How to Calculate Bond Prices

Updated on May 5, 2020
one2get2no profile image

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


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


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.


    0 of 8192 characters used
    Post Comment
    • one2get2no profile imageAUTHOR

      Philip Cooper 

      8 years ago from Olney

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

    • louromano profile image


      8 years ago

      Woe. Fantastic hub. Great info.

    • one2get2no profile imageAUTHOR

      Philip Cooper 

      8 years ago from Olney

      Thank you for dropping by.

    • thumbi7 profile image

      JR Krishna 

      8 years ago from India

      Very informative hub!

      Thanks for sharing

    • profile image


      8 years ago

      I'm a student,You are?

    • one2get2no profile imageAUTHOR

      Philip Cooper 

      9 years ago from Olney

      Thank you chamilj

    • chamilj profile image


      9 years ago from Sri Lanka

      Useful investment education.

    • one2get2no profile imageAUTHOR

      Philip Cooper 

      9 years ago from Olney

      Thank you...glad you liked it.

    • AllSuretyBonds profile image


      9 years ago

      Great Hub. This is very informative information.


    This website uses cookies

    As a user in the EEA, your approval is needed on a few things. To provide a better website experience, uses cookies (and other similar technologies) and may collect, process, and share personal data. Please choose which areas of our service you consent to our doing so.

    For more information on managing or withdrawing consents and how we handle data, visit our Privacy Policy at:

    Show Details
    HubPages Device IDThis is used to identify particular browsers or devices when the access the service, and is used for security reasons.
    LoginThis is necessary to sign in to the HubPages Service.
    Google RecaptchaThis is used to prevent bots and spam. (Privacy Policy)
    AkismetThis is used to detect comment spam. (Privacy Policy)
    HubPages Google AnalyticsThis is used to provide data on traffic to our website, all personally identifyable data is anonymized. (Privacy Policy)
    HubPages Traffic PixelThis is used to collect data on traffic to articles and other pages on our site. Unless you are signed in to a HubPages account, all personally identifiable information is anonymized.
    Amazon Web ServicesThis is a cloud services platform that we used to host our service. (Privacy Policy)
    CloudflareThis is a cloud CDN service that we use to efficiently deliver files required for our service to operate such as javascript, cascading style sheets, images, and videos. (Privacy Policy)
    Google Hosted LibrariesJavascript software libraries such as jQuery are loaded at endpoints on the or domains, for performance and efficiency reasons. (Privacy Policy)
    Google Custom SearchThis is feature allows you to search the site. (Privacy Policy)
    Google MapsSome articles have Google Maps embedded in them. (Privacy Policy)
    Google ChartsThis is used to display charts and graphs on articles and the author center. (Privacy Policy)
    Google AdSense Host APIThis service allows you to sign up for or associate a Google AdSense account with HubPages, so that you can earn money from ads on your articles. No data is shared unless you engage with this feature. (Privacy Policy)
    Google YouTubeSome articles have YouTube videos embedded in them. (Privacy Policy)
    VimeoSome articles have Vimeo videos embedded in them. (Privacy Policy)
    PaypalThis is used for a registered author who enrolls in the HubPages Earnings program and requests to be paid via PayPal. No data is shared with Paypal unless you engage with this feature. (Privacy Policy)
    Facebook LoginYou can use this to streamline signing up for, or signing in to your Hubpages account. No data is shared with Facebook unless you engage with this feature. (Privacy Policy)
    MavenThis supports the Maven widget and search functionality. (Privacy Policy)
    Google AdSenseThis is an ad network. (Privacy Policy)
    Google DoubleClickGoogle provides ad serving technology and runs an ad network. (Privacy Policy)
    Index ExchangeThis is an ad network. (Privacy Policy)
    SovrnThis is an ad network. (Privacy Policy)
    Facebook AdsThis is an ad network. (Privacy Policy)
    Amazon Unified Ad MarketplaceThis is an ad network. (Privacy Policy)
    AppNexusThis is an ad network. (Privacy Policy)
    OpenxThis is an ad network. (Privacy Policy)
    Rubicon ProjectThis is an ad network. (Privacy Policy)
    TripleLiftThis is an ad network. (Privacy Policy)
    Say MediaWe partner with Say Media to deliver ad campaigns on our sites. (Privacy Policy)
    Remarketing PixelsWe may use remarketing pixels from advertising networks such as Google AdWords, Bing Ads, and Facebook in order to advertise the HubPages Service to people that have visited our sites.
    Conversion Tracking PixelsWe may use conversion tracking pixels from advertising networks such as Google AdWords, Bing Ads, and Facebook in order to identify when an advertisement has successfully resulted in the desired action, such as signing up for the HubPages Service or publishing an article on the HubPages Service.
    Author Google AnalyticsThis is used to provide traffic data and reports to the authors of articles on the HubPages Service. (Privacy Policy)
    ComscoreComScore is a media measurement and analytics company providing marketing data and analytics to enterprises, media and advertising agencies, and publishers. Non-consent will result in ComScore only processing obfuscated personal data. (Privacy Policy)
    Amazon Tracking PixelSome articles display amazon products as part of the Amazon Affiliate program, this pixel provides traffic statistics for those products (Privacy Policy)
    ClickscoThis is a data management platform studying reader behavior (Privacy Policy)