Bond Price Calculator
Calculate the fair price of a coupon-bearing bond given its face value, coupon rate, yield to maturity, and time to maturity.
How to use this tool
- Enter face value (par value), annual coupon rate, yield to maturity (ytm), years to maturity and coupon frequency in the fields above.
- Results update instantly as you type — or click Calculate.
- Read your bond price and the full breakdown beneath it.
⚠ This tool provides general estimates for education only and is not financial, tax or legal advice. Figures may not reflect your situation — verify with a qualified professional.
Formula
P = C × [1 − (1+y/m)−nm] / (y/m) + F × (1+y/m)−nm
Where C = F·c/m (periodic coupon), y = YTM, m = periods per year, n = years, F = face value.
How it works
A bond's price is the present value of all its future cash flows — periodic coupon payments plus the face value at maturity — discounted at the yield to maturity (YTM). When the coupon rate equals the YTM, the bond prices at par; when the coupon rate is below YTM, the bond trades at a discount; when above, at a premium.
This calculator uses the standard annuity + lump-sum present value formula, assumes equal-length coupon periods and settlement on a coupon date (no accrued interest). For semiannual bonds, the YTM is halved and the number of periods is doubled, consistent with U.S. Treasury market conventions.
Worked example
$1,000 bond, 6% annual coupon, 8% YTM, 5 years
- Annual coupon = $1,000 × 6% = $60; periodic rate = 8%/1 = 8%
- PV of coupons = $60 × [1−(1.08)^−5] / 0.08 = $60 × 3.9927 = $239.56
- PV of face value = $1,000 / (1.08)^5 = $1,000 / 1.46933 = $680.58
- Bond price = $239.56 + $680.58 = $920.15
Bond price = $920.15 (trades at a discount because coupon rate < YTM)
Common mistakes to avoid
- Entering the coupon rate as a decimal (e.g., 0.05) when the calculator expects a percentage (5), or vice versa, which misprices the bond by a factor of 100.
- Using annual compounding periods for a bond that pays semi-annual coupons without halving the rate and doubling the periods.
- Confusing YTM (required input) with current yield (output): YTM is the expected return if held to maturity; current yield is annual coupon divided by price.
Key terms
- Face value (par value)
- The principal amount of the bond repaid to the investor at maturity; also the base on which coupons are calculated.
- Coupon rate
- The annual interest rate stated on the bond, applied to the face value to determine the dollar amount of periodic interest payments.
- Yield to maturity (YTM)
- The total annualised return an investor earns if the bond is bought at the current price and held to maturity, with all coupons reinvested at the same rate.
- Current yield
- Annual coupon income divided by the current market price; a simplified yield measure that ignores capital gains or losses at maturity.
- Discount / Premium
- A bond trades at a discount when its price is below par (coupon rate < YTM) and at a premium when its price is above par (coupon rate > YTM).
Frequently asked questions
- Why does a bond price fall when interest rates rise?
- The bond's fixed coupon payments become less attractive compared to newly issued bonds at the higher rate. Buyers discount the price until the bond's yield matches the market rate.
- What is the difference between par, premium, and discount bonds?
- A par bond prices at face value (coupon rate = YTM). A premium bond prices above par (coupon rate > YTM). A discount bond prices below par (coupon rate < YTM).
- Does a bond always mature at face value?
- For standard coupon bonds, yes — the issuer repays the face (par) value at maturity regardless of the market price during the bond's life. Callable or convertible bonds can terminate differently.