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Interest Rates
Interest rates are determined by the demand for loans and the supply of loans (as we discussed in chapter 5)

Real Interest Rates
The amount of growth or interest quoted to you by your friendly neighborhood bank (or loan shark) in money terms is the Money or Nominal Interest Rate. But, underlying that is a real interest rate, that reflects the opportunity cost of lending to you. The nominal interest rate also includes an additional factor for inflation, sometimes called the "inflationary premium."

So (approximately) the nominal interest rate, real interest rate and expected or anticipated inflation rate are related by the formula

Nominal interest rate = real interest rate + inflation (expected)

As time passes, and the actual inflation that occurs is observed, the relationship becomes

Nominal interest rate = actual real interest rate + actual inflation

If you wanted to figure out the real interest rate from the nominal interest rate you are charged and the actual amount of inflation that occurs, you could use the formula

actual real interest rate (real rate of return, yield) =
nominal interest rate - actual inflation

The real interest rate includes such things as the risk that the money won't be repaid, and the rate of preference for things in the present over receiving things in the future, called the rate of time preference.

Interest Rates, Assets, and the "Money Time Machine"

Interest rates reflect more than just how much you have to pay back when you borrow. They also help us realize that money values change over time. Since any money you have could be saved or invested and thus earn interest over time, decisions involving money and spending over time are related to the interest rate. In a way, the interest rate is part of a "money time machine." It helps us to evaluate values of things over time.

To see this, suppose you were to put some money (called the "principal") into an interest bearing savings account today. The amount of money you would have in a year can be found by computing

principal + principal times interest rate =future value

Since the money you are putting into the account now is the amount you have now, we call it the "present value." Thus, this calculation could be written

present value + (present value x interest rate) =future value

Or, if we abbreviate "present value" as PV, "future value" as FV, the interest rate as i,

PV + (PV x i) =FV

Doing a little algebra (trust me if you don't like to think about such things) gives us the formula in a handy form

PV (1+ i) = FV

So far, we've just gone from the present to the future using the interest rate. If we waited a year, we would have the amount in the formula above.

But suppose we want to bring some future amount of money, to be received in one year, into the present. We can just divide both sides of the formula by (1+i) to get

Asset Values

An item that a person owns and that gives the person benefits, either now or in the future, is called an asset. The present value of an asset that gives the person future value is inversely related to the interest rate, as can be seen from the formulas above.

One application of this is an asset known as a bond. A bond is a promise to pay some future value; it is simply an "I.O.U." for some future payment. However, its present value or price will be inversely related to the interest rate, since the formula relating present values to future values and the interest rate will apply. So

bond values in the present or bond prices are inversely related to interest rates

Going on Forever (Practically)

Suppose that we have a piece of property or other asset that lasts (practically) forever, and gives us some benefit or income for as long as we could possibly want. Technically, this would be called a "perpetuity."

"perpetuity" means it goes on forever

A valuable piece of real estate or other asset that gives a particular benefit to its owner every year forever, or nearly forever, will have a present value described by a special (and simple) formula: