What this calculator does
Yield to maturity is the return a bond delivers if held to the end, counting both the coupons received and the gain or loss between the purchase price and the face value repaid at maturity.
It explains why a bond price and its yield move in opposite directions. A 5 per cent bond bought at par yields exactly 5.00 per cent, but bought at $850 it yields 7.12 per cent, because the buyer also collects $150 of capital gain over the remaining term.
The formula
Yield to maturity is the discount rate at which the present value of all coupons plus the face value equals the current market price. There is no closed-form solution, so it is found by iteration.
| Term | Meaning |
|---|---|
| Yield to maturity | The total annualised return if the bond is held to maturity and coupons are reinvested at that rate. |
| Current yield | Annual coupon divided by price, ignoring any capital gain or loss. |
| Premium and discount | Trading above or below face value, which happens when the coupon differs from prevailing rates. |
The inputs explained
| Field | What to enter |
|---|---|
| Face value ($) | The face value repaid at maturity, usually 1,000. |
| Current market price ($) | The current market price of the bond. |
| Coupon rate (%) | The annual coupon rate as a percentage of face value. |
| Years to maturity | Years remaining until maturity. |
| Payments per year | Coupon payments per year. Most bonds pay semi-annually. |
When to use it
Comparing two bonds
Yield to maturity puts bonds with different coupons, prices and maturities on a single comparable basis.
Assessing a bond bought at a discount
The capital gain to maturity can contribute more than the coupon does.
Understanding a price move
When market rates rise, existing bond prices fall until their yields match what is newly available.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How does price drive the yield?
The same bond at four market prices.
| Market price | Yield to maturity | Current yield |
|---|---|---|
| $850 | 7.12% | 5.88% |
| $920 | 6.08% | 5.43% |
| $1000 | 5.00% | 5.00% |
| $1080 | 4.02% | 4.63% |
Questions
Why do bond prices fall when rates rise?
Because a bond paying a fixed 5 per cent is less attractive once new bonds pay 7 per cent. Its price falls until the total return to maturity matches what is newly available, which is the whole mechanism of the bond market.
What is the difference between current yield and yield to maturity?
Current yield only counts the coupon against the price. Yield to maturity also includes the gain or loss between the price paid and the face value returned, which is why the two differ whenever a bond trades away from par.
Does yield to maturity assume anything?
Yes, and it is a significant assumption: that every coupon is reinvested at the same yield. If rates change, the realised return will differ from the quoted figure.
Why can a bond trade above face value?
Because its coupon exceeds what new bonds pay. Buyers will pay a premium for the higher income, accepting a capital loss at maturity in exchange, which leaves the yield in line with the market.
For how sensitive that price is to rate changes, see the bond duration and convexity calculator. For a callable bond's return, see the yield to call calculator.