Bond price calculator
Turn a yield into a price. Enter the yield to maturity, coupon and term to get the clean and dirty price, then see how sensitive that price is to interest rates.
Clean price per 100
96.103
$961.03 for $1,000 face at a 5.000% yield, compounded semiannually.
- Accrued interest
- $0.00
- Dirty price
- $961.03
- Discount to face value
- $38.97
- Current yield
- 4.682%
Settles on a coupon date, so no interest has accrued.
Interest-rate sensitivity
- Macaulay duration
- 8.117 yrs
- Modified duration
- 7.919
- Convexity
- 75.30
- Value of 0.01% (DV01)
- $0.76
| Change | Actual | Duration only | + convexity |
|---|---|---|---|
| Yield −1 point (4.00%) | 104.088 | 103.713 | 104.075 |
| Yield +1 point (6.00%) | 88.842 | 88.492 | 88.854 |
Pricing a bond from its yield
Each remaining coupon and the face value are discounted at the yield per period and added up. That total is the dirty price; take away the accrued interest and you have the clean price bonds are quoted at. A yield above the coupon rate prices the bond at a discount to face value, and a yield below it at a premium.
Duration and convexity
Macaulay duration is the present-value-weighted average time to the bond's cash flows, an idea Frederick Macaulay set out in 1938. Modified duration divides it by (1 + y/f) and approximates the percentage price change for a one-point move in yield. Convexity measures the bend in the curve: the dashed duration line sits below it, so adding convexity brings the estimate closer. DV01 is the dollar change for a 0.01% move.
% price change ≈ − modified duration × Δy + ½ × convexity × (Δy)²
Example: at a 5% yield, a 10-year bond with a 4.5% semiannual coupon is worth 96.103 per 100. With a modified duration of 7.919, a rise to 6% should cost about 7.9%; the true price, 88.842, sits a little above the duration-only estimate of 88.492.
Sources
- U.S. Treasury, 31 CFR Part 356, Appendix B, section II: formulas for converting yields to prices, with worked examples.
- Municipal Securities Rulemaking Board, Rule G-33, Calculations: price from yield with compound discounting, and simple interest when one coupon period or less remains.
- Frederick R. Macaulay, Some Theoretical Problems Suggested by the Movements of Interest Rates, Bond Yields and Stock Prices in the United States since 1856 (NBER, 1938), chapter The Concept of Long Term Interest Rates: the origin of duration.
- Microsoft Support, MDURATION function and PRICE function: their worked examples (5.736 and 94.63) are among the cases this calculator is tested against.
Questions
Why does the price fall when the yield rises?
The coupons and face value are fixed, so a higher discount rate makes each one worth less today. A buyer will only accept the old coupon at a higher yield by paying less for the bond.
Is duration the same as the time to maturity?
No. Coupons arrive before maturity, so the weighted average time is shorter. Only a zero-coupon bond has a Macaulay duration equal to its time to maturity.
Why is the accrued interest zero?
With a whole number of coupon periods, such as 10 years paid semiannually, the bond settles on a coupon date and nothing has accrued. Enter dates, or a term such as 7.3 years, to see accrued interest and the gap between clean and dirty price.