Bond Price Calculator — coupons and face value at the market yield

How it works

Two discounted pieces, summed. The coupons: c = F × coupon rate ÷ k each period — simple-interest arithmetic on the face — valued as a payment stream with the annuity present-value formula at the market yield. The face: F ÷ (1 + y/k)^(k·n), the single-sum discount from maturity. Their sum is the price, and the identity worth internalizing falls straight out: at y equal to the coupon rate the two pieces rebuild the face exactly — par. The yield sweep prices the same bond a point and two points either side of its coupon, making premium, par, and discount three rows of one table. Current yield — annual coupons over the price — completes the picture: above the coupon rate for discount bonds, below it for premium ones.

Worked example

Each pricing step rests on a published pair. The stream step is LibreTexts' present-value example: $400 a month for 4 years at 12% is worth $15,189.58 today — the same annuity formula that values a coupon stream. The face step is the compound pair inverted: $3,932.39 arriving in four years at 7% is $3,000 today. On the default bond — $1,000 face, 5% coupon paid semiannually, ten years, priced at a 6% market yield — this calculator sums the two pieces to about $925.61, a discount of $74 to par: its own composition of the two published steps.

Frequently asked questions

Why does a bond's price move opposite to yields?

Because the payments are fixed: when market yields rise, the same fixed coupons are worth less next to new bonds paying more, so the price falls until the buyer's return matches the market — and vice versa. The sweep shows the see-saw in dollars on your bond.

What do par, premium, and discount mean?

Par is price equal to face — which happens exactly when the market yield equals the coupon rate. A premium bond prices above face (its coupon beats the market); a discount bond below (the market beats its coupon). The signed output names which side your inputs land on.

What is the current yield?

Annual coupon dollars divided by the price actually paid — a discount bond's current yield runs above its coupon rate because the same coupons cost less to buy. It ignores the pull to par at maturity, which is why yield to maturity (the rate this page discounts at) is the fuller measure.

How is the coupon payment calculated?

Face value times the coupon rate, divided by the payments per year — $1,000 at 5% paid semiannually is $25 per period. It is fixed at issue; the price is what adjusts to the market, never the coupon.

What happens to the price as maturity approaches?

It pulls to par: fewer periods remain to discount, so both pieces converge on the face value regardless of where yields sit. Shortening the years input shows the pull — the same yield gap moves the price less on a two-year bond than a twenty-year one.

Is this yield to maturity?

The market yield you enter plays that role: the single rate discounting all payments. Solving the reverse — what yield a quoted PRICE implies — is the same bisection the irr calculator performs on cash flows; enter the bond's flows there to recover a quoted bond's implied yield.

How accurate is this, and what does it exclude?

Exact for the entered yield, a fixed coupon, and payments held to maturity. It excludes accrued interest between coupon dates (clean vs dirty price), credit risk beyond what the yield embeds, callable features, and taxes. Treasury and corporate market conventions also differ in day counts, which this page does not model.