Financial Calculators
Bond Price & Yield-to-Maturity Calculator
Calculate bond price from yield-to-maturity, or solve YTM from price. See current yield, Macaulay duration, modified duration, convexity, and a full cash-flow schedule.
Cash Flow Schedule
| Period | Time (yr) | Cash Flow | Present Value |
|---|---|---|---|
| 1 | 0.50 | $25.00 | $24.27 |
| 2 | 1.00 | $25.00 | $23.56 |
| 3 | 1.50 | $25.00 | $22.88 |
| 4 | 2.00 | $25.00 | $22.21 |
| 5 | 2.50 | $25.00 | $21.57 |
| 6 | 3.00 | $25.00 | $20.94 |
| 7 | 3.50 | $25.00 | $20.33 |
| 8 | 4.00 | $25.00 | $19.74 |
| 9 | 4.50 | $25.00 | $19.16 |
| 10 | 5.00 | $25.00 | $18.60 |
| X | Cash Flow | Present Value |
|---|---|---|
| P1 | $25.00 | $24.27 |
| P2 | $25.00 | $23.56 |
| P3 | $25.00 | $22.88 |
| P4 | $25.00 | $22.21 |
| P5 | $25.00 | $21.57 |
| P6 | $25.00 | $20.94 |
| P7 | $25.00 | $20.33 |
| P8 | $25.00 | $19.74 |
| P9 | $25.00 | $19.16 |
| P10 | $25.00 | $18.60 |
| P11 | $25.00 | $18.06 |
| P12 | $25.00 | $17.53 |
| P13 | $25.00 | $17.02 |
| P14 | $25.00 | $16.53 |
| P15 | $25.00 | $16.05 |
| P16 | $25.00 | $15.58 |
| P17 | $25.00 | $15.13 |
| P18 | $25.00 | $14.68 |
| P19 | $25.00 | $14.26 |
| P20 | $1,025.00 | $567.52 |
Bond pricing formula
The fair price of a bond is the present value of all future cash flows discounted at the yield-to-maturity:
Price = Σ [C / (1 + y/n)^t] + F / (1 + y/n)^N
where C is the periodic coupon, y is the annual YTM, n is the coupon frequency (payments per year), F is the face value, t runs from 1 to N, and N is the total number of coupon periods.
Solving for yield-to-maturity
There is no closed-form solution for YTM. This calculator uses Newton-Raphson iteration (with a bisection fallback) to find the yield that equates the present value of all cash flows with the market price. Convergence is guaranteed for any positive price.
Duration and interest rate risk
Macaulay duration is the weighted-average time to receive the bond's cash flows, measured in years. Modified duration is Macaulay duration divided by (1 + y/n) and directly estimates the price sensitivity:
ΔPrice% ≈ −Modified Duration × ΔYield%
Convexity improves this approximation for large yield changes. A higher convexity means the bond price falls less (or rises more) than duration alone predicts.
Discount vs. premium bonds
When the YTM is above the coupon rate, the bond trades at a discount (price < face value). When YTM is below the coupon rate, it trades at a premium. At maturity the price always converges to face value, meaning discount bond holders earn a capital gain and premium bond holders take a capital loss (offset by the higher coupons they received).
Yield types glossary
| Yield type | Definition |
|---|---|
| Current yield | Annual coupon ÷ current market price. Ignores capital gain/loss at maturity. |
| Yield to maturity (YTM) | Total annualized return if held to maturity and coupons are reinvested at the same rate. |
| Yield to call (YTC) | YTM calculated to the earliest call date rather than maturity. Relevant for callable bonds. |
| Yield to worst (YTW) | The lowest of YTM, YTC, and all other yield-to-call dates. The most conservative yield estimate. |
Bond laddering
A bond ladder is a portfolio of bonds with staggered maturity dates - e.g., one bond maturing each year for five years. As each bond matures, proceeds are reinvested at the long end of the ladder. This strategy reduces reinvestment risk (you are never fully exposed to a single interest rate environment) and provides periodic liquidity. The same principle applies to CDs - see the CD Ladder Calculator for an interactive example.
Federal, corporate, and municipal bonds
Bond type affects after-tax yield significantly:
- US Treasury bonds: exempt from state and local income taxes; subject to federal income tax. Considered the lowest credit risk available in USD.
- Corporate bonds: fully taxable at all levels. Higher coupon rates compensate for credit risk and full tax exposure.
- Municipal bonds ("munis"): typically exempt from federal income tax, and exempt from state tax if purchased in your home state. The tax-equivalent yield (TEY) = muni yield ÷ (1 − your marginal tax rate) allows direct comparison with taxable bonds.