Bond Yield to Maturity Calculator
Quickly compute bond yield maturity with accurate formulas. See amortization schedules, growth projections, and side-by-side comparisons.
Reviewed for accuracy by Sahil, Senior Finance & Tax Editor
Bond Yield to Maturity Calculator
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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 APY vs APR in crypto yield?
APR is the simple annual rate without compounding. APY includes the effect of compounding. A 10% APR compounded daily equals roughly 10.52% APY. Always compare APY to APY for accurate yield comparisons.
References
Reviewed for accuracy by Sahil, Senior Finance & Tax Editor · Editorial policy
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