If you’ve ever saved or borrowed money, you are familiar with interest rates. There are thousands of different interest rates. Some of them are related to personal finance, like the interest rate on a savings account or the interest rate on a credit card. Other interest rates are related to government finance, like the 10-year Treasury yield. And the world of corporate finance includes a range of interest rates from investment grade to high yield.

Interest rates are the price of moving money across time.

Some people have more money than they need for their current spending. These people who save their money for future spending are savers. Other people do not have enough money for their current spending. These people who borrow money are borrowers. Savers want to push money into the future and borrowers want to pull money into the present. The world of finance provides a conduit that connects savers and borrowers.

Money today is worth more than money tomorrow. Why is that? Money is like a tool that can be used to accomplish certain goals. If you need a tool to do something today, you are willing to pay for it. This is why borrowers pay to borrow money. The money that the borrowers borrow is the money that the savers save. You can think of borrowers as buying money from savers. Borrowing and saving are two sides of a transaction — the borrowers are buying money and the savers are selling money. An interest rate is the price of this transaction. Interest rates are the price of buying or selling money for future repayment.

The time value of money measures the cost of moving money across time. When the time value of money is high, it is more costly to pull money into the present. When the time value of money is low, it is less costly. The time value of money can change. Sometimes it is high and sometimes it is low. Interest rates measure the time value of money. When the time value of money is high, interest rates are high. Low time value of money means low interest rates.

The time value of money tends to increase in a growing economy and decrease in a slowing economy. This is driven primarily by the demand for money. In a growing economy, there are more opportunities for using money (as a tool) so there is greater demand for money. In other words, there are more people who want to borrow money to pull into the present. Their increased demand for money increases the price of borrowing money. This is an increase in the time value of money. This is why interest rates tend to rise in a growing economy. In contrast, there are fewer opportunities for using money in a slowing economy so there is less demand for money. The time value of money declines, which is why interest rates tend to fall in a slowing economy.

The terms present value and future value are connected by interest rates. Let’s start with the perspective of a saver:

FV = PV * (1 + i)

The future value (FV) of the amount saved equals the present value (PV) multiplied by 1 plus the interest (i). In other words, the saver receives back the principal plus interest. This is the one-period saving model. Suppose the saver saves their money for two periods. Then the equation is:

FV = PV * (1 + i)²

The saver earns interest on the principal in the first period and then earns interest on the principal as well as the first-period interest in the second period. This is called compound interest. Because the interest in each period is earned on the growing amount from the previous period, this is called compound interest. With compound interest, the savers money will start to grow exponentially over time.

The perspective of the borrower is simply the flip side of the saver. We can arrange the saving equation to be the following:

PV * (1 + i) = FV

The borrower borrows the present value (PV) and pays interest on that amount, which equals the larger amount of the future value.

Hopefully these examples make sense in terms of personal finance. Interest rates are money earned by savers and the money paid by borrowers. However, we can transition from personal finance to corporate finance by using this same equation in a slightly different form. Rearranging the previous equation, we have:

PV = FV / (1 + i)

This is the most basic present value formula. It shows how the value of money that will be received one period in the future can be converted into present value. The interest rate is in the denominator on the right hand side, dividing the future value. Here we can see how the interest rate serves as a discount factor in the present value calculation. Recall that interest rates measure the time value of money. When interest rates are high, the time value of money is high and the discount factor is large. This means that the future value (FV) will be discounted more when converting it to present value (PV).

We can also rearrange the two-period compounding formula to the following:

PV = FV / (1 + i)²

This is the formula for discounting a future value that is two-periods in the future. It shows that money received in two periods is discounted more than money received in one period. The time value of money implies that money received further in the future will be discounted even more than money received in the near future.

The concept of interest rates as discount factors is a fundamental building block of asset pricing. Think of the future value (FV) as future cash flows from a financial security. For a stock, this could be expected dividends and, for a bond, this could be coupon payments. Interest rates are the discount factor that discounts those future payments to the present. This makes this formula the basis of the discounted cash flow (DCF) model.

Now think about how the level of interest rates affects security prices. When interest rates are high, future cash flow is discounted more, meaning it is worth less today. Therefore, high interest rates mean low present values. In contrast, low interest rates mean high present values. This illustrates how interest rates have a powerful influence on asset pricing. High interest rates mean lower asset prices and low interest rates mean higher asset prices.

If you recall, central banks set short-term interest rates. Raising rates is a form of monetary contraction and lowering rates is a form of monetary stimulus. When the central bank raises rates, this tends to lower asset prices, and when the central bank lowers rates, this tends to raise asset prices. In the current environment of ultra-low interest rates, this could be considered a significant factor in stock prices being high.

One final aspect of interest rates to keep in mind is the role of inflation. Inflation changes the value of money over time, so it clearly needs to be factored in to an interest rate. The value of future cash flow will depend on the purchasing power of that cash in that future. When inflation is high, the purchasing power of cash is declining at a high rate. Therefore, investors are most interested in the real value of that future cash flow.

The Fisher Equation is a simple way of decomposing interest rates into two components:

i = r + π^e

This equation shows that nominal interest rates (i) equal real interest rates (r) plus expected inflation (π^e). “Nominal” means observed. In other words, nominal interest rates are the interest rates that we see in the financial system. They are the interest rates written into contracts and priced into markets. These nominal interest rates include expected inflation. This makes sense if you think about inflation as an erosion of purchasing power in future cash flows. If expected inflation is high, then nominal interest rates will be high. Nominal interest rates include expected inflation as a way of compensating the saver for inflation. The “real” interest rate is the nominal interest rate net of inflation. The Fisher Equation can be rearranged as

r = i – π^e

to calculate the real interest rate.

Treasury Inflation Protected Securities (TIPS) are U.S. Treasuries whose coupon payment is adjusted for inflation. In this way, they provide a “real” interest rate. The difference in yield between Treasuries and TIPS is used as a measure of inflation expectations.

This concept of interest rates and inflation highlights the importance of inflation to the investment world. Inflation is not just something that changes the price of goods for the consumer. It is a factor that changes the value of money over time. In the world of discounted future cash flows, this is extremely important. Stable inflation expectations (π^e) are critical to a smoothly functioning financial system. This also highlights how inflation is a risk factor in investing. If inflation is higher than expected, then the value of future cash flows will be lower than expected. This is especially important in the bond market, where the value of fixed-income securities will rise and value with the changing outlook for inflation.