance on a credit card for 25 years with 20% interest, you’ll pay an extra \$4000 in interest because of the extra compounding.

Many department store credit cards claim that the interest rate is 28.8%, but this is really 2.4% per month which compounds to about 33% per year!

I assume that this form of legalized lying is permitted because of historical precedent. I’d like to see it stop, but I won’t hold my breath.

1. This effect you comment on has nothing to do with lying about interest rates. The reason for the increase that if you don't pay the interest you owe more money so the same rate results in higher interest.

ex.
\$100 at 6% after 6 months interest is due, if you don't pay, your balance is \$103 for the next six months you pay 6% on \$103 which is \$3.09. You pay the interest rate that they say on the money that you owe.

What you are hoping for is Annual Percentage Yield, they have that some places.

2. Derek: You're not right about this. 3% every six months means the same thing as 6.09% per year. To advertise a rate of 6% per year, the interest after 6 months should be about 2.96% (the rate that compounds twice to 6%).

Banks switch back and forth between simple and compound interest in a way that increases interest paid. Just because we have become used to this doesn't make it honest.

It is true that Annual Percentage Yield (APY) is (usually) used to mean the truthful yearly interest rate. There is little excuse for not using this real interest rate all the time.

3. There is nothing dishonest about using the mathematically correct definition of rate.

The reason you pay more then \$6 is because you owe more than \$100 for the last six months. Not because the interest rate is higher.

4. Derek: There is nothing mathematically correct about this definition of rate. You could just as easily look at it on a monthly basis and decide that the interest is 0.5% per month. Then the total amount owed after a year would be \$6.17 instead of \$6.09.

The fundamental problem is that when you go from 6% per year to either 3% per half year or 0.5% per month, you are assuming that simple interest is being used. Then when applying this rate, interest is compounded. This is not honest.

The only kind of interest that makes any sense is compound interest. Compound interest should be applied when computing interest over a shorter interval. Using 6% per year is the same as 2.96% per half year or 0.487% per month.

Jumping back and forth between simple and compound interest to pump up the amount owed is dishonest.