Bond Calculator
Calculate a bond’s fair price from its coupon rate, face value and the market yield, plus its current yield.
How to use this calculator
- 1Enter the bond’s face value, coupon rate and time to maturity from the bond’s terms.
- 2Enter the current market yield for comparable bonds — this is what moves the price away from face value.
How the calculation works
Price = C × [1 − (1 + y)⁻ⁿ] / y + F / (1 + y)ⁿ- C
- Coupon payment per period
- y
- Market yield per period
- n
- Number of coupon periods remaining
- F
- Face value, repaid at maturity
This is the present value of two cash-flow streams: the coupon payments (an annuity) and the single face-value repayment at maturity, both discounted at the market yield.
When the coupon rate equals the market yield, the two effects cancel exactly and price equals face value — bond pricing is fundamentally a present-value problem, not a separate formula.
Worked example
$1,000 face value, 5% coupon, 10 years, 6% market yield, semi-annual
- 1.Semi-annual coupon: 1,000 × 5% ÷ 2 = $25 every 6 months, for 20 periods.
- 2.Semi-annual yield: 6% ÷ 2 = 3%.
- 3.Present value of the coupons: 25 × [1 − 1.03⁻²⁰] / 0.03 ≈ $371.98.
- 4.Present value of the $1,000 face value: 1,000 ÷ 1.03²⁰ ≈ $553.68.
- 5.Price ≈ $371.98 + $553.68 = $925.61 — below par, because the 5% coupon is under the 6% market yield.
Result: $925.61 — trading at a discount
What a bond is
A bond is essentially an IOU. A government or company that wants to borrow money issues bonds instead of taking a bank loan, promising to pay the lender — the bondholder — regular interest payments and to return the original amount at a set future date. Buying a bond means becoming a lender, not an owner: unlike a share of stock, a bond gives no claim on the issuer's profits or any say in how it is run, only a contractual right to be repaid.
The vocabulary bonds are built from
A handful of terms recur across every bond, and understanding them is most of what is needed to read a bond's terms.
- Face value (par) — the amount the issuer promises to repay at maturity, and the amount the coupon rate is calculated against — usually a round figure like $1,000 for individual bonds.
- Coupon rate — the fixed annual interest rate the bond pays, expressed as a percentage of face value. The name is a holdover from when bondholders literally clipped physical coupons to redeem each payment.
- Maturity — the date the issuer repays the face value and the bond ends. Terms range from a few months for short-term government debt to 30 years or more for long bonds.
- Yield to maturity — the total annualized return an investor gets by buying at the current price and holding to maturity — it accounts for the coupon payments and any gain or loss as the price converges to face value.
- Credit rating — an independent assessment of how likely the issuer is to repay in full and on time, from top-rated governments and blue-chip companies down through progressively riskier, higher-yielding issuers.
Why bond prices move opposite to interest rates
A bond's coupon is fixed the day it is issued. If market interest rates rise afterward, newly issued bonds start paying more, which makes the older, lower-coupon bond less attractive by comparison — its price has to fall so that its effective yield catches up to what the market now offers. The reverse happens when rates fall: an existing bond's fixed coupon suddenly looks generous, and its price rises.
This is why bonds are not automatically "safe" in the sense of never losing value — a bond fund or portfolio can decline noticeably in a period of rising rates, even though every bond in it is still paying exactly as promised and will still return full face value at maturity if held that long.
Not all bonds carry the same risk
The word "bond" covers a wide range of risk profiles, largely driven by who is doing the borrowing.
- Government bonds — issued by national treasuries. Bonds from stable, developed governments that borrow in their own currency are generally considered among the lowest-risk fixed-income investments available.
- Municipal bonds — issued by state or local governments, often to fund public projects. In the US, interest is frequently exempt from federal income tax and sometimes state tax as well, which affects their comparative appeal.
- Corporate bonds — issued by companies, spanning investment-grade issuers with strong balance sheets down to high-yield ("junk") bonds from riskier borrowers, which pay noticeably more to compensate for a real chance of default.
Why investors hold bonds at all
Bonds serve a different role than stocks in a portfolio: steadier, more predictable income, and a history of holding up — or even gaining — during periods when stock markets fall sharply, which is why they are widely used to balance the volatility of an equity-heavy portfolio rather than to maximize growth on their own.
What this assumes, and where it stops
Assumptions
- The bond pays a fixed coupon and has no call, put or conversion features.
- The market yield is constant across the whole remaining life of the bond.
Limitations
- Does not model callable bonds, credit risk / default probability, or accrued interest between coupon dates.
- Real-world bond prices also reflect liquidity and supply/demand, not purely the discounted cash flows shown here.
Common questions
Why does a bond’s price fall when interest rates rise?
A bond’s coupon is fixed at issue. When market yields rise above that coupon rate, new bonds pay more, so an existing bond with a lower coupon becomes less attractive — its price has to fall until its yield matches what the market now demands. This is why bond prices and yields move in opposite directions.
What is the difference between current yield and yield to maturity?
Current yield is just the annual coupon divided by the current price — a snapshot. Yield to maturity accounts for the whole picture: coupons received, plus the gain or loss from the price converging to face value by maturity. YTM is the more complete measure of return.
Formula and content last reviewed on .
Results are estimates for information only, not professional advice.
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