Yield to Maturity Calculator
What a bond really returns if held to the end, counting both the coupons and the gain or loss against face value.
Results
What this tool does
A bond's coupon tells you what it pays; its yield to maturity tells you what it earns. The two differ whenever the price is not exactly face value, because buying below par adds a capital gain at redemption and buying above par subtracts one. Working the yield out means finding the rate that makes all the future payments add up to today's price, and there is no formula for it — it has to be searched for. This page does that, and shows the textbook approximation alongside so you can see how far off the shortcut is.
Formula
find y such that price = Σ coupon ÷ (1+y)^t + face value ÷ (1+y)^n · no closed-form solution
Variables
| Symbol | Meaning | Unit |
|---|---|---|
face | Face value | — |
coupon | Coupon rate | % |
price | Bond price | — |
years | Years to maturity | — |
freq | Coupons per year | — |
YT | Yield to maturity | % |
PO | How it trades | — |
EY | Effective annual yield | % |
CY | Current yield | % |
PY | Yield per period | % |
AX | The textbook approximation | % |
CP | Each coupon | — |
CT | All the coupons together | — |
CG | Gain or loss at maturity | — |
TR | Everything you get back | — |
NP | Periods | — |
Worked example
- Face value1000
- Coupon rate6 %
- Bond price950
- Years to maturity5
- Coupons per year2
- Yield to maturity7.2087 %
- How it tradesBelow face value
- Effective annual yield7.3387 %
- Current yield6.3158 %
- Yield per period3.604374 %
- The textbook approximation7.1795 %
- Each coupon30.00
- All the coupons together300.00
- Gain or loss at maturity50.00
- Everything you get back350.00
- Periods10
Limitations
- This is an informational calculator, not personalised financial advice. Rates, fees, taxes and contract conditions vary between institutions and countries.
- The tool works with whatever currency you use for the inputs; it does not convert between currencies.
Frequently asked questions
Why is the yield higher than the coupon?
Because you are paying less than face value and will be repaid the full face value at the end. A bond bought at 950 that repays 1,000 gives you 50 of capital gain on top of every coupon, and that gain is part of the return. The rule is symmetrical: below face value the yield beats the coupon, above it the yield falls short, and exactly at face value the two are identical. The page says which of the three you are in.
What does the yield to maturity quietly assume?
Three things, all of which can fail. That you hold the bond to the end — sell early and you get the market price, not this. That the issuer pays everything, on time; a yield that looks unusually generous is usually the market pricing in doubt, not a bargain. And that every coupon you receive is reinvested at this same yield, which is rarely possible and is the reason the realised return of a bond held to maturity so often differs from the figure quoted when it was bought.