Borrowers are sellers

Notice what happens when we look at the market in this way. Buyers have become sellers, and sellers have become buyers. Borrowers are sellers: they sell the promise to pay. Lenders are buyers: they purchase the promise to pay. If we are looking at the same group of buyers and sellers as before, then the current equilibrium price of this asset would be $100. The nominal interest rate and the nominal rate of return defined through these two markets must be the same. If not, there would be an arbitrage possibility. Imagine, for example, that the interest rate is 5 percent but the price of the asset is $90. In this case, the rate of the return on asset is 11090−1, which is 22.2 percent. So you could make a lot of money by borrowing at a 5 percent interest rate and then purchasing the promises to pay $110 at price of $90. If you could do this, so also could many major financial institutions—except that they would operate on a much larger scale, perhaps buying millions worth of assets and borrowing a lot in credit markets. So the demand for credit would shift outward, as would the demand for assets. This would cause the interest rate to increase and the asset price to increase, so the rate of return on the asset decreases. This would continue until the arbitrage opportunity disappeared. In summary, we would say there is no arbitrage opportunity when the nominal rate of return on asset = nominal interest rate. The rate of return on the asset, in other words, is equivalent to the interest rate on the asset. Equivalently this means that

price of asset = repayment amount

1 + nominal rate of return on asset

= repayment amount

nominal interest factor .

In the second line we replaced (1 + nominal interest rate) with the nominal interest factor. The two are equivalent, but sometimes we find it more convenient to work with interest factors rather than interest rates. The argument that we have just made should seem familiar. It is analogous to the argument for why there cannot be distinct dollar-euro and euro-dollar markets; they are just ways of looking at the same asset. Likewise, we can think of the sale of any asset as equivalent to borrowing, while for any example of credit we can also think of there being an underlying asset. Different Assets Very often economists and others talk about “the” interest rate, as if there were just a single asset in the economy. In fact, there are many different assets that you could buy with your $100, each with an associated interest rate.