What is a Bond?
A bond is a fixed-income instrument representing a loan made by an investor to a borrower (typically corporate or governmental). Think of it as an I.O.U. between the lender and borrower that includes the details of the loan and its payments. Bonds are used by companies, municipalities, states, and sovereign governments to finance projects and operations.
When you buy a bond, you are lending the issuer your money for a set period. In return, the issuer promises to pay you interest—known as the coupon—at predetermined intervals, and to return the original sum (the face value or principal) on the maturity date.
How to Use This Calculator
This calculator functions in two primary modes to cover all common bond valuation scenarios:
- Time to Maturity Mode: Best for evaluating bonds exactly on a coupon payment date, or for quick theoretical estimates based on years remaining until maturity.
- Specific Dates Mode: Best for real-world trading scenarios where bonds are purchased between coupon payment dates. It calculates exact days elapsed, accrued interest, and invoice (dirty) prices based on industry-standard day-count conventions.
Clean Price vs. Dirty Price
In the real world, bonds rarely trade exactly on a coupon payment date. Instead, they are bought and sold on any business day. Because interest accumulates daily, the buyer must compensate the seller for the interest earned between the last payment date and the settlement date.
Clean Price: The price of a bond excluding any interest that has accrued since issue or the most recent coupon payment. This is typically the price quoted in financial markets and news outlets because it reflects the actual market value of the bond itself without the distortion of a specific settlement date.
Dirty Price (Invoice Price): The price of a bond including any interest that has accrued since issue or the most recent coupon payment. This is the exact, total amount that the buyer pays to the seller.
The Bond Pricing Formula
The core mathematical principle behind bond pricing is Present Value (PV). The price of a bond is equal to the present value of all its future cash flows (the coupon payments) plus the present value of the final principal repayment.
Where:
P = Clean Bond Price
C = Coupon payment per period
r = Yield to maturity per period (Discount rate)
n = Number of periods until maturity
FV = Face Value (Principal)
Day-Count Conventions
Day-count conventions determine how interest accrues over time on a variety of investments, including bonds. They establish how to count the days in a month and the days in a year.
- Actual/Actual: The most precise method, primarily used for government bonds like US Treasuries. It counts the exact number of days in the period and the exact number of days in the year.
- 30/360 (Bond Basis): Assumes every month has 30 days and the year has 360 days. Commonly used for corporate, agency, and municipal bonds.
- Actual/360: Uses actual days elapsed, but assumes a 360-day year. Used heavily in money market instruments.
- Actual/365: Uses actual days elapsed but assumes a 365-day year. Common for government bonds outside the US.
Frequently Asked Questions
Bond prices share an inverse relationship with interest rates. When overall market interest rates rise, the fixed coupon payments of an existing bond become less attractive compared to newly issued bonds offering higher yields. To attract buyers, the existing bond's price must decrease. Conversely, if rates fall, existing bonds with higher coupons become more valuable, driving their prices up.
A bond trades at a premium (above its face value) when its coupon rate is higher than the current market yield to maturity. It trades at a discount (below its face value) when its coupon rate is lower than the current market yield. If the coupon rate matches the yield, it trades exactly at "par" (face value).
Yield to Maturity is the total return anticipated on a bond if the bond is held until it matures. YTM is expressed as an annual rate and takes into account the current market price, par value, coupon interest rate, and time to maturity. It assumes all coupon payments are reinvested at the same rate as the current yield.
Accrued interest is the portion of a bond's coupon payment that has been earned by the seller but not yet paid because the transaction occurred between official coupon dates. The buyer pays this amount to the seller, and later receives the full coupon payment on the next scheduled date.
Current yield is an investment's annual income (interest or dividends) divided by the current price of the security. For bonds, it is the annual coupon payment divided by the current clean price. Unlike YTM, current yield does not account for capital gains or losses realized if the bond is held to maturity.