Bond Calculator · Practical guide
How to Calculate Yield to Maturity
YTM blends coupon income with your gain or loss at maturity — here is the formula and a worked example.
At a glance
The Quick Answer
Yield to maturity is the total annualized return if you hold a bond to the end, combining coupon payments with the gain or loss between the purchase price and face value. A widely used approximation is YTM ≈ [C + (F − P) ÷ T] ÷ [(F + P) ÷ 2], where C is the annual coupon, F the face value, P the price, and T the years to maturity — the same approximation this calculator reports.
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A Worked Example
Take a $1,000 face-value bond with a 5% coupon and 10 years left, priced at a market rate of 6%. Its fair price discounts to $926.40. The approximate YTM is (50 + (1000 − 926.40) ÷ 10) ÷ ((1000 + 926.40) ÷ 2) = 57.36 ÷ 963.20 ≈ 5.96% — close to the true 6% market rate, which is what the approximation is designed to estimate.
YTM vs Current Yield
Current yield is simpler: annual coupon divided by price. On the same bond that is 50 ÷ 926.40 = 5.40%. Current yield ignores the $73.60 you gain when the bond matures at face value, which is why it understates the total return on discount bonds and overstates it on premium bonds. YTM captures both pieces.
Reading the Three Cases
- Price below face (discount): YTM is higher than the coupon rate — you earn the coupon plus the pull up to par.
- Price at face (par): YTM equals the coupon rate exactly.
- Price above face (premium): YTM is lower than the coupon rate — part of each coupon is offset by the loss at maturity.
Where the Approximation Falls Short
The true YTM solves the bond pricing equation iteratively, assuming coupons are reinvested at the same rate. The shortcut formula above gets within a few tenths of a percent for typical maturities and is ideal for quick comparisons — enter your numbers above to see price, current yield, and approximate YTM together.
Frequently Asked Questions
Is yield to maturity the same as the interest rate?
Not exactly. The coupon rate is fixed at issuance; YTM is the market-driven return based on today's price. When a bond trades at face value the two are equal, but they diverge as soon as the price moves.
Can YTM be negative?
Yes, in theory — if you pay such a high premium that coupons cannot cover the loss at maturity, total return turns negative. This happened with some European government bonds in the 2010s.
Does YTM assume I reinvest the coupons?
Yes. The formal definition assumes every coupon is reinvested at the YTM itself. If you spend the coupons or reinvest at a lower rate, your realized return will be lower.
Why does the calculator show an approximate YTM?
Solving for exact YTM requires iterative trial and error. The approximation formula [C + (F − P)/T] / [(F + P)/2] lands within a few tenths of a percent and is standard for hand calculations.