Bond Yield Calculator

A bond's yield is the actual return on a bond and almost never matches the interest rate listed on the bond. If a bond is purchased below par value, its yield will be above the stated interest rate, and if it is purchased above par value, its yield will be below the stated interest rate.

This calculator calculates the yield to maturity based on the bond price, coupon, and time until maturity, and also shows current yield, effective annual yield, and coupon rate so you can get a full picture in one place. If you enter a yield, this tool will calculate the corresponding price. If you enter a yield, it will calculate the price required to achieve the stated yield.

What is a bond yield?

A bond is essentially a loan to a government or company. Bonds pay fixed interest, called coupons, and are repaid at face value at the end of their term. Yield captures these payments and price in an annualized return. When talking about the yield on a bond, one usually refers to the yield to maturity. This is the return that will be earned if a bond is bought at its current price, receives all coupon payments, and held until maturity. It essentially represents the internal rate of return (IRR) on the bond market.

Four types of yields

A bond has not one but several yields; each type of yield answers a different question. The coupon rate is the fixed interest rate set at the time of issue of the bond. The current yield is the annual coupon payment divided by the current price and reflects only income. The yield to maturity is the most comprehensive measure, as it takes into account both the interest payments and any gains or losses that will be realized when the bond's price reverts back to its face value at the end of its term. The effective annual yield represents the yield to maturity in a way that accounts for the effects of compounding within one year, allowing bonds with different coupon payment schedules to be compared.

For a bond purchased below par, the four types of yields increase in the following order: coupon yield, current yield, yield to maturity and finally effective annual rate. If a bond is purchased above par, then the order is reversed. Comparing these values side by side is the quickest way to understand how bonds are priced.

Instructions for using this calculator:

Enter the bond price, par value, annual coupon rate, number of years remaining until maturity date and frequency of interest payments. The calculator will calculate the yield and display the result. If you want to calculate a yield backwards, enter your desired yield and clear the price to get the price required to achieve that yield. For more detailed analysis, you can open additional options. Here you can see the prepayment yield for bonds that can be prepaid by the issuer, the tax-equivalent yield of municipal bonds, the duration to assess interest rate risk, and the range of price sensitivity which indicates how the yield changes when the purchase price fluctuates slightly.

Understanding the formula for yield to maturity.

The yield to maturity is the interest rate at which the present value of all future payments equals the price paid. Since it's not possible in this equation to isolate and extract just the interest rate, the calculator uses numerical algorithms to find the interest rate.

where P is the price, C is the coupon per period, F is the face value, N is the number of periods and i is the yield per period. The coupon per period is the product of the annual coupon rate and the face value divided by the number of payments per year. When the calculator finds a value for i, it displays an annualized value.

Suppose a bond has a price of 950, a par value of 1,000, a coupon rate of 5 percent, pays interest semi-annually and has 7 years to maturity.

The coupon amount per period is 25 and the number of periods is 14. The result shows a yield per period of approximately 2.94 percent.

If you double that, the yield to maturity is about 5.88 percent.

The effective annual rate is about 5.97 percent while the current yield is approximately 5.26 percent, which is calculated by dividing 50 by 950. All three values exceed the nominal interest rate of 5 percent. This is because this bond was purchased at a discount price. The following table summarizes each input in this example and provides the corresponding value.

Why yields diverge from nominal interest rates

The nominal interest rate is set when a bond is issued while the price changes daily in the market. If the price falls below par, the same interest payment combined with the gain made if the price recovers to par will result in an overall higher return. So the yield is higher than the nominal interest rate. If the price rises above par, the yield is lower than the nominal interest rate. Price and yield always move in opposite directions.

This also explains why the yield of a bond will gradually approach its coupon rate over time as it gets closer to maturity. With less time left, there is less impact from gains or losses and the price pulls back towards par value. Traders call this phenomenon "pull to par".

Early repayment yield and minimum yield

Many bonds are callable, meaning that the issuer can buy back the bond early at a usually fixed price, typically when interest rates have fallen. This limits upside potential so that the yield to maturity may overstate actual return. Yield to call is calculated in the same manner except that the date and price of the call are used as the end point. The minimum yield is the lower of the two. When comparing callable bonds this figure should be considered since it represents the worst case outcome.

Factors that affect bond yields include:

Yield varies with the overall economic environment. When inflation rises, yields tend to rise as well. This is because investors want their capital to keep pace with inflation and central banks often raise interest rates in response. Credit risk also affects yield. Issuers with weaker credit ratings must offer higher yields to attract buyers. So a significantly higher yield than similar bonds is usually not a sign of a bargain, but rather a warning. Maturity is also important, as longer-term bonds carry more interest rate risk and therefore often offer slightly higher yields.

Tips for understanding bond yields:

Compare the effective annual yield for different coupon payment schedules. This allows you to compare on a level playing field. Note that current yield is a snapshot of earnings and not total return as it ignores the effect of getting back to par value. Match your coupon frequency with the bond in question, most corporate bonds and US Treasury bonds pay interest semi-annually. For callable bonds do not rely on the stated yield to maturity but rather the minimum yield.