Yield to Maturity Calculator
Solve a bond’s exact yield to maturity from its price, coupon, frequency and time to maturity — with yield to call and yield to worst, effective annual yield, current yield, duration, convexity, a cash-flow table and a price–yield curve.
How it works
Price = Σ (C ÷ m) ÷ (1 + i)^t + F ÷ (1 + i)^n, solved for i by iteration; YTM = i × m · Effective annual yield = (1 + i)^m − 1 Approx. YTM = (C + (F − P) ÷ years) ÷ ((F + P) ÷ 2) · Current yield = C ÷ P Macaulay duration = Σ t × PV(CF) ÷ P ÷ m · Modified duration = Macaulay ÷ (1 + i) where C = annual coupon = face × coupon rate, F = face, P = price, m = coupons a year, t = periods to each payment
Yield to maturity is the single discount rate that makes the present value of a bond’s remaining coupons and its final repayment equal to the price you pay today. It is your annual return if you hold the bond to the end, every payment arrives, and each coupon is reinvested at that same rate. There is no closed-form formula, so the calculator searches for the exact rate by bisection and also shows the textbook shortcut, so you can see how close it gets. YTM is stated as a nominal rate compounded at the coupon frequency (the bond-equivalent yield for semi-annual bonds); the effective annual yield converts it to true annual compounding. For a callable bond, yield to call repeats the calculation to the first call date and call price, and yield to worst is the lower of the two. Duration measures how sensitive the price is to yields: a modified duration of 7.7 means roughly a 7.7% price fall for a 1-point rise in yields, and convexity corrects that estimate for larger moves. When the time to maturity is not a whole number of periods, the next coupon is a part period away. If you enter a clean quoted price, accrued interest is added to get the full price you actually pay.
Worked example
A $1,000 bond bought for $950 with a 5% semi-annual coupon and 10 years left pays $25 every six months, 20 times. The rate that discounts those payments and the $1,000 repayment to $950 is 2.8308% a half-year, so YTM = 5.662% (5.742% effective annual). The shortcut (50 + 50 ÷ 10) ÷ 975 = 5.64% is close. The current yield is only 50 ÷ 950 = 5.26%, because it ignores the $50 gain to par. Modified duration is 7.71, so a 1-point rise in yields would cut the price by about $70 (to $880).
Sources: SEC Investor.gov — Yield to maturity · DQYDJ — Bond yield to maturity calculator (secant method, zero-coupon example)
Frequently asked questions
Is this the exact yield to maturity?
Yes. The calculator solves the bond price equation numerically to about eight decimal places. It also shows the textbook approximation, which is usually within a few hundredths of a percent for bonds near par but can be off by much more for long, deep-discount or high-coupon bonds.
Why is YTM higher than the coupon rate here?
Because the bond is bought below its face value. On top of the coupons, you collect the difference between the price and the full face value at maturity, which raises the total yield above the stated coupon. A bond bought at a premium yields less than its coupon.
How does current yield differ from YTM?
Current yield is just the annual coupon divided by the price, ignoring any gain or loss against face value at maturity. YTM includes that pull to par and the timing of every payment. For a discount bond, YTM is higher than current yield, and for a premium bond it is lower.
What are yield to call and yield to worst?
If the issuer can repay early, yield to call is the return if it does so on the first call date at the call price. Yield to worst is the lower of YTM and YTC. Issuers tend to call when rates have fallen, so for a premium callable bond, yield to worst is the conservative figure to use.
What is the difference between YTM and the effective annual yield?
YTM is quoted as a nominal annual rate, the per-period rate times the number of coupons a year. The effective annual yield compounds it: (1 + YTM ÷ m)^m − 1. A 5.662% semi-annual YTM is 5.742% effective.
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Educational estimate, not investment, tax or financial advice. Returns are never guaranteed and past performance does not predict the future. Confirm figures with a licensed advisor.