# An Equation for the Value of a Bond at Maturity i Comstock Images/Comstock/Getty Images

Calculating the value of a bond at a particular point in time usually requires a tricky equation involving the bond's face value, coupon rate, yield to maturity and coupon payment schedule, as well as the time remaining until maturity and the time remaining before the next coupon payment. (Deep breath.) Here's the good news: If you're looking for the value of a bond at maturity, you can ignore most of that stuff.

## How Bonds Work

Every bond has a face value (most commonly \$1,000, but it could be anything). You receive the face value on the bond's maturity date. Between purchase and maturity date, most bonds -- but not all -- will pay you interest. The interest you earn is determined by the bond's "coupon rate." A five-year \$1,000 bond with a 9 percent coupon rate, for example, will pay you \$90 a year. Most bonds pay semiannually, meaning you'll get your \$90 in two \$45 payments, six months apart. When the five years are up, you get the \$1,000 face value.

## Present Value

The value of a bond at any particular moment is the "present value" of all the payments that bond will produce: the remaining coupon payments and the face-value payment at maturity. The present value is how much that future payment is worth in today's dollars. And the rate you use to convert the future payments to present value is the bond's "yield." Say you paid \$1,000 for that bond discussed earlier. The \$90 you get in interest each year represents a 9 percent annual return on your money. So your yield is 9 percent -- same as the coupon rate. But if you'd paid \$950 for the bond, the 10 semiannual payments of \$45 and the \$1,000 face value payment at maturity would, taken together, represent an annual return of roughly 10.3 percent. That's the yield.

## Maturity Payment

Now that yield's been explained, don't worry about it. The point was to show that to determine the value of a bond, you usually have to adjust the future payments to present value using the yield as your "discount rate." But guess what? On the bond's maturity date, there are no more "future payments." If the bond is maturing today, then you're going to get the \$1,000 face value today. The present value of that \$1,000 payment is ... \$1,000. But there's still one more thing to consider.

## Final Coupon Payment

With the typical bond, the final coupon payment will also be due at maturity. In the preceding example, you'd get your final \$45 interest payment on the maturity date. And since you're calculating the value of the bond on the maturity date, you don't have to adjust that amount, either, because it's already at present value. So, to wrap things up, an equation for the value of a typical bond at maturity is:

(CR/2 x FV) + FV

"CR" is the coupon rate. You divide it by 2 because each coupon payment is half the annual rate. "FV" is the face value.

In the example, the math works like this: (0.09/2 x \$1,000) + \$1,000 = \$1,045.

## Other Bonds

The equation works even for "zero-coupon" bonds -- those that don't make interest payments. Since the coupon rate is zero, "(CR/2 x FV)" is also zero, so the value at maturity is just the face value. For bonds with annual rather than semiannual coupon payments, replace "(CR/2 x FV)" with "(CR x FV)." For bonds with irregular coupon payments, replace "(CR/2 x FV)" with the dollar amount of the final coupon payment.