Bond Yield Calculator
YTM is the discount rate where PV of all bond cash flows equals market price. Example: $1,000 face, 5% coupon ($25 semi-annual), 10 years, price $950 → YTM ≈ 5.58%. Current yield = Annual Coupon / Price = $50/$950 = 5.26% (lower than YTM because YTM includes the $50 gain at maturity). Discount bond: YTM > coupon rate. Premium bond: YTM < coupon rate. Modified duration approximates price sensitivity: duration 7.5 yr → 1% rate rise ≈ −7.5% price drop.
Calculate bond yield to maturity (YTM), current yield, Macaulay duration, and modified duration. Enter face value, coupon rate, years to maturity, and market price to get the full yield picture. Supports annual, semi-annual, quarterly, and monthly coupon payments. Shows premium vs. discount status.
Bond Parameters
Results
How to Use
- 1
Enter face value and coupon rate
Face value is the par value you receive at maturity (typically $1,000). Coupon rate is the stated annual interest rate on the face value — not on the market price.
- 2
Set years to maturity
Enter the remaining time until the bond matures and returns face value. For example, a 2030 bond purchased in 2026 has 4 years to maturity.
- 3
Enter the market price
Type the actual price you pay today — not the face value. A price below $1,000 means a discount bond; above $1,000 means a premium bond.
- 4
Choose payment frequency
Select how often coupon payments are made. Most US bonds pay semi-annually (2/year). Government bonds and some corporate bonds may differ.
- 5
Read YTM and duration
YTM is the complete annualized return if held to maturity. Modified duration tells you how much the price will change per 1% move in interest rates. Higher duration = more interest rate sensitivity.
Frequently Asked Questions
- What is yield to maturity (YTM)?
- Yield to maturity (YTM) is the total annualized return you earn if you buy a bond today at market price, hold it to maturity, and reinvest all coupon payments at the same YTM rate. It is the internal rate of return (IRR) of the bond's cash flows. YTM > coupon rate means the bond is trading at a discount (price < face). YTM < coupon rate means a premium bond (price > face). Example: $1,000 face bond, 5% coupon, 10 years, bought at $950 → YTM ≈ 5.58%. YTM is the standard measure for comparing bonds with different coupons and maturities.
- What is the difference between YTM and current yield?
- Current yield = Annual Coupon / Market Price × 100. YTM accounts for the capital gain or loss from buying at a discount or premium. Example: $1,000 face, 5% coupon ($50/year), price $950 → Current yield = 5.26%. YTM ≈ 5.58% (higher, because you also gain $50 when the bond matures at face value). For a premium bond (price $1,050): Current yield ≈ 4.76%, YTM ≈ 4.42% (lower, because you lose $50 at maturity). Current yield is a quick approximation; YTM is the complete picture.
- What is Macaulay duration and why does it matter?
- Macaulay duration is the weighted average time (in years) to receive all of a bond's cash flows, where each payment is weighted by its present value. It measures interest rate sensitivity: a bond with duration 7 years will lose approximately 7% of value if interest rates rise 1%. Higher coupon bonds have shorter duration (you receive cash sooner). Zero-coupon bonds have duration equal to their maturity (all cash at end). Modified Duration = Macaulay Duration / (1 + YTM/periods) and is the direct price sensitivity measure: a 1% rate change causes approximately Modified Duration × 1% change in bond price.
- When does a bond trade at a discount vs premium?
- A bond trades at a discount when its coupon rate < prevailing market rates — investors pay less than face value to compensate for the below-market coupon. YTM > coupon rate. Example: 4% coupon bond when market rates are 6% → price drops below $1,000. A bond trades at a premium when its coupon rate > market rates — investors pay more than face value for the above-market coupon. YTM < coupon rate. Example: 7% coupon bond when market rates are 5% → price rises above $1,000. At maturity, all bonds converge to face value regardless of starting price.
- How does interest rate risk affect bond prices?
- Bond prices move inversely with interest rates — when rates rise, existing bonds lose value; when rates fall, they gain. The magnitude depends on duration: a bond with 8-year modified duration loses ~8% in price for each 1% rise in rates. Long-maturity, low-coupon bonds have the highest duration and are most sensitive to rates. Short-maturity, high-coupon bonds have low duration and are least sensitive. To reduce interest rate risk: choose shorter maturities, higher coupon bonds, or floating-rate bonds. To benefit from expected rate cuts: buy long-duration bonds before rates fall.
- What is a good bond yield to target?
- A "good" bond yield depends on credit risk, maturity, and your alternatives. General benchmarks (2026): US 10-year Treasury ≈ 4.2–4.8% (near risk-free baseline); investment-grade corporate bonds (BBB–AAA) ≈ 5–6.5%; high-yield corporate bonds (junk, below BBB) ≈ 7–10%+; municipal bonds ≈ 3.5–5% pre-tax (tax-exempt, compare on after-tax basis). The yield spread over Treasuries is the credit spread — compensation for default risk. A 2% spread over Treasuries on a corporate bond means 2% additional yield for taking on default risk. Compare YTM to your required return after accounting for credit and reinvestment risk.
- What is the YTM formula and how is it calculated?
- YTM is the rate r that satisfies: Market Price = Σ [Coupon / (1+r)^t] + Face / (1+r)^n, where t goes from 1 to n (total periods). This cannot be solved algebraically — it requires iteration. Common methods: trial-and-error, the Newton-Raphson algorithm, or bisection. Most financial calculators and spreadsheets (Excel RATE() or YIELD() function) use iterative solvers. Approximation formula: YTM ≈ [Annual Coupon + (Face − Price)/Years] / [(Face + Price)/2]. This approximation is accurate within 0.1–0.3% for most bonds but misses compounding effects for high-yield or long-maturity bonds.