Bond Price from Yield Calculator
Price a fixed-coupon bond from its yield to maturity by discounting every coupon and the face value at the required yield.
How it works
Price = C · [1 − (1 + y)^−n] / y + F · (1 + y)^−n · C = coupon/period, y = ytm/freq, n = years×freq
A bond’s fair price is the present value of its cash flows: a stream of coupons plus the face value repaid at maturity, each discounted at the periodic yield. When the yield equals the coupon rate the bond prices at par; a higher required yield drives the price below par (a discount) and a lower yield pushes it above par (a premium). This inverse price–yield relationship is the foundation of bond math.
Worked example
A $1,000 bond with a 5% annual coupon paid semiannually ($25 each) over 10 years (20 periods), priced to yield 6% (3% per period): Price = 25 · [1 − 1.03^−20] / 0.03 + 1,000 · 1.03^−20 = 371.96 + 553.68 = $925.64 — a discount, because the 6% yield exceeds the 5% coupon.
Sources: Bond valuation — Wikipedia
Frequently asked questions
Why does a bond trade at a discount?
When the market yield rises above the coupon rate, the fixed coupons look small next to what investors could earn elsewhere, so the price falls below face value until the bond offers the going yield.
What is current yield versus yield to maturity?
Current yield is just the annual coupon divided by the price and ignores any gain or loss to maturity. Yield to maturity is the single rate that discounts all cash flows back to the price, so it captures both coupons and the pull to par.
Does coupon frequency matter?
Yes. Most bonds pay semiannually, so the annual yield is halved per period and the years are doubled into periods. Using the wrong frequency will misprice the bond.
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Educational financial-math tool, not investment or financial advice.