Yield to maturity

Yield to maturity (YTM) is the single discount rate that equates a bond's current market price with the present value of all its remaining cash flows, representing the total annualised return earned if the bond is held to maturity.

ByHoang TruongUpdated June 30, 2026

FrameworkBond pricing

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A bond priced at €980 promises a €60 coupon each year for two years plus €1,000 of face value at maturity. Yield to maturity is the single discount rate that makes the present value of those coupons and the face value exactly equal the €980 price. Solving 980 = 60/(1+y) + 1,060/(1+y)² numerically gives y ≈ 7.1%, the bond's internal rate of return.

Where it fits

SubjectCorporate FinanceCoreTopicBond & Equity ValuationCore

The formula

LaTeX

\sum_{t=1}^{n} \frac{C}{(1+y)^t} + \frac{FV}{(1+y)^n} = P \quad (\text{solve for } y)

Variables

$y$: yield to maturity — the unknown; the bond's internal rate of return (decimal per period)
$C$: periodic coupon payment (€)
$F V$: face value repaid at maturity (€)
$n$: total number of periods to maturity
$P$: current market price of the bond (€)

There is no closed-form solution for y; YTM is found numerically using a financial calculator, spreadsheet solver, or trial and error. It is the bond's IRR.

Check yourself

PracticeCORE

A bond is currently priced below its face value. An investor who buys this bond today and holds it to maturity will earn a total annualised return that is:

Select an answer to check your understanding.