How to use the bond yield calculator
- Enter the face (par) value of one bond, the annual coupon rate and the price you pay.
- Enter the years to maturity and how often the bond pays its coupon. Years times payments per year must be a whole number.
- Optionally open the advanced fields and add a call price and years to call to see the yield to call.
- Read the yield to maturity, the current yield and the table showing how the price would change if yields moved.
Formula
Current yield = annual coupon / price
Price = sum of C / (1 + y)^k for k = 1 to n, plus Face / (1 + y)^n
C = face x coupon rate / payments per year, n = years x payments per year
Yield to maturity = y x payments per year, found by bisection
Effective annual yield = (1 + y)^(payments per year) - 1
Yield to maturity is the single rate that makes the present value of all remaining coupons and the face value equal to the price. It has no closed form, so the tool solves it numerically.
Worked example
A bond with a $1,000 face value, a 5% coupon paid twice a year, 10 years left and a price of $950 pays $25 every six months. The current yield is $50 / $950 = 5.263%.
The yield to maturity is 5.662% a year, because you also collect the $50 gain at maturity. The effective annual yield is 5.742%. If the same bond could be called at $1,000 after 5 years, the yield to call is 6.178%. A bond bought at exactly $1,000 yields its 5% coupon.
Current yield versus yield to maturity
Current yield only looks at the coupon income compared with the price. It ignores the gain or loss when the bond is repaid at face value. Yield to maturity includes it and also assumes you reinvest each coupon at the same yield, which makes it a better single measure of return for a bond you hold to the end.
Prices and yields move in opposite directions
When market yields rise, the price of an existing bond falls, because new bonds pay more. The table shows the price if the yield moved up or down by half a point or a full point. A longer bond moves more than a shorter one. For related math see the present value calculator and the APY to APR converter.
Taxes, accrued interest and risk
This tool does not subtract taxes or fees and assumes the issuer pays in full. If you buy between coupon dates you also pay accrued interest, which is not modeled here. Compare outcomes with the CAGR calculator when you want a growth rate instead.
Assumptions and limits
- You buy on a coupon date and receive every coupon and the face value on time.
- Coupons are not reinvested in the dollar result. The yield to maturity formula assumes reinvestment at the same yield.
- The price is for one bond in dollars. Accrued interest, taxes, fees and credit risk are not modeled.
- Day count conventions are ignored. Time is counted in whole coupon periods.
Frequently asked questions
How do you calculate yield to maturity?
Find the rate that makes the present value of all future coupons and the face value equal to the price. It is solved by trial, which the tool does automatically.
What is a good bond yield?
It depends on the issuer, the length and market rates. A higher yield usually means more risk or a longer term, so compare bonds that are alike.
Why is the yield to maturity higher than the current yield for a bond under par?
Because you buy below face value and are repaid at face value, so you earn a gain on top of the coupons.
What is yield to call?
It is the yield if the bond is called early at the call price. Callable bonds are often valued at the lower of the yield to call and the yield to maturity.