Bond Yield Calculator

Current yield and yield-to-maturity (YTM) for a fixed-coupon bond, solved numerically via Newton-Raphson.

Inputs

The principal repaid at maturity. Most US corporates quote $1,000 par; some munis use $5,000.

The bond's stated coupon as a % of face. Total annual coupon = face × rate.

What you pay today (clean price, ignoring accrued interest). Below face = "discount", above = "premium".

US Treasuries and most US corporates pay coupons semi-annually. Frequency affects YTM by changing the discounting periods.

Result

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How to use this calculator

  • Enter face value ($1,000 for most US corporates; $100 par convention is sometimes used for Treasuries).
  • Enter the annual coupon rate as a percent (a "5% coupon" bond on $1,000 face pays $50/yr total).
  • Enter the current market price you can buy at (clean price, not dirty).
  • Enter years remaining to maturity.
  • Set coupon frequency — semi-annual is the US default.

About this calculator

Two yield numbers fixed-income investors use, and they are NOT the same: **current yield** (annual coupon ÷ today's price — quick, ignores maturity) and **yield-to-maturity** (the true internal rate of return assuming you hold the bond to maturity and reinvest coupons at the same rate — the comparable rate against any other investment). When the price is below par (a "discount" bond), YTM is above the coupon rate; when it is above par (a "premium" bond), YTM is below the coupon. YTM is solved numerically because the pricing equation cannot be inverted analytically. This calculator uses Newton-Raphson, the standard textbook method. Semi-annual coupon frequency is the US bond-equivalent-yield (BEY) convention used by the Treasury Department and the major bond indices (Bloomberg US Aggregate, ICE BofA).

Frequently asked

What's the difference between current yield and YTM?+
Current yield = annual coupon ÷ price. It is a snapshot. YTM is the full internal rate of return assuming you hold to maturity and reinvest coupons at the same rate. For a bond bought at par, both equal the coupon rate; for discount/premium bonds, they diverge. YTM is the apples-to-apples comparison rate; current yield is the back-of-envelope.
Why is YTM higher than the coupon when I buy at a discount?+
Because you also collect the difference between purchase price and face value at maturity, as a capital gain. A $1,000 bond bought for $950 returns the $50 capital gain on top of the coupons; YTM amortizes that gain over the remaining life.
How does coupon frequency change YTM?+
It shifts the discounting periods. The same nominal yield is worth more in compound terms if paid semi-annually vs annually, so the bond-equivalent yield convention (US Treasury) reports a number you can compare across coupon schedules. Use the semi-annual setting for US Treasuries and most US corporates.
What is "yield to call" — and is it the same?+
No — YTC uses the call date and call price instead of maturity. Many premium bonds are likely to be called, so YTC is often the rate the issuer plans to give you. This calculator solves YTM only; for callable bonds, calculate yield to the call date by setting "Years to maturity" = years-to-call and "Face value" = call price.
Is there a closed-form YTM?+
No — the YTM equation P = Σ(C/(1+y)^t) + F/(1+y)^n is a polynomial of degree n in (1+y), so for n > 4 there is no algebraic solution. Numerical methods (Newton-Raphson, bisection, secant) are required. Newton-Raphson with a good seed (the textbook approximation) converges in fewer than 20 iterations for any reasonable bond.
What is the textbook YTM approximation formula?+
y ≈ (C + (F − P)/n) / ((F + P)/2). It is the seed I use for Newton-Raphson and is accurate to within ~10 basis points for most coupon bonds. Quick mental-math estimate, not for trading.

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