Yield to Maturity Calculator

Solve for a bond's annualized yield to maturity from its face value, current price, coupon rate, years to maturity, and payment frequency using standard discounted cash flow bond pricing.

Quick Facts

Formula
Price = Σ C/(1+y/m)^t + F/(1+y/m)^N
Solved for y with an iterative numerical search, since no algebraic formula isolates y directly.
Rule of thumb
Price below face → YTM above coupon rate
Price above face gives YTM below the coupon rate; price at face makes YTM equal the coupon rate.

Your Results

Calculated
Yield to Maturity
-
Annualized, market-implied yield
Current Yield
-
Annual coupon ÷ price
Annual Coupon Payment
-
Coupon rate × face value
Total Return to Maturity
-
Coupons received plus price gain or loss at par

Ready

Enter face value, price, coupon rate, years to maturity, and payment frequency, then press Calculate.

How the Yield to Maturity Calculator works

Yield to maturity (YTM) is the single annualized discount rate that ties a bond's current market price to every cash flow it will pay between now and maturity: each coupon plus the face value returned at the end. It is the standard way to compare bonds that have different prices, coupon rates, and maturities on one common scale.

The bond pricing equation

A bond's price is the present value of its remaining cash flows discounted at the periodic yield. For face value F, a coupon payment per period C (annual coupon rate × F, divided by payments per year m), N total remaining payments (years to maturity × m), and periodic yield y/m:

Price = Σt=1N C / (1 + y/m)t + F / (1 + y/m)N

There is no algebraic rearrangement that isolates y on one side of this equation, so the calculator searches for it numerically: it repeatedly narrows a range of candidate annual yields with a bisection search, computing the price each guess would produce and comparing it to the price you entered, until the two match to a very small tolerance.

Worked example

Take a $1,000 face-value bond with a 5% annual coupon paid semiannually, 10 years to maturity, currently priced at $950. Each period pays $25 (half the $50 annual coupon) over 20 periods. Because the bond trades below its $1,000 face value, its YTM comes out above the 5% coupon rate — roughly 5.66% annualized — since the buyer collects both the coupons and the $50 gain as the price converges to par at maturity. The current yield, by contrast, is just $50 / $950 ≈ 5.26%, since it ignores that price convergence entirely.

What moves YTM most

  • Price relative to face value: the single biggest driver. A discount bond (price below face) always has YTM above its coupon rate; a premium bond (price above face) always has YTM below its coupon rate.
  • Coupon rate: a higher coupon delivers more cash sooner, which raises YTM for a given price and maturity, all else equal.
  • Years to maturity: for a discount or premium bond, a shorter remaining term concentrates the pull-to-par effect into fewer years, which moves YTM further from the coupon rate than the same price gap would over a longer term.
  • Payment frequency: more frequent compounding of the same nominal annual coupon changes the periodic discounting slightly, so the frequency you select must match how the bond actually pays.

What YTM assumes

YTM assumes the bond is held to maturity, every coupon is reinvested at that same YTM rate, and every payment arrives on schedule with no default. It does not account for callable features, credit risk, taxes, or transaction costs, so a bond's realized return can differ from its quoted YTM if any of those assumptions do not hold.

Frequently Asked Questions

How is yield to maturity calculated?
Yield to maturity is the discount rate y that makes the present value of all future coupon payments plus the face value repaid at maturity equal to the bond's current price: Price = the sum of C/(1+y/m)^t for each period t, plus F/(1+y/m)^N, where C is the coupon payment per period, F is face value, m is payments per year, and N is total remaining payments. There is no algebraic formula that isolates y, so the calculator finds it with an iterative numerical search (bisection) that converges on the rate solving the equation.
Why is YTM different from the coupon rate?
The coupon rate is fixed at issuance and applies to face value, while YTM reflects today's market price. A bond trading below face value (a discount) has a YTM above its coupon rate, because the buyer also captures the gain as the price rises to par at maturity. A bond trading above face value (a premium) has a YTM below its coupon rate, since part of the coupon income offsets the loss of paying more than par. A bond trading at exactly face value has YTM equal to its coupon rate.
What does YTM assume, and what does it ignore?
YTM assumes the bond is held to maturity, that every coupon is reinvested at the same rate as the YTM itself, and that the issuer pays every coupon and the face value on schedule. It does not price in default risk, call provisions, tax treatment, or transaction costs. A callable bond redeemed early may deliver a different realized return, commonly measured separately as yield to call or yield to worst.
How does payment frequency affect the result?
Payment frequency sets how the annual coupon rate is split into periodic payments and how often compounding occurs in the pricing equation. U.S. bonds typically pay semiannually, so entering the wrong frequency for the same annual coupon rate will shift the solved YTM. The calculator reports YTM as a nominal annual rate (the periodic rate multiplied by payments per year), the convention used for most published bond yields.

Related calculators