A bond calculator finds what a bond is worth today by discounting its coupons and face value at the current market yield. Formula: Price = c x (1-(1+r)^(-n))/r + face/(1+r)^n with c and r per period; special case r=0. A $1,000 bond paying 5% twice a year for 10 years is worth about $1,039.91 at a 4.5% yield and $925.61 at 6%.
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How to use the bond calculator
- Enter the face value, usually $1,000.
- Enter the annual coupon rate and the market yield.
- Enter the years to maturity and how often coupons are paid.
- Read the price.
What formula does the bond calculator use?
A bond’s price is the present value of its future payments: every coupon plus the face value at maturity, each discounted at the yield the market requires.
- Price = C × [1 − (1 + r)−n] ÷ r + F ÷ (1 + r)n
- F = face value, C = coupon per period = F × coupon rate ÷ payments per year
- r = yield ÷ payments per year, n = years × payments per year
Bond calculator worked example
Take a $1,000 bond with a 5% coupon paid twice a year and 10 years to maturity. Each coupon is $25 and there are 20 payments. If the market yield is 4.5%, the period rate is 2.25%. The coupons are worth $25 × [1 − 1.0225−20] ÷ 0.0225 ≈ $399.13 and the face value is worth $1,000 ÷ 1.022520 ≈ $640.78, for a price of about $1,039.91.
| Market yield | Price | Trades at |
|---|---|---|
| 3.0% | $1,171.69 | Premium |
| 4.0% | $1,081.76 | Premium |
| 4.5% | $1,039.91 | Premium |
| 5.0% | $1,000.00 | Par |
| 6.0% | $925.61 | Discount |
| 7.0% | $857.88 | Discount |
Why prices fall when rates rise
The table shows the key rule: bond prices move opposite to interest rates. When the yield equals the coupon, the bond trades at par, its face value. When new bonds pay more than yours, buyers will only take your bond at a discount; when rates fall, your higher coupon is worth a premium. The SEC’s Investor.gov explains this as interest rate risk: if rates rise and you sell before maturity, you may get less than you paid. If you hold to maturity and the issuer pays, you still receive the full face value.
Longer bonds move more
The longer the time to maturity, the more the price reacts to a change in yield, because more payments are discounted. A 1-point rise in yield from 5% to 6% cuts the 10-year bond in the example by about 7.4%. Run the bond calculator with 30 years instead of 10 and the same change cuts the price by about 13.8%, to $861.62. Lower coupons also increase sensitivity, which is why zero-coupon bonds swing the most.
Coupon rate, current yield and yield to maturity
- Coupon rate: the fixed interest the bond pays on its face value, 5% here.
- Current yield: annual coupon ÷ price; $50 ÷ $1,039.91 ≈ 4.81%.
- Yield to maturity: the single discount rate that makes all future payments equal the price, 4.5% here. This is the yield the bond calculator uses.
Other bond risks
Price also depends on credit risk, the chance the issuer misses payments, which is why lower-rated bonds have higher yields. Some bonds can be called early, and inflation reduces what fixed payments will buy. The bond calculator assumes all payments arrive on time and prices the bond on a coupon date, so it ignores accrued interest; quoted market prices on other days add interest earned since the last coupon.
Estimates for education only, not financial advice. Your lender’s figures are final.
Zero-coupon bonds and Treasury bills
A zero-coupon bond pays no interest along the way. You buy it at a discount and receive the face value at maturity, so its price is simply F ÷ (1 + r)n. Enter a coupon rate of 0 in the bond calculator to price one: a $1,000 zero maturing in 10 years costs about $610.27 at a 5% yield compounded twice a year. At 6% it costs about $553.68, a drop of 9.3%, larger than the 7.4% drop for the 5% coupon bond, because all of its value arrives at the end.
U.S. Treasury bills work in a similar way: they are sold at a discount and pay face value at maturity, within a year. Treasury notes and bonds pay a coupon every six months, which is why the calculator defaults to semi-annual payments.
Related converters and calculators
Related calculators:
- Present value calculator: discounting
- Compound interest calculator: growth
- Investment calculator: investing
- Inflation calculator: inflation
Sources
Questions about this calculator
Why do bond prices fall when rates rise?
New bonds pay more, so older lower-coupon bonds must sell at a discount.
What is a bond at par?
One whose price equals its face value, when yield equals coupon.
What is a premium bond?
A bond priced above face value because its coupon exceeds the market yield.
What is yield to maturity?
The discount rate that sets the present value of all payments equal to the price.
Does the price include accrued interest?
No. It is priced on a coupon date.
Check the assumptions and units before relying on a result. Financial, tax and health estimates do not replace advice for your individual circumstances.
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