How coupon income and the price gap combine into a bond's yield
A bond's current yield compares its annual coupon with today's price. Yield to maturity additionally accounts for the difference between purchase price and face value over the remaining payments.
The two yields answer different questions and are shown in separate result cards above a cash-flow journey. A bond bought above face value can have a lower YTM than current yield because the principal repayment is below the purchase price.
Current yield and nominal yield to maturity appear as separate results. The cash-flow path explains why coupon income divided by price cannot describe the whole modeled return through maturity.
How price, face value, coupon, maturity and frequency set the yields
Current yield needs only the coupon and the price. Yield to maturity uses every field, so maturity and payment frequency move it even when current yield stays the same.
- Market price
- The amount paid for the bond, excluding accrued interest. Price moves both yields the other way: in the example, raising it from 95 to 105 drops current yield from 5.2632% to 4.7619% and nominal YTM from 6.9018% to 3.2247%. A premium bond's YTM falls below its current yield because less comes back at maturity than was paid.
- Face value
- The principal repaid at maturity, and the base the coupon rate is applied to. A quote of 98.5 against 100 face gives the same yields as 985 against 1,000. Mixing scales is the common slip: a 985 price with 100 face looks like a huge premium and returns a nominal YTM of about −52%.
- Annual coupon rate
- The yearly interest printed on the bond as a percentage of face value, so 5% on 100 face pays 5 a year whatever you paid. It is the numerator of current yield and moves that figure in direct proportion. Enter the stated coupon, not a yield from a broker screen, or the tool will treat a yield as a cash payment.
- Whole years to maturity
- The remaining life over which a discount or premium is spread. Holding the price at 95, nominal YTM is 7.796% with 2 years left, 6.9018% with 3 and 5.6687% with 10, while current yield stays at 5.2632%. Only whole years are accepted, so an odd remaining term such as 2 years and 7 months has to be rounded.
- Coupon payments per year
- Splits the annual coupon into 1, 2, 4 or 12 payments and converts the solved periodic yield back to a nominal annual figure. Moving the example from annual to semiannual payments leaves current yield unchanged but lowers nominal YTM from 6.9018% to 6.8728%, because the half-year yield is doubled without compounding. Match the schedule stated in the bond's terms.
Steps
- Enter a positive market price and face value in the same currency.
- Enter the annual coupon rate and a whole number of years to maturity.
- Choose the payment frequency and calculate to compare current yield with nominal YTM.
Reading tip: Read current yield with nominal YTM and the coupon-to-maturity journey. A negative YTM keeps its minus sign in the YTM card.
Bond-quote questions these two yields can answer
Compare bond quotes
Read current yield alongside modeled yield to maturity.
Understand coupon income
See the regular payment implied by face value and coupon rate.
Explore price changes
Check how a discount or premium affects the modeled yield.
Review payment frequency
See how annual and more frequent coupons alter the cash-flow schedule.
How the calculation works
- P
- Market price paid for the bond, in the same currency as face value.
- F / c
- Face value repaid at maturity / stated annual coupon rate as a percentage.
- m / N
- Coupon payments per year / total remaining coupon payments.
- C / y / t
- Coupon in each payment / periodic yield solved numerically / payment number from 1 to N.
- Σ
- Add the present value of each coupon payment in the schedule.
YTM is found by numerical search; it is a model for the stated cash flows, not a guaranteed return.
What every part means
- P
- Market price paid for the bond, in the same currency as face value.
- F / c
- Face value repaid at maturity / stated annual coupon rate as a percentage.
- m / N
- Coupon payments per year / total remaining coupon payments.
- C / y / t
- Coupon in each payment / periodic yield solved numerically / payment number from 1 to N.
- Σ
- Add the present value of each coupon payment in the schedule.
Calculate it step by step
Coupon per payment equals the annual coupon divided by payments per year.
This simple income ratio does not include the eventual face-value repayment.
Solve for periodic rate y across N payments; nominal annual YTM is y × payments per year × 100.
The calculator uses decimal arithmetic and a bisection search for the periodic discount rate that reproduces the entered price. It then converts that periodic rate to a nominal annual YTM using the selected coupon frequency.
See how Calculation Guide tests examples and handles calculation limits.
See it in practice
- Market price
- 95 currency units
- Face value
- 100 currency units
- Annual coupon rate
- 5 %
- Whole years to maturity
- 3 years
- Coupon payments
- Annually
F = 100, c = 5%, m = 1, P = 95, N = 3: C = 5; current yield = 5 ÷ 95 × 100 = 5.2632%. YTM solves 95 = 5/(1+y) + 5/(1+y)² + 105/(1+y)³.
- Nominal annual YTM6.9018%
- Annual coupon5
Interpretation & limitations
How to read your result
Compare the two yield cards as different definitions, not as guaranteed returns. YTM is a modeled discount rate for the assumed cash-flow schedule; selling early or missing payments changes the outcome.
Where this estimate stops
Callable features, default risk, reinvestment results, taxes, fees, accrued interest and real bond day counts are excluded. Consult the bond's prospectus and market quote for an investment decision.
Frequently asked questions
01Is current yield the same as YTM?
No. Current yield ignores the eventual repayment of face value and the time value of each future cash flow.
02Why can YTM be negative?
A very high purchase price can exceed the present value of coupons and repayment at a zero discount rate, implying a negative periodic yield.
03Why is YTM higher on a discount bond?
Receiving face value at maturity adds a gain relative to a below-par purchase price, which current yield leaves out.
04Does YTM guarantee my actual return?
No. It models the entered cash flows through maturity. Actual return also depends on payment, sale and reinvestment outcomes.
05What does the payment-frequency field change?
It divides annual coupon income into more payments and changes the number and timing of discounted cash flows.
06Can a zero-coupon bond be calculated?
Yes. Enter a 0% coupon rate; current yield is zero and YTM reflects the difference between price and face value.
07My broker quotes the price as 98.5. What do I enter for a 1,000 bond?
A price quoted per 100 of face value can be entered as it stands, with face value 100. You can also scale both and enter 985 and 1,000. The yields are identical either way: a 5% semiannual bond with 3 years left gives 5.0761% current yield and 5.5497% nominal YTM. Only the coupon amounts in the facts change scale.
08What if the bond matures in 2 years and 7 months?
The calculator accepts whole years only, so it cannot place a short first coupon period. Rounding moves YTM noticeably for a bond far from par: the example priced at 95 gives 7.796% over 2 years and 6.9018% over 3. For an odd remaining term, rely on a dealer quote or a bond calculator that uses settlement and maturity dates.