In the previous page I introduced the compound interest formula that can be used to determine how a lump sum present value will accumulate into a specific future value. The amount of the accumulated future value depends upon the size of the initial present value, the number of compounding periods and very importantly the interest rate. Since interest rates are such an important variable in all time value of money applications, I thought it would be a good idea to look at how interest rates are established in various commercial contexts.
In our modern environment we are thoroughly used to paying interest on home loans, student loans and credit card balances. We are also thoroughly used to receiving interest income on our savings account balances, though lately not very much interest. It may then strike you as very interesting that charging borrowers any rate of interest on borrowed funds was considered a sin in virtually every major religious tradition. Why would this be so?
Well, the idea seems to be that making a loan to someone in need is fundamentally a charitable act and profiting from a charitable act sort of defeats the purpose. Over time the idea of collecting interest on a debt became more acceptable by invoking the concept of an opportunity cost. If someone lending you money would have had the opportunity to earn some positive return in the form of interest income or profit from some business investment, then it was only fair that the borrower compensates the lender for the income foregone when the loan was made.
In modern societies the ethical issue has shifted from banning the charging of interest to the enforcement of laws barring excessive interest on loans. Most countries have upper bound usury laws that prohibit interest rates above a certain amount. Each state in the U.S. has separate laws prohibiting charging interest rates above a certain amount. The maximum allowed rates vary, but most set limits no greater than 15%, and many set the maximum at a far lower level.
However, there are so many allowable exceptions to these laws that for all intents and purposes these upper bounds might as well not be on the statute books at all. Credit card companies based in a state that allows a high rate of interest on credit card balances can charge customers living in a state that has a lower interest rate limit at the higher rate.
Payday loan and auto loan companies have often worked around the upper limits set by usury laws. These companies operate to some extent in “free” markets where supply and demand for credit should yield lower interest rates. But most of these companies effectively operate as cartels keeping interest rates artificially high.
Perhaps the most important interest rates in modern economies are determined not directly by market forces but by fiat through the actions of powerful central banks. In the United States the Federal Reserve Bank (The Fed) sets benchmark interest rates that chartered banks apply in making interbank loans. Interbank loans are necessary when banks have shortfalls in their required reserves and borrow from banks who have excess reserves.
The Federal Reserve also sets a discount rate which is the interest rate that it charges when it makes direct loans to banks. The Federal Reserve indirectly impacts interest rates through control of the money supply as well. When the money supply is expanded interest rates fall, when the money supply is contracted interest rates rise.
The Fed’s decisions on setting specific interest rates and interest rate targets are dictated by policy goals designed to keep the overall economy healthy. In the broadest terms a healthy economy is one in which the currency does not undergo significant inflation or deflation and the unemployment rate does not reach high levels. There is a broad consensus that national economies should grow at sustainable rates and avoid excess contractions.
Due to the great recession of 2007 and 2008 Fed targeted rates have declined significantly over historical averages. The Covid induced economic contraction has forced the Fed to bring down its interest rates to near zero. The lowering of interest rates has brought all-time lows in mortgage interest rates and commercial lending rates but has reduced yields on traditionally very safe fixed income investments like CDs and government bonds.
Given that interest rates can vary widely over time and in different economic contexts anyone performing time value of money formulas must give some careful thought to the reason a specific interest rate is chosen. Due to compounding effects even small differences in selected interest rates can produce large swings in time value of money calculations. The table below shows the difference in accumulated future balances over ten years starting with a $10,000 balance with monthly compounding.