Bond Calculator
Price a fixed-rate coupon bond. Enter the face value, coupon rate, the market yield you require (YTM), years to maturity, and how often coupons are paid — you get the fair price, a premium-or-discount verdict, and your total coupon income.
Where the price comes from
📈 Compare brokerage & bond-fund accounts
Compare platformsHow bond pricing works
A bond is a loan you make to a government or company. It promises two things: fixed coupon payments on a schedule, and the face value back at maturity. Its fair price is simply the present value of all those future payments, discounted at the yield the market currently demands for similar bonds. When the market yield is higher than the coupon rate, the fixed coupons look stingy, so the bond must sell below face value (a discount). When yields fall below the coupon rate, the bond sells above face value (a premium). Only when coupon and yield match does it trade at par.
That is why bond prices move opposite to interest rates — and why longer maturities swing harder: more payments sit far in the future where discounting bites hardest.
How it’s calculated
Price = C × (1 − (1 + r)−n) ÷ r + F × (1 + r)−n, where C = F × coupon rate ÷ f is the coupon per period, r = YTM ÷ f the per-period yield, n = years × f the number of periods, and f the payments per year. Current yield = annual coupon ÷ price. With a 0% coupon the formula reduces to the discounted face value alone.
Assumes a fixed-rate bond priced on a coupon date and held to maturity; it ignores accrued interest, credit risk, call features, taxes, and trading costs. Estimates only — not investment advice.
Worked example
A $1,000 bond pays a 5% coupon semiannually — $25 twenty times over 10 years, $500 of coupon income in total. If the market yields 6% for similar bonds, the fair price is $925.61, a $74 discount to par, and the current yield at that price is 5.40%. Flip the market yield to 4% and the same bond prices at $1,081.76 — an $82 premium. Same paper, same coupons; only the discount rate changed.
Common mistakes
- Discounting with the current yield or coupon rate instead of the yield to maturity — only YTM prices the bond correctly.
- Forgetting that payment frequency changes both the per-period rate and the number of periods — semiannual is the U.S. default.
- Comparing a quoted dirty price (with accrued interest) to this clean-price result between coupon dates.
- Ignoring credit risk and call features — a callable junk bond and a Treasury at the same YTM are not the same investment.
Where it is used
- Checking whether a broker’s secondary-market quote is close to fair value.
- Seeing how much a rate move would change the value of a bond you hold.
- Pricing zero-coupon bonds by setting the coupon to 0%.
- Finance coursework — the classic present-value-of-cash-flows exercise.
Frequently asked questions
Why does a bond's price fall when yields rise?
The coupon payments are fixed, so when investors can get a higher yield elsewhere, those fixed payments are discounted more heavily and the bond must sell for less to compete. The reverse is also true: when market yields drop below the coupon rate, the bond trades above face value.
What do premium and discount mean?
A bond trades at a premium when its price is above face value, which happens when its coupon rate is higher than the market yield. It trades at a discount when the price is below face value because the coupon is lower than what the market demands. Either way, a buyer who holds to maturity earns the yield to maturity, not the coupon rate.
Is yield to maturity the same as current yield?
No. Current yield is simply the annual coupon divided by today's price — 5.40% in the worked example. Yield to maturity also counts the gain or loss from the price converging to face value at maturity, so it is the more complete measure and the one this calculator discounts with.
How do I price a zero-coupon bond?
Enter 0 for the coupon rate. The price collapses to face value discounted alone: F divided by (1 + r) to the power n. A $1,000 zero maturing in 10 years at a 6% yield compounded semiannually prices around $554.
Does this handle bonds traded between coupon dates?
It prices a bond on a coupon date, which is the standard clean-price setup. Between coupon dates the buyer also owes accrued interest since the last payment (the dirty price adds it on), and the exact amount depends on the day-count convention such as 30/360 or Actual/Actual.