# How to Calculate Bond Prices

*Retired from investment banking and teaching, Philip has written several books on investing.*

Because bonds may be purchased in different principal amounts, a bond's price is quoted as a percentage of par. “Par value” or “face value” is the value of the bond printed on the bond certificate. It is the value used to calculate interest payments and the value of the principal paid to the bond holder at maturity, or the current price per $100 of principal. Let's see how we would quote the price of a bond with an invoice price of $963,701.

The price quoted for this bond in the market would be 96.370. From this point on in the article, prices will be quoted as a percentage of par, as shown below.

The fractional portion of the price of many bonds, such as U.S. Treasuries, is quoted in thirty-seconds of a percent, as shown below. The price we just calculated would therefore be quoted like this. Notice that a hyphen is used to separate the fractional part when it’s in thirty-seconds.

A U.S. Treasury bond has a calculated price of 102.1875. We would quote the price in the market as 102 plus a fraction:

0.1875 = 6/32, so

102.1875 = 102 6/32 = 102-06

If we are talking about a standard fixed-rate bond, we can treat the coupon stream as an annuity—that is, a series of evenly-spaced equal payments—and use this formula. The first part of the formula gives the present value of the coupon payments; the second gives the present value of the final principal payment.

We will use the formula to calculate the price of this bond. By the way, since price is always quoted per $100 of principal, we can simplify our calculations by using $100 as the principal amount. The calculation will then give us the price directly.

Bond: $1,000,000 U.S. Treasury note

Matures in 4 years

5% semi-annual coupon

Yield to maturity: 6.5%

CPN = 2.50, PRN = 100, n = 8, i = .065/2 = .0325

Price
= 2.50__( 1 - (1 + .0325)__^{-8} )
+ 100(1 + .0325)^{-8 } = 94.790^{}

.0325

Let's try another one.

Bond: Matures in 4 years

4% annual coupon

Yield to maturity: 5%

CPN = 4, PRN = 100, n = 4, i = .05

Price = 4( 1 - (1 + .05)^{-4} ) + 100(1 + .05)^{-4 } = 96.454

.05

Now let's look at a trade. A trader purchases a $1,000,000 bond at 98-12. Later that day, she sells the bond at 98-28. How do we calculate how much profit she has made?

Sold at 98-28 = 98.875

Purchased at 98-12 = __98.375__

Profit per $100 = .500

Total profit = (1,000,000/100) x .5 = $5,000

Finally we musn't forget the relationship between bonds and interest rates and bond yields and price.

$1,000,000 U.S. Treasury bond with 7.25% coupon

Matures in exactly 15 years

Purchase price: 91.484 @ 8.25% yield to maturity

If the yield for bonds of this type increases to 8.40%, the value of this bond will decrease. The relationship between bond price and bond yield is inverse.

*This article is accurate and true to the best of the author’s knowledge. Content is for informational or entertainment purposes only and does not substitute for personal counsel or professional advice in business, financial, legal, or technical matters.*

## Comments

**Philip Cooper (author)** from Olney on March 25, 2012:

I'm glad it was of help. Thanks for dropping by.

**louromano** on March 25, 2012:

Woe. Fantastic hub. Great info.

**Philip Cooper (author)** from Olney on March 08, 2012:

Thank you for dropping by.

**JR Krishna** from India on March 07, 2012:

Very informative hub!

Thanks for sharing

**nuwan** on October 31, 2011:

I'm a student,You are?

**Philip Cooper (author)** from Olney on April 03, 2011:

Thank you chamilj

**chamilj** from Sri Lanka on April 03, 2011:

Useful investment education.

**Philip Cooper (author)** from Olney on February 18, 2011:

Thank you...glad you liked it.

**AllSuretyBonds** on February 17, 2011:

Great Hub. This is very informative information.