Bond Yield Calculator
Enter the face value, bond price, coupon rate, coupon frequency and years to maturity to find the yield to maturity, the current yield and the coupon per period.
Updated
Bond Yield Calculator
Our Bond Yield Calculator finds the yield to maturity (YTM) of a bond from five inputs: the face value, the price you pay, the annual coupon rate, how often coupons are paid and the years to maturity. It shows the annual yield together with the current yield, the effective annual yield, 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 the return on a bond without solving the price equation by trial and error.
Quick answer
A 1,000 bond bought at 980 with a 6.5% annual coupon and 10 years to maturity has a yield to maturity of 6.7819%.
- Meaning: the yield to maturity is the annual return earned by buying at today's price and holding the bond until it matures.
- Method: it is the rate that makes the present value of every coupon plus the face value equal to the price.
- Price below face value: the yield is higher than the coupon rate.
- Price above face value: the yield is lower than the coupon rate.
What Is Bond Yield?
Bond yield is the return an investor earns on a bond. The most complete measure is the yield to maturity (YTM): the annual return from buying the bond at its current price, collecting every coupon and receiving the face value at maturity.
The coupon rate is fixed when the bond is issued, but the price changes in the market every day. The yield connects the two. Pay less than the face value and you earn the coupons plus a gain at maturity, so the yield is above the coupon rate. Pay more and the loss at maturity pulls the yield below the coupon rate.
This calculator returns the annual nominal yield, compounded at the coupon frequency. That is the way bond yields are normally quoted.
Bond Yield Formula
The yield to maturity is the rate y that makes the present value of all payments equal to the price:
+ F ÷ (1 + r)n
r = y ÷ m
- P
- Bond price paid today.
- y
- Yield to maturity, the unknown.
- C
- Coupon per period: F × coupon rate ÷ m.
- r
- Yield per period as a decimal.
- n
- Number of payments: years to maturity × m, rounded to a whole number.
- F
- Face value, repaid at maturity.
- m
- Coupon payments per year: 1, 2, 4, 12, 52 or 365.
The equation cannot be rearranged to give y directly, so the yield is found by trial and error: try a rate, price the bond, and move the rate up or down until the price matches. The calculator does this by bisection, halving the search range until the answer is exact to many decimal places.
How to Calculate Bond Yield
A bond has a face value of 1,000, a 6.5% coupon paid once a year and 10 years to maturity. It costs 980. Price it at a few trial yields:
| Trial yield | Price | Against 980 |
|---|---|---|
| 6% | 1,036.80 | Too high |
| 7% | 964.88 | Too low |
| 6.7% | 985.76 | Too high |
| 6.8% | 978.73 | Too low |
| 6.78% | 980.13 | Just high |
| 6.79% | 979.43 | Just low |
- Find the coupon per period. 1,000 × 6.5% = 65 a year, paid in one payment of 65.
- Count the payments. 10 years × 1 payment a year = 10.
- Pick a starting yield. The bond costs less than its face value, so the yield is above the 6.5% coupon rate.
- Price the bond at that yield. A price above 980 means the yield is too low. A price below 980 means it is too high.
- Narrow the range. The price is 980.13 at 6.78% and 979.43 at 6.79%, so the yield lies between them.
- Repeat until the price matches. The yield to maturity is 6.7819%.
Approximate Yield Formula
When a quick estimate is enough, this shortcut gets close without any trial and error:
÷ [(F + P) ÷ 2]
Here C is the annual coupon and t is the years to maturity. The top line is the average yearly income (the coupon plus the yearly share of the gain or loss at maturity) and the bottom line is the average amount invested. For the bond above:
(F − P) ÷ t = 20 ÷ 10 = 2
(F + P) ÷ 2 = 1,980 ÷ 2 = 990
YTM ≈ 67 ÷ 990 = 6.7677%
The exact answer is 6.7819%, so the shortcut is off by about 0.014 of a percentage point. The gap grows as the price moves further from the face value, which is why the calculator always solves the full equation.
Bond Yield Examples
A semi-annual bond at a discount. Face value 1,000, price 950, coupon rate 5% paid semi-annually, 10 years to maturity. The bond pays 25 every six months for 20 payments. The yield to maturity is 5.6617%, which is 2.8308% per half year, and the current yield is 50 ÷ 950 = 5.2632%.
A semi-annual bond at a premium. Face value 1,000, price 1,080, coupon rate 6% paid semi-annually, 8 years to maturity. The buyer pays 80 more than will be repaid, so the yield to maturity is 4.7847%, well below the 6% coupon rate.
A zero coupon bond. Face value 1,000, price 600, no coupons, 10 years to maturity. With no coupons the equation can be solved directly:
= (1,000 ÷ 600)0.1 − 1
= 5.241%
More examples:
| Bond | Yield |
|---|---|
| 1,000 at 980, 6.5% annual 10 years | 6.7819% |
| 1,000 at 950, 5% semi-annual 10 years | 5.6617% |
| 1,000 at 1,080, 6% semi-annual 8 years | 4.7847% |
| 1,000 at 1,000, 5% semi-annual 10 years | 5% |
| 1,000 at 600, zero coupon 10 years | 5.241% |
| 1,000 at 920, 4% quarterly 5 years | 5.8573% |
| 1,000 at 1,040, 7% monthly 3 years | 5.5495% |
| 1,000 at 1,100, 2% annual 2 years | −2.7916% |
The last bond has a negative yield: the buyer pays 1,100 and gets back only 1,040 in total, so the investment loses money if held to maturity. The amounts carry no currency symbol, so the calculator works in any currency.
How Price Changes the Yield
Price and yield move in opposite directions. The cheaper the bond, the higher the yield, because the same coupons and face value are bought for less. A 1,000 bond with a 5% annual coupon and 10 years to maturity:
| Price | Yield | Trades at |
|---|---|---|
| 800 | 7.9776% | Discount |
| 850 | 7.1505% | Discount |
| 900 | 6.3835% | Discount |
| 950 | 5.6687% | Discount |
| 1,000 | 5% | Par |
| 1,050 | 4.3721% | Premium |
| 1,100 | 3.7805% | Premium |
| 1,200 | 2.6921% | Premium |
If you know the yield and want the price instead, use the Bond Price Calculator.
Coupon Rate, Current Yield and Yield to Maturity
Three different percentages describe the same bond. For the 1,000 bond bought at 980 with a 6.5% annual coupon and 10 years left:
| Measure | Value |
|---|---|
| Coupon rate annual coupon ÷ face value | 6.5% |
| Current yield annual coupon ÷ price | 6.6327% |
| Yield to maturity coupons plus gain or loss at maturity | 6.7819% |
- Discount bond: coupon rate < current yield < yield to maturity.
- Par bond: all three are equal.
- Premium bond: coupon rate > current yield > yield to maturity.
The current yield only looks at one year of income. The yield to maturity also counts the gain or loss between the price and the face value and the timing of every payment. For the income measure alone, see the Bond Current Yield Calculator.
Why Coupon Frequency Matters
The frequency sets the coupon per period, the number of payments and how often the yield compounds. For the same price, more frequent coupons give a slightly lower nominal yield, because the same return is reached with more compounding. The 1,000 bond at 980 with a 6.5% coupon and 10 years left:
| Coupons paid | Payments | Yield |
|---|---|---|
| Annually | 10 | 6.7819% |
| Semi-annually | 20 | 6.7786% |
| Quarterly | 40 | 6.777% |
| Monthly | 120 | 6.7759% |
| Weekly | 520 | 6.7755% |
| Daily | 3,650 | 6.7754% |
To compare bonds that pay at different frequencies, use the effective annual yield, which the calculator also shows:
A semi-annual bond with a nominal yield of 5.6617% has an effective annual yield of 5.7418%.
The Five Inputs
- Face value
- The principal repaid at maturity, also called par value. Often 1,000 or 100.
- Bond price
- What the bond costs today, in the same units as the face value.
- 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, weekly or daily.
- Years
- The time left until the bond matures.
What the Calculator Assumes
- Held to maturity. The yield is earned only if the bond is kept until it matures. Selling early gives a different return.
- Coupons reinvested. Every coupon is assumed to be reinvested at the same yield.
- A plain bond. Fixed coupons, face value repaid at maturity, and no call, put or conversion feature.
- A coupon date. The price is taken with no accrued interest, and years × payments per year is rounded to a whole number of payments.
- No default, taxes or fees. Every payment arrives in full and on time, and nothing is deducted.
How to Use the Bond Yield Calculator
- Enter the face value and the bond price. Type the face value, such as 1,000, and the price the bond costs today, such as 980.
- Enter the coupon rate. Type the annual coupon rate as a percentage, such as 6.5. Use 0 for a zero coupon bond.
- Choose how often coupons are paid. Pick annually, semi-annually, quarterly, monthly, weekly or daily.
- Enter the years to maturity. Type the years left until the bond matures, such as 10.
- Read and copy the result. The yield to maturity appears as you type, with the current yield, the discount or premium, the effective annual yield, the annual coupon and the coupon per period. Press Copy to copy the yield, or Clear or Esc to start again.
Example: a face value of 1,000, a price of 950, a 5% coupon paid semi-annually and 10 years to maturity. The result is a yield to maturity of 5.6617%, a current yield of 5.2632% and a coupon of 25 per period.
Who Can Use This Calculator?
Frequently Asked Questions (FAQs)
What is bond yield?
Bond yield is the return an investor earns on a bond. The yield to maturity is the annual return from buying the bond at its current price, collecting every coupon and receiving the face value at maturity.
How do you calculate the yield of a bond?
Find the rate that makes the present value of every coupon plus the face value equal to the price. There is no direct formula, so the rate is found by trial and error. A 1,000 bond bought at 980 with a 6.5% annual coupon and 10 years left has a yield to maturity of 6.7819%.
What is the approximate formula for yield to maturity?
YTM is roughly [C + (F − P) ÷ t] ÷ [(F + P) ÷ 2], where C is the annual coupon, F the face value, P the price and t the years to maturity. For a 1,000 bond at 980 with a 65 coupon and 10 years left it gives 6.7677%, close to the exact 6.7819%.
What is the difference between current yield and yield to maturity?
Current yield is the annual coupon divided by the price, so it measures income only. Yield to maturity also includes the gain or loss between the price and the face value and the timing of every payment. A 1,000 bond at 980 with a 6.5% coupon has a current yield of 6.6327% and a yield to maturity of 6.7819%.
Why does the yield rise when the bond price falls?
The coupons and the face value are fixed. Paying less for the same payments means a higher return, so the yield rises. Paying more means a lower return, so the yield falls.
Is the yield higher or lower than the coupon rate?
It depends on the price. Below face value (a discount) the yield is higher than the coupon rate. At face value (par) the two are equal. Above face value (a premium) the yield is lower than the coupon rate.
Can a bond yield be negative?
Yes. If the price is higher than all the remaining coupons plus the face value, the investor gets back less than was paid. A 1,000 bond with a 2% annual coupon and 2 years left bought at 1,100 has a yield to maturity of −2.7916%.
How do you find the yield of a zero coupon bond?
Enter a coupon rate of 0. The yield is then (F ÷ P)^(1 ÷ n) − 1. A 1,000 zero coupon bond bought at 600 with 10 years left yields 5.241%.
Is the Bond Yield Calculator free?
Yes. It is completely free, needs no sign-up, and can be used as many times as you like.
Sources
- Wikipedia. Yield to maturity.
- Corporate Finance Institute. Yield to Maturity (YTM).
- Wall Street Prep. Understanding Yield to Maturity (YTM).
- WallStreetMojo. Yield to Maturity (YTM).
- OpenStax. Principles of Finance, 10.2 Bond Valuation.
- Wikipedia. Current yield.
Try our Bond Yield Calculator to find the yield to maturity of any fixed coupon bond in seconds.