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Finance

Bond Yield to Maturity (YTM) Calculator

Yield to maturity (YTM) is the single discount rate that equates a bond's future cash flows (every coupon plus the face value at maturity) to its current market price. It is the annualised internal rate of return earned by holding the bond to maturity, and the standard yardstick used to compare bonds across maturity, coupon and credit. There is no closed-form solution for N > 1, so this tool finds the per-period yield r by bisection, then annualises it (YTM = r × m) to six-decimal precision.

Yield to maturity (YTM)

Current yield

Coupon per period

Total coupons to maturity

Total cash flow (incl. face)

Total periods

Formula

P = C × (1 − (1+r)^−N)/r + F · (1+r)^−N — solved numerically for the per-period yield r via bisection, then annualised as YTM = r × m.

Enter the clean price (excludes accrued interest). Assumes the next coupon is exactly one period away — accurate on the issue date or any coupon date.

Formula

P = Σ [C / (1 + r)^t] + F / (1 + r)^N, where C = F · couponRate / m, r = YTM / m, N = years × m

Frequently asked

What is the difference between YTM and current yield?

Current yield = annual coupon / market price is just "cash you receive now ÷ cash you pay now", ignoring any capital gain or loss at maturity. YTM discounts every future cash flow including the face value, so it is the actual annualised return if you hold to maturity. For a 5% coupon, $1000 face bond bought at $900 with 10 years to go: current yield = 50/900 ≈ 5.56%, but YTM ≈ 6.37% — the extra 0.8% is the pull-to-par gain. Investment decisions should generally focus on YTM, because it reflects total holding-period return.

Why is semi-annual YTM called the "bond-equivalent yield"?

In the US market the convention is: solve for the per-period yield r (the 6-month yield) and quote 2 r as the annual yield — that is the bond-equivalent yield (BEY). It is not the true effective annual return because it ignores compounding within the year. The effective annual yield (EAY) = (1 + r)² − 1. So a 6% BEY corresponds to EAY = (1.03)² − 1 = 6.09%; the gap widens at higher yields. When comparing bonds to other compounding instruments (CDs, savings products), convert to EAY for an apples-to-apples comparison.

Why can't YTM be solved algebraically?

The bond price is an N-degree polynomial in r: P(r) = C·(1+r)^(N−1) + C·(1+r)^(N−2) + … + (C+F)/(1+r)^N. Galois proved in 1832 that no general algebraic solution exists for N ≥ 5, so numerical methods are required. Common choices: (1) Newton-Raphson — fast but can diverge from a bad starting guess; (2) bisection — slow but bullet-proof; (3) hybrid methods like Brent's. This tool uses bisection: because price is strictly decreasing in r, a sign-change is guaranteed within the search window of −100 %/m to +500 % annual yield, and convergence to machine precision happens in <60 iterations.

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