The interest rate is the price that people pay for borrowing money. It is also the price that businesses or people receive for lending money.
The nominal interest rate is the interest rate that banks list as their lending rate. The real interest rate is the nominal rate minus the inflation rate. If a bank charges an interest rate of 10%, and the inflation rate is 8%, then the bank generates interest of 2% in real terms.
Interest Rate Determination
In a free market, interest rates are determined the same way as prices of goods and services. In the graph below, the demand and supply of loanable funds (loans) intersect at an equilibrium interest rate of 8% and an equilibrium quantity of loanable funds of 200.
If the demand for loanable funds increases, interest rates increase, and vice versa. If the supply of loanable funds increases, interest rates decrease, and vice versa. The graph below illustrates the effect of an increase in loanable funds demand on the equilibrium interest rate.
In free market economies, general interest rates vary with changes in supply and demand. The interest rate on a specific loan also varies based on the risk and the cost of making the loan. If a lender has evidence that the borrower is very likely to pay back the loan, then the interest rate will be lower. If the lender does not find the borrower credit-worthy, the interest rate will be higher. The length of the loan also affects the risk. The longer the loan term, the more risky it is and, therefore, the higher the interest will be. The cost of making the loan affects the interest rate. A small loan is more expensive relative to the interest earned, and the lender will charge a higher interest rate.
Present Value
Would you rather have $1,000 now, or $1,000 one year from now? Most people prefer $1,000 now. Would you rather have $1,000 or $1,050 one year from now? This is a little more difficult to decide. How much is $1,000 worth in one year? If you were to invest $1,000 at an interest rate of 6%, then you would have $1,000 + ($1,000 x .06) = $1,000 + $60 = $1,060. From a purely financial perspective, if the interest rate is 6%, $1,000 now is the same as $1,060 one year from now. We say that the present value of $1,060 received in one year is $1,000.
The formula for the present value (PV) of any future amount (F) is
PV = F / (1 + i) nSo the present value of a sum of money equals the future value of money you expect to receive, divided by 1 plus the interest rate to the power of n. Here, i is the market interest rate per period of time, and the exponent n is the number of periods (for example, years) we have to wait to receive the future amount.
Example 1
Problem: Let’s say that someone promises to pay you $2,000 one year from today. Assume a yearly market interest rate of 6%. What is the present value of this amount?
Solution: PV = $2,000 / (1 + .06) 1 = $2,000 / 1.06 = $1,886.79.
Example 2
Problem: Let’s say that someone promises to pay you $2,000 two years from today. Assume a yearly market interest rate of 6%. What is the present value of this amount?
Solution: PV = $2,000 / (1 + .06) 2 = $2,000 / 1.1236 = $1779.99.
What was the Price of a Gallon of Milk 80 Years Ago?
Example 3
Problem: Let’s say that the price of a gallon of milk is $3 this year. Assume that the price of a gallon of milk has increased by 3.5% each year since 80 years ago. What must the price have been 80 years ago?
Solution: The present value formula can be used with price increases instead of interest, as well. Using the present value formula from the previous paragraph, $3 today equates to the following 80 years ago:
$3 / (1 + .035) 80 = $3 / 15.68 = $.19
Another way of saying this is that if the price of a gallon of milk increased by 3.5% each year (this is relatively accurate for the inflation rate in the United States of the past 80 years) a gallon of milk that is $3 now, was 19 cents 80 years ago.
For a video explanation of how to calculate the present value of a future sum of money, please watch:
The United States Bureau of Labor Statistics has a handy calculator to equate the buying power of any dollar amount in a previous year, using the consumer price index as a measure of the yearly inflation rate. Click HERE to use this BLS inflation calculator.
