Bond YTM Calculator
Enter the face value, bond price, coupon rate, coupon frequency and years to maturity to find the yield to maturity (YTM), the current yield and the total you receive.
Updated
Bond YTM Calculator
Our Bond YTM Calculator works out the yield to maturity 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 left until maturity. Alongside the YTM it shows the current yield, the effective annual yield, the coupon per period, the number of payments, the total you receive and whether the bond trades at a discount, at a premium or at par. It saves investors, students and analysts from solving the bond price equation by hand.
Quick answer
A 1,000 bond bought at 920 with a 5% coupon paid semi-annually and 8 years to maturity has a yield to maturity of 6.2878%.
- Definition: YTM is the single annual rate that discounts every remaining coupon and the face value back to today's price.
- What it measures: the yearly return from buying now and holding the bond until it matures.
- Discount bond: YTM is above the coupon rate.
- Premium bond: YTM is below the coupon rate.
- No direct formula: the rate is found by trial and error.
What Is Yield to Maturity (YTM)?
Yield to maturity (YTM) is the total annual return an investor earns by buying a bond at today's price and holding it until it matures. It counts three things together: the coupons, the gain or loss between the price and the face value, and the timing of every payment.
In other words, YTM is the internal rate of return of the bond. It is the one discount rate at which the present value of all the remaining payments equals the price.
YTM is quoted as an annual nominal rate, compounded at the coupon frequency. A semi-annual bond with a YTM of 6.2878% earns 3.1439% every half year. Because it puts bonds with different prices, coupons and maturities on one scale, YTM is the standard number for comparing them.
YTM Formula
YTM is the rate y that makes this equation true:
+ 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 first part is the present value of the coupons and the second part is the present value of the face value. The equation cannot be rearranged to give y on its own, so YTM is found by trying rates until the right side equals the price. The calculator does this by bisection: it halves the search range again and again until the answer is exact to many decimal places.
How to Calculate YTM Step by Step
A bond has a face value of 1,000 and a 5% coupon paid semi-annually. It matures in 8 years and costs 920.
- Find the coupon per period. 1,000 × 5% = 50 a year, paid as 25 every six months.
- Count the payments. 8 years × 2 payments a year = 16.
- Choose a first guess. The price is below the face value, so the YTM must be above the 5% coupon rate. Start at 6%.
- Price the bond at the guess. At 6% the bond is worth 937.19, more than 920, so the guess is too low.
- Move the guess and repeat. At 7% the bond is worth 879.06, less than 920, so the YTM lies between 6% and 7%.
- Keep narrowing. The price is 920.46 at 6.28% and 919.87 at 6.29%. The YTM is 6.2878%.
| Trial YTM | Price | Against 920 |
|---|---|---|
| 6% | 937.19 | Too high |
| 7% | 879.06 | Too low |
| 6.2% | 925.21 | Too high |
| 6.3% | 919.28 | Too low |
| 6.28% | 920.46 | Just high |
| 6.29% | 919.87 | Just low |
A price that comes out too high means the trial rate is too low, and the other way round. Price and yield always move in opposite directions.
Approximate YTM Formula
For a quick estimate without trial and error, use the approximation:
÷ [(F + P) ÷ 2]
C is the annual coupon and t is the years to maturity. For the bond above:
(F − P) ÷ t = 80 ÷ 8 = 10
(F + P) ÷ 2 = 1,920 ÷ 2 = 960
YTM ≈ 60 ÷ 960 = 6.25%
The exact YTM is 6.2878%, so the estimate is about 0.038 of a percentage point too low. It is good enough for a rough check and a sensible first guess, but it drifts further from the true figure as the price moves away from the face value.
YTM Examples
A premium bond. Face value 1,000, price 1,050, coupon rate 7% paid annually, 5 years to maturity. The buyer collects 70 a year but loses 50 at maturity, so the YTM is 5.8189%. That is below both the 7% coupon rate and the current yield of 70 ÷ 1,050 = 6.6667%.
A zero coupon bond. Face value 1,000, price 700, no coupons, 6 years to maturity. With a single payment the equation can be solved directly:
= (1,000 ÷ 700)1 ÷ 6 − 1
= 6.1248%
A bond bought above everything it will pay. Face value 1,000, price 1,150, coupon rate 3% paid annually, 3 years to maturity. The bond pays 1,090 in total (three coupons of 30 plus 1,000) for a price of 1,150, so the YTM is negative: −1.8192%.
More results from the calculator:
| Bond | YTM |
|---|---|
| 1,000 at 920, 5% semi-annual 8 years | 6.2878% |
| 1,000 at 1,050, 7% annual 5 years | 5.8189% |
| 1,000 at 700, zero coupon 6 years | 6.1248% |
| 1,000 at 990, 4.5% quarterly 3 years | 4.8602% |
| 100 at 97.5, 3% semi-annual 2 years | 4.3182% |
| 1,000 at 1,020, 6% monthly 4 years | 5.4425% |
| 5,000 at 4,600, 4.2% semi-annual 15 years | 4.9625% |
| 1,000 at 1,000, 4% semi-annual 7 years | 4% |
The amounts carry no currency symbol, so the calculator works in any currency. A bond bought exactly at its face value always has a YTM equal to its coupon rate.
YTM vs Coupon Rate and Current Yield
The same bond can be described by three percentages. For the 1,000 bond bought at 920 with a 5% semi-annual coupon and 8 years left:
| Measure | Value |
|---|---|
| Coupon rate annual coupon ÷ face value | 5% |
| Current yield annual coupon ÷ price | 5.4348% |
| Yield to maturity coupons, gain or loss and timing | 6.2878% |
- Bought at a discount: coupon rate < current yield < YTM.
- Bought at par: all three are the same.
- Bought at a premium: coupon rate > current yield > YTM.
The coupon rate never changes and the current yield ignores what happens at maturity. Only YTM includes the 80 gained when a bond bought at 920 is repaid at 1,000. For the income measure on its own, use the Bond Current Yield Calculator. To go the other way, from a yield to a price, use the Bond Price Calculator.
How Time to Maturity Changes YTM
A discount or premium counts for more when there is little time to spread it over. Take a 1,000 bond with a 5% annual coupon, bought at 950 or at 1,050:
| Years left | At 950 | At 1,050 |
|---|---|---|
| 1 | 10.5263% | 0% |
| 2 | 7.796% | 2.4093% |
| 3 | 6.9018% | 3.2247% |
| 5 | 6.1932% | 3.8806% |
| 10 | 5.6687% | 4.3721% |
| 20 | 5.4155% | 4.6119% |
| 30 | 5.3379% | 4.6863% |
With one year left, the 50 gain on the bond bought at 950 is earned in a single year and lifts the YTM to 10.5263%. Spread over 30 years the same 50 adds only about a third of a percentage point.
YTM and Reinvested Coupons
YTM assumes every coupon is reinvested at the YTM itself until the bond matures. The return you really end up with, called the realized yield, depends on the rate the coupons actually earn. For the 1,000 bond bought at 920 (16 coupons of 25):
| Coupons earn | At maturity | Realized |
|---|---|---|
| 6.2878% | 1,509.68 | 6.2878% |
| 3% | 1,448.31 | 5.7534% |
| 0% | 1,400 | 5.3176% |
So YTM is a promise only if rates stay where they are. When coupons are reinvested at lower rates the realized yield falls short of the YTM, and when they are reinvested at higher rates it beats it. A zero coupon bond has no coupons to reinvest, so its YTM is locked in when it is held to maturity.
The Five Inputs
- Face value
- The principal repaid at maturity, also called par value. Often 1,000 or 100.
- Bond price
- The market price paid today, in the same units as the face value.
- Coupon rate
- The annual interest on the face value, as a percentage. Enter 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. Decimals such as 7.5 are fine.
Limits of YTM
- Held to maturity. Selling before maturity gives a different return, because the sale price depends on rates at that time.
- Callable bonds. If the issuer can repay early, yield to call or yield to worst is the safer number. This calculator does not model call or put features.
- 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. Every coupon and the face value are assumed to arrive in full and on time.
- Before taxes and fees. Tax on coupons and dealing costs lower the return you keep.
How to Use the Bond YTM 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 920.
- Enter the coupon rate. Type the annual coupon rate as a percentage, such as 5. Enter 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 8.
- Read and copy the YTM. The yield to maturity appears as you type, with the current yield, the discount or premium, the effective annual yield, the coupon per period, the number of payments and the total received. Press Copy to copy the YTM, or Clear or Esc to start again.
Example: a face value of 1,000, a price of 920, a 5% coupon paid semi-annually and 8 years to maturity. The result is a YTM of 6.2878%, a current yield of 5.4348%, a coupon of 25 per period and 1,400 received in total.
Who Can Use This Calculator?
Frequently Asked Questions (FAQs)
What is yield to maturity (YTM)?
Yield to maturity is the total annual return from buying a bond at its current price and holding it until it matures. It is the single discount rate that makes the present value of every remaining coupon plus the face value equal to the price.
How do you calculate the YTM of a bond?
Find the rate at which the present value of all coupons plus the face value equals the price. There is no direct formula, so the rate is found by trial and error. A 1,000 bond bought at 920 with a 5% semi-annual coupon and 8 years left has a YTM of 6.2878%.
What is the approximate YTM formula?
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 920 with a 50 coupon and 8 years left it gives 60 ÷ 960 = 6.25%, close to the exact 6.2878%.
Is YTM the same as the coupon rate?
Only when the bond is bought at its face value. Below face value the YTM is higher than the coupon rate, and above face value it is lower, because YTM also counts the gain or loss at maturity.
What is the difference between YTM and current yield?
Current yield is the annual coupon divided by the price, so it measures income for one year. YTM also includes the gain or loss between the price and the face value and the timing of every payment. A 1,000 bond at 920 with a 5% coupon has a current yield of 5.4348% and a YTM of 6.2878%.
What is a good YTM?
There is no single good figure. A YTM is judged against bonds of similar credit quality and maturity and against government bond yields. A much higher YTM than similar bonds usually signals higher risk, not a bargain.
Can YTM be negative?
Yes. If the price is higher than all the remaining coupons plus the face value, the buyer gets back less than was paid. A 1,000 bond with a 3% annual coupon and 3 years left bought at 1,150 has a YTM of −1.8192%.
How do you find the YTM of a zero coupon bond?
Enter a coupon rate of 0. The YTM is then (F ÷ P)^(1 ÷ n) − 1. A 1,000 zero coupon bond bought at 700 with 6 years left has a YTM of 6.1248%.
Does YTM assume coupons are reinvested?
Yes. YTM assumes each coupon is reinvested at the same rate until maturity. If coupons earn less, the realized yield is lower than the YTM. With no reinvestment at all, the 6.2878% bond above would return 5.3176% a year.
Is the Bond YTM 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. Bond valuation.
Try our Bond YTM Calculator to find the yield to maturity of any fixed coupon bond in seconds.