How to use the bond yield calculator
- Enter the price you would pay, in dollars per bond. A $1,000 bond quoted at 104 costs $1,040. Use the clean (quoted) price; if the maturity falls between coupon dates, the calculator adds accrued interest itself.
- Enter the face value, the coupon rate and the years to maturity. They are in the bond’s description at your broker. Decimals such as 9.5 years are fine.
- Choose the coupon frequency. Most US bonds pay semiannually.
- For a callable bond, enter the call price and the years to the first call date. Both are in the bond’s call schedule. Leave the two fields empty for a bond that cannot be called.
The results show every yield at once. The chart plots the yield to maturity and the yield to call against the price, and the table lists both at prices from 90 to 110 percent of face value.
How bond yields are calculated
Price = Σk=1…N (C ÷ f) ÷ (1 + YTM ÷ f)k + F ÷ (1 + YTM ÷ f)N
Effective annual yield = (1 + YTM ÷ f)f − 1C is the annual coupon in dollars, F the face value, f the coupons per year and N the number of coupons left. The yield to maturity is the YTM that solves the second line; it has no closed form, so the calculator finds it numerically to many decimal places.
The yield to call solves the same equation with two changes: N counts the coupons until the call date, and the final payment is the call price instead of the face value. The yield to worst is the lower of the two yields.
YTM is quoted as a bond-equivalent yield: for a semiannual bond, the yield per half-year multiplied by two. That is the convention for US Treasury and corporate bond quotes.
A worked example
A $1,000 bond with a 6% semiannual coupon matures in 10 years and costs $1,040. The issuer can call it at $1,020 in 4 years.
The coupons pay $60.00 a year, so the current yield is 5.77%. But $40.00 of the price will be lost by maturity, and spreading that loss over 10 years brings the yield to maturity down to 5.48%, or 5.55% compounded.
If the issuer calls the bond in 4 years, you receive $1,020 instead of $1,000, and the premium is lost over a much shorter time. The yield to call is 5.33%, so the yield to worst is 5.33%.
Premium and discount bonds
The relationship between the three yields tells you where the bond’s price stands:
| Price | Current yield | Yield to maturity | Yield to call |
|---|---|---|---|
| $950 (discount) | 6.32% | 6.69% | 7.92% |
| $1,000 (par) | 6.00% | 6.00% | 6.45% |
| $1,040 (premium) | 5.77% | 5.48% | 5.33% |
Below par, the price gain to maturity lifts the YTM above the current yield, and an early call at a premium would raise the return further, so the yield to maturity is the worst case. Above par, the order reverses: the premium drags the YTM below the current yield, and a call would lock in the loss sooner. That is why the yield to worst on premium bonds is often the yield to call.
Which yield should you look at?
- Current yield answers “how much income will I receive each year?” It suits income planning but ignores the price change to maturity, so it flatters premium bonds.
- Yield to maturity answers “what return do I lock in if I hold to the end?” It is the standard figure for comparing bonds with different prices and coupons.
- Yield to worst answers “what is the lowest yield I can get if the issuer calls when it suits it?” For callable bonds it is the safer number to plan on, because issuers tend to call when rates have fallen, exactly when reinvesting the money would be hardest.
- Effective annual yield puts a bond on the same footing as an APY. With annual coupons instead of semiannual, the same $1,040 bond yields 5.47% to maturity, almost the same quote, yet its effective annual yield is 5.47% against 5.55%, because half of each year’s income arrives six months later.
What this calculator does not include
- Only one call date. Many bonds can be called on several dates at stepped-down prices; the true yield to worst is the lowest yield across all of them. Enter each date in turn to check. Make-whole calls, which pay a price based on Treasury yields, are not modeled.
- Default risk. YTM is a promised yield. On a risky bond, the expected return is lower than the YTM.
- Reinvestment. The yield assumes coupons are reinvested at the same rate. Our bond total return calculator lets you set a different reinvestment rate.
- Taxes, inflation and costs. Coupon income is taxed differently from price gains, and municipal bond interest is often tax-exempt. Compare taxable and tax-free bonds with the tax-equivalent yield calculator, and subtract any dealer markup from your price.