Bond Yield to Maturity Calculator
Quickly compute bond yield maturity with accurate formulas. See amortization schedules, growth projections, and side-by-side comparisons.
Bond Yield to Maturity Calculator
Calculator
Adjust values & calculateEnter your values below. Every result is computed in your browser — no data is sent to any server.
Formula: P = Σ [C / (1 + r)^t] + F / (1 + r)^N
Worked example — YTM ≈ 7.28% | Current Yield = 6.52% | Bond trades at Discount
Formula
P = Σ [C / (1 + r)^t] + F / (1 + r)^N
The bond price equals the present value of all future coupon payments plus the present value of the face value at maturity. YTM (r) is the discount rate that equates this present value to the current market price. It is solved iteratively using the Newton-Raphson method.
Worked Examples
Example 1: Discount Bond YTM Calculation
Problem:A bond with a $1,000 face value, 6% annual coupon rate (semiannual payments), currently trading at $920 with 8 years to maturity. Find YTM.
Solution:Face Value = $1,000, Coupon = 6% semiannual = $30 per period Current Price = $920, Periods = 8 × 2 = 16 Using iterative solving: YTM ≈ 7.28% Current Yield = $60 / $920 = 6.52% Capital Gain at Maturity = $1,000 − $920 = $80
Result:YTM ≈ 7.28% | Current Yield = 6.52% | Bond trades at Discount
Example 2: Premium Bond YTM Calculation
Problem:A bond with $1,000 face value, 8% coupon (semiannual), trading at $1,100 with 5 years to maturity. Find YTM.
Solution:Face Value = $1,000, Coupon = 8% semiannual = $40 per period Current Price = $1,100, Periods = 5 × 2 = 10 Using iterative solving: YTM ≈ 5.75% Current Yield = $80 / $1,100 = 7.27% Capital Loss at Maturity = $1,000 − $1,100 = −$100
Result:YTM ≈ 5.75% | Current Yield = 7.27% | Bond trades at Premium
Frequently Asked Questions
What is yield to maturity (YTM)?
Yield to maturity (YTM) is the total return an investor can expect to earn if they hold a bond until it matures and all coupon and principal payments are made as scheduled. It accounts for the bond's current market price, par value, coupon interest rate, and time to maturity. YTM is essentially the internal rate of return (IRR) of a bond investment, assuming all coupon payments are reinvested at the same rate. It is expressed as an annual percentage and serves as the most comprehensive measure of a bond's potential return, making it the standard metric for comparing bonds with different coupon rates and maturities.
How is YTM different from current yield?
Current yield is simply the annual coupon payment divided by the bond's current market price, giving you a snapshot of income return without considering capital gains or losses at maturity. YTM, on the other hand, is far more comprehensive because it factors in the difference between the purchase price and face value that will be realized at maturity, the time value of money, and the reinvestment of coupon payments. For a bond trading at par, current yield and YTM are identical. For discount bonds (trading below par), YTM will be higher than current yield because it includes capital appreciation. For premium bonds, YTM will be lower than current yield due to capital depreciation.
What is the relationship between bond price and yield?
Bond prices and yields have an inverse relationship: when bond prices rise, yields fall, and vice versa. This happens because a bond's coupon payments are fixed at issuance. If market interest rates increase, newly issued bonds offer higher coupons, making existing lower-coupon bonds less attractive, so their prices fall to compensate — raising their effective yield. Conversely, when rates drop, existing bonds with higher coupons become more valuable, pushing prices up and yields down. This inverse relationship is not linear; it follows a convex curve, meaning price sensitivity to yield changes varies depending on the yield level, coupon rate, and time to maturity.
What is bond duration and why does it matter?
Bond duration measures the sensitivity of a bond's price to changes in interest rates. Macaulay duration is the weighted average time until all cash flows are received, measured in years. Modified duration estimates the percentage price change for a 1% change in yield. For example, a bond with a modified duration of 7 would be expected to decrease approximately 7% in price if yields rise by 1%. Duration is crucial for portfolio risk management because it helps investors understand and hedge interest rate risk. Longer-duration bonds are more sensitive to rate changes, while shorter-duration bonds are less volatile but typically offer lower yields.
What assumptions does the YTM calculation make?
The YTM calculation makes several important assumptions that investors should understand. First, it assumes the bond is held to maturity and not sold before the maturity date. Second, it assumes all coupon payments are reinvested at the same YTM rate, which is rarely achievable in practice due to changing interest rates — this is called reinvestment risk. Third, it assumes the issuer does not default on any payments. Fourth, the calculation does not account for taxes, transaction costs, or inflation. Because of these assumptions, the actual return may differ from the calculated YTM. Investors often use YTM as a benchmark for comparison rather than as a precise prediction of future returns.
What is yield to call, and when does it matter more than YTM?
For a callable bond the issuer can redeem early, usually when rates have fallen. Yield to call recomputes the internal rate of return assuming redemption at the first call date and call price rather than at maturity. Analysts compare YTM with the yield to each call date and quote the lowest of them as the yield to worst, the conservative figure to use for a premium callable bond, since a call becomes likely exactly when it hurts the holder most.
How is YTM actually solved for?
There is no closed-form solution for a coupon bond, because the yield appears in every discount factor. The price function is strictly decreasing in yield for a standard bond, which guarantees a single root, so numerical methods converge reliably: bisection is robust, and Newton-Raphson, used by Bond Yield to Maturity Calculator, converges quickly by stepping along the derivative of price with respect to yield. A rough starting estimate comes from the approximate yield formula that averages coupon income and annualised capital gain.
How does bond-equivalent yield differ from the effective annual yield?
With semiannual coupons the iteration solves for a semiannual yield. Doubling it gives the bond-equivalent yield, the market convention used for quoting. Compounding it instead gives the effective annual yield: one plus the semiannual yield, squared, minus one. A 3% semiannual yield is a 6% bond-equivalent yield but a 6.09% effective annual yield. The distinction matters when comparing a bond against an annually compounded instrument such as a certificate of deposit quoted as APY.
What is reinvestment risk and how does it change realised return?
YTM assumes every coupon is reinvested at the YTM itself. If rates fall after purchase, coupons are reinvested at less, and the realised compound return over the holding period comes in below the quoted YTM; if rates rise, the opposite happens and the reinvestment gain partly offsets the capital loss. The effect grows with maturity and with a high coupon, since more cash needs reinvesting. A zero-coupon bond held to maturity removes reinvestment risk entirely.
How do taxes change the yield an investor actually keeps?
Coupon interest on most bonds is taxed as ordinary income, so the after-tax yield is roughly the YTM multiplied by one minus your marginal rate, while any discount accreted toward par has its own tax treatment. To compare a tax-exempt municipal bond with a taxable one, convert the municipal yield to a taxable-equivalent yield by dividing it by one minus your marginal rate. Bond Yield to Maturity Calculator reports pre-tax figures, so that comparison has to be done separately.
References
Reviewed for accuracy by Sahil, Senior Finance & Tax Editor · Editorial policy
Related Calculators
🧮Bond Yield Calculator
Calculate current yield, yield to maturity, and yield to call for fixed income investments.
🧮Investment Return Calculator
Calculate investment return with inputs, formulas, and instant results.
🧮Bond Duration Convexity Calculator
Calculate bond duration convexity with inputs, formulas, and instant results.
🧮Bond Price Calculator
Calculate bond price with inputs, formulas, and instant results.
🧮Portfolio Rebalance Calculator (3-Asset)
Enter current and target allocations for stocks, bonds, and cash to see exact buy/sell amounts, drift, and turnover.
🧮Inflation Adjusted Return Calculator
Calculate inflation adjusted return with inputs, formulas, and instant results.
🧮Cash on Cash Return Calculator
Calculate cash on cash return with inputs, formulas, and instant results.
🧮High Yield Savings Calculator
Calculate high yield savings with inputs, formulas, and instant results.