Bond Calculator

Calculate a bond's fair price from its face value, coupon rate, years to maturity, and market yield (YTM). See the price, total coupon income, current yield, and whether it trades at a premium or discount.

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Bond Calculator

Price & yield of a fixed-coupon bond

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Bond Price
Total Coupon Income
Current Yield
Premium / Discount
Coupon Payment

How a Bond Is Priced

A bond's fair price is the present value of all its future cash flows — the periodic coupon payments plus the face value repaid at maturity — discounted at the market yield (yield to maturity, or YTM). When the YTM equals the coupon rate, the bond is worth exactly its face value (par). When market yields rise above the coupon rate, the bond is worth less than par (a discount); when yields fall below the coupon rate, it's worth more than par (a premium). This inverse relationship between yields and prices is the central fact of bond investing.

For example, a $1,000 bond with a 5% coupon paid semi-annually, maturing in 10 years, priced to a 6% market yield, is worth about $925.61 — a discount, because newer bonds offer a higher 6% yield. The calculator also shows the current yield (annual coupon ÷ price) and total coupon income over the bond's life.

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Price & Yield Move Opposite

When market yields rise, existing bond prices fall, and vice versa. Longer maturities are more sensitive to yield changes.

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Premium vs Discount

Coupon > YTM → premium (price above par). Coupon < YTM → discount (price below par). Coupon = YTM → par.

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Current Yield

Annual coupon ÷ current price. A quick income measure, though YTM is the complete return including price changes to maturity.

Formula & Logic

A bond's price is the present value of its future cash flows: periodic coupons plus the principal returned at maturity, all discounted at the yield the market currently demands. Because the coupon is fixed and the discount rate moves, price and yield are inversely related — when market rates rise, existing bonds must fall in price until their effective yield matches. That is the whole mechanism behind bond fund losses in a rising-rate environment, and it is why duration, which measures price sensitivity to rate changes, matters more than coupon for anyone who might sell before maturity.

Price = Σ [ Coupon ÷ (1 + y)^t ] + Face ÷ (1 + y)^nCurrent yield = Annual coupon ÷ PriceTrades at a discount when coupon < yield; at a premium when coupon > yieldApproximate price change ≈ −Duration × change in yield

where:

Coupon
the fixed annual interest payment
y
yield to maturity — the market's required return
n
years to maturity
Face
principal repaid at maturity, normally $1,000

Assumptions: Assumes coupons are reinvested at the yield to maturity, which rarely holds exactly. Credit risk is not modelled — a higher yield often reflects default risk rather than a bargain.

Step-by-Step Example: A 4.5% Coupon Bond When Yields Are 5.2%

Price a bond whose coupon is below current market yield.

  • Face value$1,000
  • Coupon4.5% ($45/yr)
  • Maturity10 years
  • Market yield5.2%
  1. Discount each of the ten $45 coupons at 5.2%: their present value totals $344.13.
  2. Discount the $1,000 principal: $1,000 ÷ 1.052¹⁰ = $602.34.
  3. Price: $344.13 + $602.34 = $946.47.
  4. The bond trades at a $53.53 discount because its coupon is below market yield.
  5. Current yield: $45 ÷ $946.47 = 4.75%, between the coupon and the YTM.
  6. If yields fell to 4.0%, the price would rise to about $1,040.55.

Result$946.47 — a $53.53 discount to par

The discount is not a bargain; it is the market repricing a below-market coupon so the total return matches 5.2%. Note the asymmetry of the rate move: a 0.7-point rise cost $53.53 while a 1.2-point fall would gain $94.08, which is convexity working in the holder's favour.

FAQ

Because new bonds are issued at the higher prevailing rate, an older bond paying a lower coupon must drop in price until its yield matches the market. The fixed coupon becomes relatively less attractive, so buyers will only pay a discounted price — pushing its effective yield up to the new market level.
The coupon rate is the fixed annual interest the bond pays on its face value. The YTM (yield to maturity) is the total annualized return you'd earn buying at the current price and holding to maturity, including coupon income plus any gain or loss from price versus par. Price is set so that YTM, not the coupon, reflects the market return.
It's how often the bond pays interest. Most US corporate and Treasury bonds pay semi-annually (twice a year), so a 5% coupon on a $1,000 bond pays $25 every six months. Some bonds pay annually or quarterly. Frequency affects the present-value math and slightly changes the price.

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✔ Written & reviewed by Dr Sam — 20+ yrs in management & research leadership📅 Last updated June 2026📑 How we build & check these