Yield to Maturity (YTM)
Keep future coupons and principal fixed, then change today's price to solve for the balancing .
Known future payments, solve for the rate
Why does a lower purchase price mean a higher YTM?
This bond has 1,000 face value, a 5% coupon, five years remaining, and semiannual coupons. Change only today's market price; future coupons and principal stay fixed.
Price equals face value. Under these standard fixed-coupon assumptions, YTM equals the coupon rate.
Substitute the numerically solved YTM into ten coupon periods and principal
- YTM is solved numerically at full precision; the displayed yield is rounded and t indexes coupon periods. Timeline selection highlights one fixed payment.
Selecting t₀ shows a fixed cash flow. Moving price changes only the $1,000.00 paid today, not that future payment.
The discount/par/premium comparison assumes the standard bond here pays its promised fixed cash flows on schedule. YTM is not a guaranteed realized return.
Bond Price starts with YTM and finds price. Here the price is known, and we solve for the YTM that makes the future cash flows' present value match it. See the Bond Price guide →
What did you just see?
A lower purchase price generally implies a higher yield for the same coupons and .
Rate, periods, and valuation timing
This page assumes purchase on a coupon date, with N = remaining years × coupon payments per year m as a whole number of periods. is nominal annual yield, discounted at YTM ÷ m per period, rather than an effective annual rate. Realized compound return also depends on coupon reinvestment and timely payments.
Infer a rate from the full payment stream
determines promised payments and compares annual income with price. YTM instead connects purchase price, every coupon and redemption through time value.
The model discounts scheduled payments at YTM divided by payment frequency until their PV equals the purchase price. Compare bonds using consistent yield conventions, credit conditions and cash-flow assumptions.
Why bond prices usually fall as yields rise
If new bonds offer a higher required return, an older bond's fixed payments look less attractive. Its price generally needs to fall to compete.
Formally, largely fixed future payments are worth less today when discounted at a higher periodic YTM/m. This comparison holds cash flows, credit, and other assumptions constant.
The same income yield, different time to redemption
A US$1,000 bond paying 4% annually and bought for US$900 has a current yield of 4.44%. With one year remaining, YTM is 15.56%; with five years remaining, it is approximately 6.40%. Waiting longer for the same redemption gain changes the implied rate even though the income ratio is identical.
YTM reverses bond pricing. Fix the purchase price, then find the rate that equates it to the present value of all promised payments. Coupon dates and redemption matter. YTM is neither the coupon rate nor total five-year profit divided by five.
An internal rate is not a terminal-wealth promise
Computing YTM does not require coupons actually to be reinvested: it is an internal rate for a payment stream. Interpreting it as a compound terminal-wealth return does require reinvestment at the same periodic rate and payments arriving as promised. Selling early also exposes the exit price to future market yields.
This tool quotes nominal annual YTM, discounting each period at YTM divided by payments per year. A semiannual nominal 6% means 3% each half-year and a 6.09% effective annual rate. Compare like conventions, and separately assess credit risk, calls, taxes, fees and accrued interest between coupon dates.
Another example
- Enter 1,000 face value, 950 market price, and a 5% coupon rate.
- Set five years to maturity with semiannual coupons.
- YTM is about 6.18%. Because price is below face value, this is a discount bond and YTM exceeds the coupon rate.
Show formal definition and formula
Yield to maturity is the annualized rate making scheduled cash flows' present value equal the market price.
Bond price equals the present value of all coupons and principal discounted at the yield to maturity.
YTM is the nominal annual yield that equates discounted coupons and maturity principal to market price, usually solved numerically. Coupon is payment per period; Face is maturity principal; m is payments per year and N remaining periods, so the periodic discount rate is YTM/m. Valuation is on a coupon date with fixed payments held to maturity; default, fees, taxes and early calls are excluded.
Common mistakes
Do not confuse YTM with coupon rate or a guaranteed realized return.
Frequently asked questions
How does YTM differ from current yield?
Current yield is annual coupon divided by price. YTM also includes principal at maturity and time value.
Is YTM a guaranteed return?
No. It assumes scheduled payments and holding to maturity, excluding default, taxes, fees, and reinvestment differences.
Why is discount-bond YTM higher?
Besides coupons, holding to maturity returns face value above the purchase price.
You can now explore…
- Solve YTM from a price
- Distinguish YTM from the coupon rate
Term reference6 terms
Open a term when you need a reminder. Underlined words in the article work too.