1 – Time Value of Money and Interest Rates

Time Value of Money and Interest Rates

The most fundamental idea in finance is that a dollar received today is worth more than a dollar received tomorrow. Why?  Because you can loan your money to someone else and earn interest.

Interest Rates

We’ve all heard of interest rates, but most of us only know them with regard to how expensive a loan is.  Interest is the cost of renting someone else’s money. In a formula, the interest rate is represented by a lowercase “r”.

Fun Fact: The “percent” in interest rates comes from “Per Cent”, as in “Per 100”.  Centum is Latin for 100.  So when you hear that mortgage rates are at 4%, you’ll know that it means 4 per 100, or “I owe this freaking bank $4 per year because they loaned me $100.” 

A lot of thought (and math) goes into interest rates, but for the sake of simplicity we will only worry about one rate: The 10-year U.S. Treasury rate.  This interest rate is the amount you can earn by lending money to the U.S. government for 10-years by purchasing a treasury bond.  This rate is also known as the risk-free rate because payment is guaranteed by the U.S. government; there is no risk.  At the time of this writing, the annual interest rate for the 10-year treasury was 1.75%.  This means that my $100 investment today, would earn me $1.75 next year, and $1.75 the year after, and $1.75 the year after that, etc., until the 10th year when I’m paid my final interest payment of $1.75, and I get my original $100 back.  The U.S. Government will rent our money for 1.75% per year for ten years, then give us our money back.  Not too bad!

Risk Premium

So, if the government can rent our money for 1.75%, why does the bank charge you 4% to rent their money when taking out a mortgage?  I’m sorry, dear reader, but your credit score is not the same as Uncle Sam’s; you are much riskier to lend to.  This increase in interest rates reflects the extra risk in loaning money and is called the risk premium.  If the risk-free rate is 1.75%, and my interest rate is 4%, then I’m paying a risk premium of (4% – 1.75%) = 2.25%.  The risk premium is responsible for the large variety of interest rates on different loans.  (There are other premiums as well: Time-to-maturity premium, inflation premium, etc., but the risk premium is a big one).

Definition: When a borrower doesn’t pay their interest on time, they are in default, or, they have defaulted on their loan.

Let’s pretend Warren Buffett wants to borrow $10 from you.  How much interest would you charge him?  Given that he is one of the wealthiest individuals on the planet, and has a reputation for integrity, we could safely say that loaning money to Warren involves very little risk.  We could charge him 1.75%, the risk free rate.  Now, pretend that your neighbor, Chuck Poorhouse wants to borrow $10.  Now Chuck just lost his job and defaulted on all of his loans.  What kind of risk premium would you attach to your loan to Chuck?  Probably quite a lot, say 25%?

Time Value of Money

Getting back to the time value of money, money received today is worth more than money received next year (or tomorrow for that matter), because money received today can be loaned out and we can earn interest.  The value of time is reflected in the risk-free rate.

Given an interest rate of 1.75% (or $1.75 per $100), there is no difference between getting paid $100 today and $101.75 next year. The value is the same.  However, given an interest rate of 1.75%, $100 today and $100 next year is not the same!  By getting paid $100 next year, we have foregone interest income of $1.75.

This idea, that time has value, is fundamental to finance.

Fun Fact: We now know that interest is simply the rent one pays for using someone else’s money.  But interest used to be called usury, and usury was not allowed by the Christian or Islamic Faith.  The Jewish religion, however, did allow usury (at least when loaning money to Christians and Muslims).  This is one reason why Jews rose to prominence in the world of banking and finance, and perhaps why they were so hated and discriminated against by their neighbors.