Yield to Maturity Calculator

YTM is the internal rate of return on a bond if you buy it at today's market price, collect every coupon on schedule, hold it to maturity, and reinvest each coupon at the same YTM until redemption. It is the discount rate that makes the present value of future coupons and face value equal the purchase price. Selling early or reinvesting at another rate changes the realized return.

The closed-form approximation, (C + (F - P) / n) / ((F + P) / 2), gives you a mental-math estimate in one step: annual coupon plus straight-line gain or loss to maturity, divided by the average of face and price. It is fast and intuitive but typically off by 10 to 50 basis points, especially on long-dated bonds at deep discounts. The numerical answer uses Newton-Raphson to iteratively solve the actual bond pricing equation to roughly ten decimal places of precision. Use the approximation to sanity-check the solver, and the solver result for the real number.

If you pay $900 for a bond that redeems at $1,000 in ten years, you collect the regular coupon every period plus a $100 capital gain at maturity. YTM rolls both pieces into one annualized return, which pulls it above the stated coupon rate. The reverse applies to a premium bond: paying $1,050 for a $1,000 par bond means a $50 capital loss at maturity, so YTM lands below the coupon rate. At par (price equals face), YTM equals the coupon rate exactly because there is no capital gain or loss to amortize.

YTM is a contract-style return only if you actually reinvest every coupon at YTM until the bond matures. In practice, the rate you can earn on reinvested coupons depends on the prevailing interest rate environment when each coupon arrives. If rates have fallen, you reinvest at lower yields and your realized return ends up below the original YTM. If rates have risen, the opposite happens. Reinvestment risk is largest for long-maturity, high-coupon bonds (more coupons, more reinvestment decisions) and smallest for zero-coupon bonds (no coupons to reinvest, so realized yield equals YTM if held to maturity).

Many corporate and municipal bonds are callable: the issuer has the right to redeem the bond early at a stated call price (often par, sometimes a small premium). If rates fall, the issuer will call the bond and refinance at a lower coupon, leaving you to reinvest at lower yields. Yield to Call uses the call date and call price instead of the maturity date and face value, and is the more conservative number to evaluate a callable bond at. The rule of thumb is to quote the lower of YTC and YTM (yield to worst). This calculator solves YTM only; for callable bonds, plug the call date as years to maturity and the call price as face value to get YTC.