About the Bond Calculator
A bond is a stream of fixed coupons plus a face value returned at maturity. Its market price is simply the present value of those cash flows at whatever yield the market demands today. When market yields rise, existing bonds fall in price, and vice versa — the fundamental bond-market relationship.
This tool prices a bond under semi-annual coupon convention (how US Treasury and corporate bonds pay), and labels the premium or discount versus face, plus the current yield the coupon pays on that price.
The formula behind it
Price = discounted coupons + discounted face value (semi-annual periods):
Price = Σ (coupon/2)/(1+y/2)^t + Face/(1+y/2)^{2n}coupon = face × coupon rate; y = market annual yield; n = years; t = 1…2n periods of 6 months. When market yield < coupon, price > face (premium); when yield > coupon, price < face (discount).
Worked example
Defaults — a 10-year bond with 5% coupon when the market wants 4%:
- Each 6-month period pays $25 (5% of $1000, half-yearly); 20 periods of coupons at a 2% discount each.
- Coupon stream discounts to ≈ $409; the face value at 2% over 20 periods ≈ $673.
- Price ≈ $1,082 — an 8.2% premium, since 5% coupons beat today’s 4% market yield.
Takeaway: The premium isn’t a windfall: buying at $1,082 means the seller’s 5% coupon must first be earned back over 10 years before net gain over par. Premiums shrink as maturity approaches.
What moves the result
- Maturity — longer maturities move more for a given rate change (this is duration in action).
- Coupon level — high-coupon bonds carry back smaller price swings than zero-coupon of the same term.
- Credit quality — the yield required (discount rate) reflects the market’s risk view of the issuer.
- Yield vs coupon gap determines premium vs discount and the current yield the price implies.
Practical tips
- When buying a premium bond, check yield-to-maturity (not just current yield) — it always includes the eroded premium.
- If rates are expected to rise, longer maturities carry bigger risk on paper — ladder maturities instead of one long bond.
- Compare bond YTM with yields on Treasury yields for risk premia: is the issuer paying much over riskless?
- For a precise DV01/duration view, use the PV calculator with several rate scenarios, one at a time.
- Check bid/ask and accrued interest on every bond quote — the tool gives you clean market pricing you can compare against.
Frequently asked questions
Why did my bond’s price fall when I checked it last?
Market yields moved up.bond prices move inversely to yields. If your coupon is below today’s yield, the bond is priced as a discount issue.
What is the difference between coupon rate and yield?
Coupon is fixed at issuance (what you receive); yield is the return the market requires today, which is what drives price — when the former and the latter diverge, price must reconcile them.
Does the tool handle zero-coupon bonds?
Set coupon to 0% — the price reduces to the discounted face value, which is exactly what zero-coupon instruments are priced on.