Bond Calculator
- Updated
- Formula shown
- Free, no sign-up
Results
At a 6% yield, a 5% 10-year bond is worth $925.61 (92.561 per 100), at a discount
| Period | Years | Cash flow | Present value |
|---|---|---|---|
| 1 | 0.5 | $25.00 | $24.27 |
| 2 | 1 | $25.00 | $23.56 |
| 3 | 1.5 | $25.00 | $22.88 |
| 4 | 2 | $25.00 | $22.21 |
| 5 | 2.5 | $25.00 | $21.57 |
| 6 | 3 | $25.00 | $20.94 |
| 7 | 3.5 | $25.00 | $20.33 |
| 8 | 4 | $25.00 | $19.74 |
Valued on a coupon date, with no accrued interest. The yield to maturity assumes the bond is held to maturity, every payment is made and coupons are reinvested at the same yield.
How to use the bond calculator
- Choose whether to find the price from a yield, or the yield from a price.
- Enter the face value (usually $1,000.00), the coupon rate, how often coupons are paid and the years left to maturity.
- Enter the yield to maturity, or the price you would pay.
- Read the price or yield, then the duration figures to see how sensitive the bond is to rate changes.
Bond price, yield and duration formulas
Current yield = annual coupon ÷ price
Macaulay duration = Σ (t ÷ f) × PV(CFt) ÷ price
Modified duration = Macaulay ÷ (1 + y)
C is the coupon per period (face × coupon rate ÷ f), F the face value, f the coupons per year, n the number of coupon periods and y the yield per period (YTM ÷ f). The yield to maturity is the single rate that makes the present value of all the cash flows equal the price; it has no direct formula, so the calculator solves for it numerically, like a spreadsheet's RATE or YIELD function. Macaulay duration is the present-value-weighted average time to the cash flows. Modified duration converts it into price sensitivity: the approximate percentage price change for a one-point change in yield.
Worked example
A 10-year bond with a $1,000.00 face value pays a 5% coupon twice a year, $25.00 every six months. If similar bonds yield 6%, the rate per period is 3% over 20 periods, and the price is $925.61: a discount, because the coupon is below the market yield. The current yield is 50 ÷ 925.61 = 5.402%.
The Macaulay duration is 7.89 years and the modified duration 7.67. If yields rose to 7%, modified duration predicts a price of about $854.66; the exact price is $857.88, a little higher because of convexity. Going the other way, buying the same bond at $950.00 gives a yield to maturity of 5.662%.
Textbook checks: a 20-year 10% semi-annual bond at an 11% yield is priced at $919.77, and a 3-year 10% annual bond at par has a Macaulay duration of 2.7355 years.
Price of a 5% semi-annual bond
Price per $1,000.00 of face value, by yield to maturity and years to maturity.
| Yield | 2 years | 5 years | 10 years | 30 years |
|---|---|---|---|---|
| 3% | $1,038.54 | $1,092.22 | $1,171.69 | $1,393.80 |
| 4% | $1,019.04 | $1,044.91 | $1,081.76 | $1,173.80 |
| 5% | $1,000.00 | $1,000.00 | $1,000.00 | $1,000.00 |
| 6% | $981.41 | $957.35 | $925.61 | $861.62 |
| 7% | $963.27 | $916.83 | $857.88 | $750.55 |
At a 5% yield every maturity is priced at par. The longer the maturity, the further the price moves when yields change.
Interpreting the results
- Prices and yields move in opposite directions. When market yields rise, existing bonds with fixed coupons become worth less.
- Clean and dirty prices. Quoted prices usually exclude accrued interest. Between coupon dates the buyer also pays the seller the interest earned since the last coupon; this calculator values the bond on a coupon date.
- YTM is a promise, not a forecast. It assumes you hold to maturity, every payment arrives and coupons are reinvested at the same yield. Callable bonds may be redeemed early, so also check the yield to call.
- Related tools. Discount any single future amount with the present value calculator, or compare with a CD in the CD calculator.
Frequently asked questions
How do you calculate the price of a bond?
Discount each coupon and the face value at the yield per period and add them up. A 10-year $1,000 bond with a 5% semi-annual coupon, at a 6% yield, is worth $25 × the annuity factor for 20 periods at 3% plus $1,000 ÷ 1.03^20 = $925.61.
How do you find the yield to maturity?
It is the rate that makes the present value of the cash flows equal the price, found by trial or a solver. Buying the bond above for $950 gives a yield to maturity of about 5.662%, higher than its 5% coupon because you also gain $50 at maturity.
What is the difference between current yield and yield to maturity?
Current yield is just the annual coupon divided by the price: $50 ÷ $925.61 = 5.402%. Yield to maturity also counts the gain or loss to face value at maturity and the timing of every payment, so it is 6% for that bond.
What does modified duration tell me?
The approximate percentage change in price for a one-point change in yield. The example bond has a modified duration of about 7.67, so a rise from 6% to 7% would cut its price by roughly 7.7%, a little less in reality because of convexity.
Why does the price fall when interest rates rise?
The coupons are fixed. When new bonds pay more, buyers will only pay less for the old bond, enough that its yield matches the market. A 5% 30-year bond is worth $1,393.80 at a 3% yield but $750.55 at 7%.