ON THE MONEY: The vagaries of interest
Interest is a very intriguing topic: it can generate income if you are on the receiving end, or cost you money if you have to pay it. The concept of interest is straightforward: it is the usage fee that a borrower will pay to a lender for the use of the lender’s money.
When you open a savings account at your local bank, you are, in effect, loaning the bank money, and the interest that the bank pays you is a recognition of the fact that you have foregone the use of those funds while the bank has them. In return, the bank will pay you “rent” on your savings in the form of interest. The loss of the use of funds is often called “lost opportunity costs,” or the potential return that you could earn in another investment.
Interest is not the cost of money; rather it is the cost of credit. The money that you lend to another person comprises the principal, and that person has the use of that principal on credit. Simple interest is that rate paid for the use of capital without any reinvestment option.
As an example, assume I loan Jack and Jill $1,000 each to be repaid to me at the end of five years. I decide to charge Jack 8 percent simple interest but charge Jill 8 percent compound interest. In Jack’s case, the interest each year will amount to $80. I earn that same amount each year, and at the end of the fifth year, Jack repays me the principal of the loan plus the interest charge of $400, or a total of $1,400.
In Jill’s example, the charge for the use of the principal is the same $80, but the difference is that, beginning in the second year, the $80 is added to the principal and the interest rate of 8 percent is charged on $1,080, not $1,000. This continuous reinvesting or compounding takes place every year during the term of the loan, and at the end of five years, Jill will owe me $1,469.33.
Albert Einstein once said that compound interest was the most powerful force in the universe, and it is easy to see why. In our Jack and Jill example, if the loan had been for 10 years, Jack would have paid $800 in interest charges, while Jill’s charge would have totaled $1,158.92, more than the original principal.
This compounding function is what has made credit card companies a bunch of money due to financial ignorance on the part of card users.
In our example the compounding took place once each period, but assume that I decide to slip into Jill’s loan agreement a statement that the interest will be compounded daily, even though the loan interest rate remains at 8 percent. In such an example, Jill would owe $1,323.09 in interest charges at the end of the 10 years.
So, as we can see from these examples, the number of compounding periods can dramatically impact the overall cost of the loan. In the case of daily compounding, the annual effective interest rate that Jill paid the example above was not 8 percent, but rather 8.79 percent.
Interestingly, in the computation of annual effective interest rates, the underlying math assumes that the compounding frequency is once each year. To illustrate that point, in the first example in which I charged Jack 8 percent simple interest over five years, the annual effective rate was only 6.99 percent, not 8 percent.
The plot thickens: most of us would jump at the opportunity to earn a 10 percent average rate of return on our retirement investment account. But, averages can be misleading in the case of retirement income. When it comes to generating retirement income, the sequence of investment returns is often as important a factor as are the actual returns themselves.
Using a simple example will help. Two friends each earn an average of 10 percent for three years: one friend earns that amount each year, but the second friend loses 10 percent of his investment in the first year, but earns 20 percent in each of the last two years. Who did better? Assume each started with $10,000. At the end of the third year, the first friend will have $13,331, but the second friend will have only $12,960.
Investment losses that take place early in retirement may negatively impact the ability of an investment portfolio to continue to provide meaningful income that will last a lifetime.