Bond Price Calculator
Enter the face value, coupon rate, coupon frequency, years to maturity and yield to maturity to find the bond price, the annual coupon and the coupon per period.
Updated
Bond Price Calculator
Our Bond Price Calculator finds the fair price of a bond from five inputs: the face value, the annual coupon rate, how often coupons are paid, the years to maturity and the yield to maturity (YTM). It shows the bond price together with the annual coupon, the coupon per period and whether the bond trades at a discount, at a premium or at par. It is made for investors, students and analysts who want to value government bonds, corporate bonds and other fixed coupon bonds without discounting every payment by hand.
Quick answer
A 1,000 bond with a 5% annual coupon and 10 years to maturity is worth 926.40 when the yield to maturity is 6%.
- Formula: price = C × [1 − (1 + r)−n] ÷ r + F ÷ (1 + r)n.
- Meaning: the price is the present value of every coupon plus the face value.
- Yield above coupon rate: the bond trades at a discount, below face value.
- Yield below coupon rate: the bond trades at a premium, above face value.
What Is a Bond Price?
A bond is a loan from an investor to a borrower. In return the borrower pays a coupon at regular intervals and repays the face value at maturity. The bond price is what all of those future payments are worth today.
To find it, each coupon and the face value are discounted at the yield to maturity, the return the market currently asks for on that bond. A payment that arrives later is discounted more, so a higher yield or a longer wait lowers what the payment is worth now.
The coupon is fixed when the bond is issued, but the yield changes with the market. That is why the price of a bond moves every day even though its payments never change.
Bond Price Formula
The price is the present value of the coupons, which form an annuity, plus the present value of the face value:
+ F ÷ (1 + r)n
- P
- Bond price.
- C
- Coupon per period: F × coupon rate ÷ m.
- r
- Yield per period as a decimal: YTM ÷ m.
- n
- Number of periods: years to maturity × m.
- F
- Face value, repaid at maturity.
- m
- Coupon payments per year: 1, 2, 4, 12 or 365.
When the yield is exactly 0% nothing is discounted, so the price is simply every payment added up: P = C × n + F.
How to Calculate Bond Price
A bond has a face value of 1,000, a 5% coupon paid once a year, 10 years to maturity and a yield to maturity of 6%:
r = 6% ÷ 1 = 0.06
n = 10 × 1 = 10
(1.06)−10 = 0.558395
(1 − 0.558395) ÷ 0.06
= 7.360087
Coupons = 50 × 7.360087
= 368.004
Face = 1,000 × 0.558395
= 558.395
P = 368.004 + 558.395
= 926.40
- Find the coupon per period. 1,000 × 5% = 50 a year, paid in one payment of 50.
- Find the yield per period and the number of periods. 6% ÷ 1 = 0.06 and 10 × 1 = 10.
- Find the discount factor. 1.06 raised to the power of −10 is 0.558395.
- Value the coupons. 50 × (1 − 0.558395) ÷ 0.06 = 368.004.
- Value the face value. 1,000 × 0.558395 = 558.395.
- Add the two. 368.004 + 558.395 = 926.40.
The yield (6%) is higher than the coupon rate (5%), so the bond trades at a discount of 73.60 to its face value.
Bond Price Examples
A corporate bond at a discount. Face value 5,500, coupon rate 3.8% paid annually, 12 years to maturity, yield to maturity 7.7%. The coupon is 5,500 × 3.8% = 209 a year and the bond price is 3,858.08. The yield is far above the coupon rate, so investors pay much less than the face value.
A semi-annual bond at a premium. Face value 1,000, coupon rate 6% paid semi-annually, 8 years to maturity, yield to maturity 4%:
r = 4% ÷ 2 = 0.02
n = 8 × 2 = 16
(1.02)−16 = 0.728446
Coupons = 30 × 13.577709
= 407.331
Face = 1,000 × 0.728446
= 728.446
P = 407.331 + 728.446
= 1,135.78
The coupon rate is higher than the yield, so the bond is worth 135.78 more than its face value. More examples:
| Bond | Price |
|---|---|
| 1,000, 5% annual, 10 years yield 6% | 926.40 |
| 5,500, 3.8% annual, 12 years yield 7.7% | 3,858.08 |
| 1,000, 6% semi-annual, 8 years yield 4% | 1,135.78 |
| 1,000, 5% semi-annual, 10 years yield 5% | 1,000.00 |
| 1,000, 0% (zero coupon), 10 years yield 4% | 675.56 |
| 1,000, 3% quarterly, 2 years yield 4% | 980.87 |
| 1,000, 5% monthly, 7 years yield 4.2% | 1,048.45 |
| 100, 4% semi-annual, 30 years yield 5% | 84.55 |
The amounts carry no currency symbol, so the calculator works in any currency.
Discount, Premium and Par Bonds
Comparing the yield to maturity with the coupon rate tells you where the price sits against the face value:
| Bond | When | Price |
|---|---|---|
| Discount | YTM > coupon | Below face |
| Par | YTM = coupon | Equal to face |
| Premium | YTM < coupon | Above face |
A discount bond pays coupons that are lower than the market asks for, so the buyer is made whole by paying less and collecting the full face value at maturity. A premium bond pays more than the market asks for, so the buyer pays extra for it. The calculator shows which of the three applies and by how much.
How Yield to Maturity Changes the Price
Yield to maturity is the total return an investor earns by holding the bond until it matures, assuming every coupon is reinvested at the same rate. Bond prices move in the opposite direction to yields: when the yield rises the price falls, and when the yield falls the price rises. A 1,000 bond with a 5% annual coupon and 10 years to maturity:
| Yield | Price | Trades at |
|---|---|---|
| 2% | 1,269.48 | Premium |
| 3% | 1,170.60 | Premium |
| 4% | 1,081.11 | Premium |
| 5% | 1,000.00 | Par |
| 6% | 926.40 | Discount |
| 7% | 859.53 | Discount |
| 8% | 798.70 | Discount |
| 10% | 692.77 | Discount |
If you know the price and want the yield instead, use the Bond YTM Calculator.
Why Coupon Frequency Matters
Bonds pay interest at different intervals. Many corporate and government bonds pay semi-annually, while other instruments pay annually, quarterly or monthly. The frequency changes three things:
- The coupon per period. The annual coupon is split into that many payments.
- The number of periods. Years to maturity × payments per year.
- The yield per period. The yield to maturity ÷ payments per year.
The effect on the price is small but real. A 1,000 bond with a 5% coupon, 10 years to maturity and a 6% yield:
| Coupons paid | Periods | Price |
|---|---|---|
| Annually | 10 | 926.40 |
| Semi-annually | 20 | 925.61 |
| Quarterly | 40 | 925.21 |
| Monthly | 120 | 924.94 |
| Daily | 3,650 | 924.81 |
Maturity and Interest Rate Risk
The longer the maturity, the more the price reacts to a change in yield, because more of the value sits in payments that are far away. A 1,000 bond with a 5% annual coupon, priced at a 6% yield and at a 4% yield:
| Years | At 6% | At 4% |
|---|---|---|
| 1 | 990.57 | 1,009.62 |
| 2 | 981.67 | 1,018.86 |
| 5 | 957.88 | 1,044.52 |
| 10 | 926.40 | 1,081.11 |
| 20 | 885.30 | 1,135.90 |
| 30 | 862.35 | 1,172.92 |
A 1% rise in yield from the coupon rate costs the 2 year bond 18.33 and the 30 year bond 137.65. To measure this sensitivity, see the Bond Convexity Calculator.
The Five Inputs
- Face value
- The principal repaid at maturity, also called par value. Often 1,000 or 100.
- Coupon rate
- The annual interest paid on the face value, as a percentage. Use 0 for a zero coupon bond.
- Coupons paid
- How often the coupon is paid: annually, semi-annually, quarterly, monthly or daily.
- Years
- The time left until the bond matures.
- Yield
- The yield to maturity (YTM) as an annual percentage, the return the market requires.
What You Can Use It For
- Compare bonds. Price bonds with different coupon rates and maturities at the same yield.
- Test yield changes. Change the yield to see how far the price would move if market rates shift.
- Check a quote. See whether a quoted price is above or below the value at the return you require.
- Plan a bond ladder. Price bonds of several maturities side by side.
- Learn bond valuation. Check present value, compounding frequency and time value of money problems.
What the Calculator Assumes
- A plain bond. Fixed coupons, face value repaid at maturity, and no call, put or conversion feature.
- A coupon date. The result is the price with no accrued interest. If years × payments per year is not a whole number, the formula is applied with that fractional number of periods, which is an approximation.
- One yield. Every payment is discounted at the same yield to maturity, compounded at the coupon frequency.
- No default. Every coupon and the face value are paid in full and on time.
How to Use the Bond Price Calculator
- Enter the face value and the coupon rate. Type the face value, such as 1,000, and the annual coupon rate as a percentage, such as 5.
- Choose how often coupons are paid. Pick annually, semi-annually, quarterly, monthly or daily.
- Enter the years to maturity. Type the years left until the bond matures, such as 10.
- Enter the yield to maturity. Type the yield to maturity as a percentage, such as 6.
- Read and copy the result. The bond price appears as you type, with the discount or premium, the value of the coupons and of the face value, the annual coupon and the coupon per period. Press Copy to copy the price, or Clear or Esc to start again.
Example: a face value of 1,000, a 6% coupon paid semi-annually, 8 years to maturity and a 4% yield. The result is a bond price of 1,135.78, a premium of 135.78, with a coupon of 30 per period.
Who Can Use This Calculator?
Frequently Asked Questions (FAQs)
What is a bond price?
A bond price is the present value of all the future payments of a bond: every coupon plus the face value repaid at maturity, each discounted at the yield to maturity.
How do you calculate the price of a bond?
Use price = C × [1 − (1 + r)^−n] ÷ r + F ÷ (1 + r)^n, where C is the coupon per period, r is the yield per period, n is the number of periods and F is the face value. A 1,000 bond with a 5% annual coupon and 10 years left is worth 926.40 at a 6% yield.
Why does the bond price change when the yield to maturity changes?
Bond prices move in the opposite direction to yields. A higher yield discounts the same future payments more heavily, so the price falls. A lower yield discounts them less, so the price rises.
How does payment frequency affect the bond price?
The frequency sets the coupon per period, the number of periods and the yield per period. A semi-annual bond splits the annual coupon and the yield in two and doubles the number of periods. A 1,000 bond with a 5% coupon and 10 years left at a 6% yield is worth 926.40 with annual coupons and 925.61 with semi-annual coupons.
What is the difference between coupon rate and yield to maturity?
The coupon rate is the fixed interest rate stated on the bond and sets the coupon payments. The yield to maturity is the return investors require at current market conditions. The price adjusts so that the fixed coupons deliver that required yield.
Why is my bond priced below its face value?
A price below face value means the bond trades at a discount. This happens when the yield to maturity is higher than the coupon rate: the coupons pay less than the market requires, so the price falls to make up the difference.
How do you price a zero coupon bond?
Enter a coupon rate of 0. The price is then just the face value discounted to today: F ÷ (1 + r)^n. A 1,000 zero coupon bond with 10 years left at a 4% yield is worth 675.56.
Can this calculator be used for different types of bonds?
Yes. It works for government, corporate, municipal and other bonds that pay a fixed coupon and repay the face value at maturity. It does not allow for call features, floating coupons or accrued interest.
Is the Bond Price Calculator free?
Yes. It is completely free, needs no sign-up, and can be used as many times as you like.
Sources
- Wikipedia. Bond valuation.
- OpenStax. Principles of Finance, 10.2 Bond Valuation.
- Corporate Finance Institute. Bond Pricing.
- WallStreetMojo. Bond Pricing Formula.
- Investor.gov. Bonds.
- Wikipedia. Yield to maturity.
Try our Bond Price Calculator to find the fair price of any fixed coupon bond in seconds.