Bond Price Calculator
Why a Bond Rarely Trades at Face Value
A bond promises a fixed schedule of coupon payments plus a lump-sum repayment of face value at maturity. Those cash flows never change once the bond is issued — but the price investors are willing to pay for them does, moving inversely to prevailing interest rates. When market yields rise above the bond's coupon rate, its price falls below face value to compensate buyers; when yields fall below the coupon, the price rises above face value. This calculator prices a bond exactly, by discounting every promised cash flow back to the present at the current market yield.
The Formula
Each coupon payment is discounted back by the number of periods until it's received, then all the discounted coupons are summed together with the discounted face value repayment. Here y is the market yield per period (annual yield divided by the number of coupon payments per year) and n is the total number of periods to maturity.
Where Bond Pricing Matters
- Secondary-market trading — a bond issued years ago with a 3% coupon has to reprice to compete with newly issued bonds paying 5%, and this formula is exactly how that repricing is quantified.
- Portfolio valuation — bond funds and individual holdings are marked to market using this same present-value logic, not the bond's original face value.
- Comparing a quoted price to fair value — before buying a bond on the secondary market, discounting its cash flows at your required yield tells you whether the asking price is a bargain or overpriced.
- Interest rate sensitivity — running this calculation at several yield levels shows exactly how much a bond's price would move if rates shifted, without needing a separate duration estimate.
A 10-Year, $1,000 Face Value Bond With a 5% Coupon
| Market Yield | Price | Relative to Face Value |
|---|---|---|
| 3% | $1,171.69 | Premium |
| 4% | $1,081.76 | Premium |
| 5% | $1,000.00 | Par |
| 6% | $925.61 | Discount |
| 7% | $857.88 | Discount |
| 8% | $796.15 | Discount |
When the market yield exactly equals the coupon rate, price always equals face value — a useful check on any bond pricing formula.
How to Use This Calculator
- Enter the bond's Face Value.
- Enter the Annual Coupon Rate as a percentage.
- Enter the Years to Maturity.
- Enter the Market Yield / Discount Rate the bond should be priced at.
- Enter Coupon Payments per Year (leave at the default of 2 for standard semiannual bonds).
- Select Calculate to get the bond's price and whether it's trading at a premium, discount, or par.
Related Calculations
Solve the same relationship in reverse with the Yield to Maturity Calculator, or measure a bond's interest-rate sensitivity with the Bond Duration Calculator.