## Monday, January 4, 2021

### The Myth of Simple Interest on Loans

A persistent myth is that you don’t pay compound interest on installment loans, such as mortgages, car loans, and other personal loans.  I’ll show that this is nonsense.

One example of this myth comes from an Investopedia article on car loans: “Auto loans include simple interest costs, not compound interest.”  The reasoning is that if your payments cover all the interest that accrues each payment period, then there is no opportunity to build interest on top of interest.

However, money is fungible.  Why can’t we think of each payment as going against principal and leaving the interest owing?  Then there would be interest building on top of interest.  We could also think of payments applied proportionally.  For example, if a payment represents 5% of the remaining amount owed, we could think of the payment covering 5% of the remaining principal and 5% of accrued interest.  This proportional method is the most useful way to think about how payments apply, but arguing about which way of thinking about payments seems most correct won’t get us anywhere.

Let’s look at a practical question.  How much do you benefit when you make an extra payment against a loan?  Suppose you have a 4-year \$30,000 car loan at 6%.  The monthly payment works out to \$704.55.  After a year of payments, your remaining debt will be \$23,159.31.

What if you had put an extra \$1000 down on the car in the beginning, but you decided to leave the payments at \$704.55 per month so you’d have it paid off in less than 4 years?  Your starting debt would have been only \$29,000.  After a year of payments, the remaining debt would be \$22,097.64.

The difference between the debt after a year in the two scenarios is \$1061.68.  Somehow, you’ve saved \$61.68 instead of the \$60 that you’d expect to save with a 6% simple interest calculation.  Not coincidentally, if we compound 0.5% interest for 12 months, the annual rate is 6.168%, which exactly matches the savings you get from putting an extra \$1000 down on the car.

I’ve shown that when you make extra payments against a loan, the benefits you get are based on compound interest.  This is because you are paying compound interest on the loan.  Any useful way of looking at installment loans leads to the same conclusion: the interest compounds.