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输入面值、市价、票面利率与剩余年限，精确计算债券持有至到期的年化收益率。
YTM ≈ [C + (F - P) / n] / [(F + P) / 2] × 100%
C=Annual Interest, F=Face Value, P=Current Price, n=Years to Maturity
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Yield to Maturity (YTM) is the total annualized return you can expect to earn if you hold a bond until it matures, assuming all coupon payments are reinvested at the same rate. It synthesizes the bond's current price, coupon interest, principal repayment, and time remaining into a single percentage, allowing you to directly compare bonds with different prices and maturities. Our calculator helps you figure out this exact number instantly.
The core formula discounts all future cash flows back to the present, setting the sum of these present values equal to the current market price:
P = C/(1+r)1 + C/(1+r)2 + … + C/(1+r)n + F/(1+r)n
Where P is the current price, C is the annual coupon payment (face value × coupon rate), F is the face value, n is the years to maturity, and r is the YTM you are solving for.
This equation cannot be solved for r algebraically by hand. Our calculator uses numerical iteration methods (like the Newton-Raphson method) in the background to successively approximate the rate. It plugs in a guessed r, checks the difference between both sides of the equation, and repeats until the variance is less than one in a million. The resulting YTM is then displayed on your screen.
If the price you have includes accrued interest (dirty price), we recommend deducting the accrued interest first and entering the clean price. This ensures the resulting YTM accurately reflects the clean price yield.
Assume a corporate bond has 5 years left to maturity, a face value of 1000, a 6% coupon rate paid annually, and a current market price of 920. Here is how you enter it into the calculator:
Formula: 920 = 60/(1+r) + 60/(1+r)2 + 60/(1+r)3 + 60/(1+r)4 + 1060/(1+r)5.
Using trial and error, we find r ≈ 7.94%, and the calculator's YTM result will stabilize around 7.94%. This means if you buy the bond at 920, hold it for 5 years, and reinvest every coupon payment at 7.94%, your total annualized return will be 7.94%. This is nearly two percentage points higher than the 6% coupon rate because you bought it at a discount—you earn the coupon payments plus the capital appreciation as the price rises back to face value.
Premium Bonds: If the market price of the same bond rises to 1080, change the current price in the calculator to 1080 and leave the rest unchanged. The equation becomes 1080 = 60/(1+r) + … + 1060/(1+r)5, yielding a YTM of ≈ 4.12%. Although the coupon rate is still 6%, buying above face value means you will incur a capital loss when the price returns to par at maturity, lowering your actual annualized return.
Zero-Coupon Bonds: A 3-year zero-coupon bond has a face value of 1000, a market price of 850, and a coupon rate of 0. In the calculator, enter 1000 for face value, 850 for current price, 0 for annual interest rate, and 3 for years to maturity. The only cash flow is the final 1000 payment: 850 = 1000/(1+r)3, yielding a YTM of ≈ 5.57%. Even though this bond pays no interest, buying it at a deep discount still provides an actual annualized return of 5.57%.
