Bond Price Calculator
Calculate present value of a bond
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Bond Price Calculator helps you calculate present value of a bond — free, instant, in your browser. Fill in Face Value, Coupon Rate (%) and Market Yield (%) on Bond Price and read your answer immediately. Bond Price displays each intermediate figure as well. Bond Price works for one check or many. You can disconnect once Bond Price has loaded; the arithmetic runs locally. Bond Price is part of the Finance collection on CalcProMaster, alongside bond price calculator present value, free online bond price calculator and more. Bond Price is designed for real people. Labels stay plain. Bond Price answers the next Finance question you meet.
What the defaults give
A $1,000 face, 5% coupon and 10 years to maturity prices at $1,081.11 when yields are 4%.
That is $405.54 of discounted coupons plus $675.56 of discounted face value — a premium of $81.11.
How a bond price is calculated
A bond price is the present value of every future payment:
Price = Σ coupon ÷ (1 + yield)ᵗ + face ÷ (1 + yield)ⁿ
$1,000 face value, 5% coupon, 4% yield, 10 years: the $50 coupons are worth $405.54 today and the face value $675.56, so the price is $1,081.11.
| Market yield | Price | Trades at |
|---|---|---|
| 3% | $1,170.60 | premium |
| 4% | $1,081.11 | premium |
| 5% | $1,000.00 | par |
| 6% | $926.40 | discount |
When the market yield is below the coupon the bond pays more than the market, so buyers pay extra and it trades at a premium; above the coupon it trades at a discount. At the same rate it is worth exactly face value. A longer maturity makes the price more sensitive to the same yield change.
Related: bond yield and yield to maturity.
The formula
Price = Σ coupon ÷ (1 + y)ᵗ for t = 1…n, plus face ÷ (1 + y)ⁿ
Every cash flow is discounted at the market yield, not the coupon rate. The coupon rate only sets the size of the payments; the yield decides what they are worth today. That is why a 5% bond does not trade at par when investors can get 4% elsewhere.
Worked examples
5% coupon, 4% yield, 10 years → $1,081.11 (premium)
5% coupon, 5% yield, 10 years → $1,000.00 (par)
5% coupon, 6% yield, 10 years → $926.40 (discount)
3% coupon, 4% yield, 10 years → $918.89
5% coupon, 4% yield, 5 years → $1,044.52
0% coupon, 5% yield, 10 years → $613.91
The three-way relationship
When the coupon equals the yield, price equals face value — no coincidence, just algebra: the cash flows discount to exactly the par amount. When the coupon is above the yield the bond trades at a premium, and when below, at a discount. The size of that premium or discount shrinks as maturity approaches, because fewer payments remain to carry the difference.
Maturity is the second lever. The same 5% coupon at 4% yields $1,044.52 over five years but $1,081.11 over ten, since the extra five years of above-market coupons are worth something. This is duration in plain terms: longer bonds move more for a given change in yield.
What this price does not tell you
The calculation assumes annual coupons and a single flat yield. Most US corporate and Treasury bonds pay semiannually, which requires halving the coupon and the yield and doubling the periods; the difference in price is small but real. Accrued interest is also excluded — the buyer pays the clean price plus the interest earned since the last coupon, which is the dirty price that actually changes hands.
Credit risk is outside the model entirely. A bond yielding 9% when Treasuries pay 4% is not a bargain, it is a bond the market expects might not pay. Price the yield you are offered against the risk of the issuer, and remember that a premium bond bought at $1,081.11 returns face value at maturity, not what you paid.
Frequently Asked Questions
Why is a 5% bond worth $1,081 when yields are 4%?
Because its coupons pay more than the market rate, so buyers pay extra for them. The $81.11 premium is the present value of that excess.
When does a bond trade at par?
When the coupon rate equals the market yield. At 5% coupon and 5% yield on a $1,000 face, the price is exactly $1,000.
Why does a longer maturity change the price more?
More coupons are discounted at the market rate, so the gap between coupon and yield compounds over more periods. $1,044.52 at five years becomes $1,081.11 at ten.
Does this price include accrued interest?
No. It is the clean price. The buyer also pays interest accrued since the last coupon, making the dirty price the amount actually settled.
How do semiannual coupons change the result?
Halve the coupon and the yield, and double the number of periods. The price shifts slightly because discounting happens twice a year instead of once.
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