www.bloomberg.com /markets/

Under "Rates & Bonds," you can access information on key interest rates, U.S. Treasuries, Government bonds, and municipal bonds.

savings account that earns interest and have more than a dollar in one year. Economists use a more formal definition, as explained in this section.

Let's look at the simplest kind of debt instrument, which we will call a simple loan. In this loan, the lender provides the borrower with an amount of funds (called the principal) that must be repaid to the lender at the maturity date, along with an additional payment for the interest. For example, if you made your friend, Jane, a simple loan of $100 for one year, you would require her to repay the principal of $100 in one year's time along with an additional payment for interest; say, $10. In the case of a simple loan like this one, the interest payment divided by the amount of the loan is a natural and sensible way to measure the interest rate. This measure of the so-called simple interest rate, i, is:

$100

If you make this $100 loan, at the end of the year you would have $110, which can be rewritten as:

$100 X (1 + 0.10) = $110 If you then lent out the $110, at the end of the second year you would have: $110 X (1 + 0.10) = $121

or, equivalently,

$100 X (1 + 0.10) X (1 + 0.10) = $100 X (1 + 0.10)2 = $121 Continuing with the loan again, you would have at the end of the third year: $121 X (1 + 0.10) = $100 X (1 + 0.10)3 = $133 Generalizing, we can see that at the end of n years, your $100 would turn into:

The amounts you would have at the end of each year by making the $100 loan today can be seen in the following timeline:

Today Year Year Year Year

This timeline immediately tells you that you are just as happy having $100 today as having $110 a year from now (of course, as long as you are sure that Jane will pay you back). Or that you are just as happy having $100 today as having $121 two years from now, or $133 three years from now or $100 X (1 + 0.10)n, n years from now. The timeline tells us that we can also work backward from future amounts to the present: for example, $133 = $100 X (1 + 0.10)3 three years from now is worth $100 today, so that:

$133

The process of calculating todays value of dollars received in the future, as we have done above, is called discounting the future. We can generalize this process by writing

Four Types of Credit Market Instruments today's (present) value of $100 as PV, the future value of $133 as FV, and replacing 0.10 (the 10% interest rate) by i. This leads to the following formula:

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