Bond Yield Calculator

Current yield = annual coupon ÷ price. YTM = the rate r where Price = Σ coupon ÷ (1+r)ᵗ + face ÷ (1+r)ⁿ. Coupon rate = annual coupon ÷ face. Yield to worst = the lower of YTM and yield to call.

The three yields, and why YTM is the one

A bond has several “yields,” and confusing them is the classic mistake. The coupon rate is fixed — the annual coupon over the face value — and never changes. The current yield divides the annual coupon by the price you pay, so it captures the income return but ignores the gain or loss as the price pulls toward face value at maturity. The yield to maturity is the complete picture: the single rate that, applied to all the future coupons and the final principal, brings them back to exactly today’s price. It’s the bond’s true total return if held to the end, and it’s what the market quotes. Because there’s no formula for it, the calculator solves it iteratively — and the cash-flow schedule, whose present values sum back to the price, is the proof the solve is right.

Worked example — a 1,000 face bond, 6% coupon (30 semi-annually), 5 years, trading at 950: Current yield = 60 ÷ 950 = 6.32%. Yield to maturity ≈ 7.21% — higher than the coupon, because the 50 discount is an extra gain captured by holding to maturity.

Premium, discount, and the price–yield curve

Price and yield move inversely, and the relationship reveals itself in three states. A bond trading below face is at a discount, and its YTM exceeds the coupon rate — you collect the coupon and a gain to par. Above face is a premium, and the YTM falls below the coupon, because you paid extra for that high coupon and lose it back toward par. At face, the bond is at par and all three yields equal the coupon rate. The price–yield curve plots this: a downward-sloping, convex line where higher yields mean lower prices, with the bond’s current point marked. Its steepness at that point is the bond’s sensitivity to rates — which the modified duration quantifies: roughly the percentage the price moves for each one-percent change in yield. A longer-dated, lower-coupon bond has more duration and swings more when rates move.

Callable bonds, zero-coupons and tax

Some refinements complete the picture. A callable bond can be redeemed early by the issuer, so its yield to call — computed to the call date and call price rather than maturity — matters, and the yield to worst (the lower of YTM and YTC) is the prudent figure to plan around, since the issuer will call when it suits them, not you. A zero-coupon bond pays no coupons at all; its entire return is the climb from a deep discount to face value, so the YTM is simply that compound growth rate. And because tax treatment varies, the calculator shows the after-tax yield for a taxable bond and the taxable-equivalent yield for a tax-free one — the pre-tax yield a taxable bond would need to match it. Educational tool only — not investment advice; yields assume coupons are reinvested at the YTM, which real markets rarely deliver exactly.