Case 1
- Face value
- 1000
- Coupon rate
- 5%
- Yield to maturity
- 6%
- Years to maturity
- 10
- Coupon payments per year
- 2
925.61
Open with these valuesBond Price Calculator
925.61
Result: 925.61A bond is worth the present value of what it will pay you. When the market yield sits above the coupon rate the bond prices below par, when it sits below the coupon rate above par, and when the two match it prices exactly at face value. Coupon rate and yield are annual rates; the payments per year split both.
Worked examples
Case 2
- Face value
- 1000
- Coupon rate
- 7%
- Yield to maturity
- 5%
- Years to maturity
- 10
- Coupon payments per year
- 2
1,155.89
Open with these valuesCase 3
- Face value
- 1000
- Coupon rate
- 0%
- Yield to maturity
- 5%
- Years to maturity
- 10
- Coupon payments per year
- 2
610.27
Open with these valuesHow it's calculated
Price = C × [1 − (1 + y)⁻ⁿ] ÷ y + Face ÷ (1 + y)ⁿ
- StepSplit the annual coupon and the annual yield by the payments per year.
- StepCount the periods: years to maturity times payments per year.
- StepDiscount the coupon stream as an annuity at the yield per period.
- ResultAdd the face value discounted over the same number of periods.
What this number means
A bond price is a present value with two cash flows instead of one, which is why this page sits at the end of the family rather than beside it. The coupons form a stream of equal payments and the face value is a single sum at the end; both are discounted at the same market yield and added. Working through the defaults makes the split visible. A 1000 bond paying a 5 % coupon twice a year over ten years is twenty payments of 25, discounted at 3 % a period because the 6 % yield is halved along with the coupon. Those twenty coupons are worth 371.94 today and the returned face value 553.68, together the 925.61 shown. So nearly sixty percent of the price of a ten-year bond is the repayment at the end, and 500 in nominal coupon money shrinks to 371.94 through timing alone. The price contains no credit risk, no tax and no dealing costs: it values a bond whose issuer pays in full and on time. The assumption worth knowing is inside the yield itself. A yield to maturity is the return you earn only if every coupon is reinvested at that same yield until maturity. Spend the coupons, or reinvest them at a different rate, and your realised return differs from the one priced here even though the bond honoured every payment.
Coupon against yield sets par, premium or discount
A market yield above the coupon rate prices the bond below face value, a yield below it above face value. When the two match, the bond prices exactly at par.
Price and yield move in opposite directions
When the yield rises the same payments are discounted harder and the price falls; when the yield falls the price rises. That inverse relationship is the whole of bond valuation.
Both rates are annual, the frequency splits them
Coupon rate and yield go in as yearly rates and are divided by the payments per year. Paid semi-annually, a 1000 bond with a 5 % coupon and a 6 % yield runs on 25 per period at 3 % over 20 periods.
This is the clean price
It excludes the interest accrued since the last coupon, which is what the market quotes. What a buyer actually hands over, the dirty price, adds that accrued interest on top.
Commonly misread
A bond trading below face value is a bargain.
It prices below face value because the market yield sits above the coupon. The smaller coupon plus the gain at maturity still only delivers the market return.
A 5 % coupon paid twice a year means 50 every six months.
On a face value of 1000 it means 25 twice a year, and the yield is halved to a rate per period in the same way.
Reference table
| Face, coupon, yield, years, payments | Position | Price |
|---|---|---|
| 1000, 5, 3, 10, 2 | Yield well below coupon | 1171.69 |
| 1000, 5, 4, 10, 2 | Premium | 1081.76 |
| 1000, 5, 5, 10, 2 | Yield equals coupon | 1000.00 |
| 1000, 5, 6, 10, 2 | Discount | 925.61 |
| 1000, 5, 7, 10, 2 | Discount | 857.88 |
| 1000, 5, 8, 10, 2 | Yield well above coupon | 796.15 |
Questions
How is a bond's price determined?
A bond's price is the present value of all its future cash flows — every coupon plus the face value repaid at maturity — discounted at the yield the market demands. When the yield rises those payments are discounted harder and the price falls; when the yield falls the price rises. That inverse relationship is the whole of bond valuation.
How do I calculate a bond's price?
Discount the coupons as an annuity and add the discounted face value: Price = C × [1 − (1 + y)⁻ⁿ] ÷ y + Face ÷ (1 + y)ⁿ, where C is the coupon per period, y the yield per period and n the number of periods. A 1000 bond with a 5 % coupon and a 6 % yield over 10 years, paid semi-annually, prices at 925.61.
Why does a bond trade below or above its face value?
It depends on how the coupon rate compares with the market yield. If the yield is higher than the coupon, buyers pay less than face value so that the smaller coupon plus the gain at maturity still delivers the market return; if the yield is lower, the bond is worth more than face value. When yield equals coupon, the bond prices exactly at par.
Does the coupon frequency change the price?
Yes, modestly. More frequent coupons are discounted over more, shorter periods, which shifts the price slightly for the same annual coupon and yield. Most US bonds pay twice a year and many European bonds once, so matching the field to the real bond matters.
Is this the clean price or the dirty price?
The clean price — the value of the bond excluding interest accrued since the last coupon. What a buyer actually hands over, the dirty price, adds that accrued interest on top. The clean price is what the market quotes, so bonds can be compared on the same basis.
Sources and last check
Information, not financial advice.