Bond Yield to Maturity Calculator
Calculate a bond yield to maturity from its price, or the price from a target yield, plus current yield, Macaulay and modified duration, convexity and the price change for a rate move.
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Price and yield move in opposite directions
A bond pays a fixed coupon. If market rates rise after it is issued, the fixed coupon is worth less relative to what a new bond would pay, so the price falls until the total return matches the market. Yield to maturity is the single discount rate that makes the present value of all remaining coupons plus the final principal equal to the current price. It is the internal rate of return of holding the bond to maturity, and it is the number that makes bonds with different coupons and maturities comparable.
Duration measures interest rate risk
Macaulay duration is the weighted average time until the bond's cash flows arrive. Modified duration converts that into a sensitivity: the approximate percentage price change for a one percentage point change in yield. A bond with a modified duration of seven will lose roughly seven percent of its value if rates rise by one point. This is why long dated bonds fell so sharply during the 2022 rate rises, and why duration is the first number a bond investor looks at after the yield.
Convexity corrects the estimate
Duration is a straight line approximation to a curved relationship, so it under states price gains when rates fall and over states losses when they rise. Convexity is the second order term that corrects for this, and it matters most for large rate moves and long maturities. For a small move duration alone is close enough; for a two point move on a thirty year bond, ignoring convexity produces a materially wrong answer.
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Frequently Asked Questions
What is the difference between current yield and yield to maturity?
Current yield is the annual coupon divided by the price, which ignores any gain or loss from a price below or above par. Yield to maturity includes that capital movement amortised over the remaining life, so it is the complete return figure.
Why does a bond trade above or below par?
Because its coupon differs from current market rates. A bond paying more than the market trades at a premium above face value; one paying less trades at a discount. The premium or discount is exactly what brings the total return into line with prevailing yields.
What does modified duration tell me?
The approximate percentage price change for a one percentage point change in yield. A modified duration of 7 means roughly a 7 percent price fall if yields rise by 1 point, and slightly more than a 7 percent gain if they fall by 1 point, because of convexity.
Does this account for credit risk?
No. Yield to maturity assumes every coupon and the principal are paid in full and on time. A high yield on a corporate bond usually reflects default risk rather than a free lunch, and this calculation cannot see that.
How does coupon frequency affect the result?
Semi-annual coupons produce slightly more value than annual ones for the same nominal rate, because half the money arrives sooner and can be reinvested. The calculator discounts at the correct period frequency rather than annualising loosely.
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How to Use
Enter face value, coupon, price and years to maturity to solve for yield, or enter a yield to get the price.
Disclaimer: This tool is provided "as is" without warranty of any kind. Results are for educational and utility purposes.
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