Bond Price Calculator
Bond value from coupon, yield, and years.
What it does
A bond is a coupon stream plus a face refund. Price is the present value of both at the market yield. When yield sits above coupon the bond sells at a discount; when below, at a premium. One yield move reprices every future dollar.
The tool above prices annual coupon bonds. A $1,000 face with a 5% coupon at 6% for 10 years pays $50.00 a year and prices at $926.40, a $73.60 discount. At matched 4% rates the same promise is exactly $1,000.00, while a 10 year zero at 5% is $613.91. Seeing coupon beside price keeps income apart from capital change.
Yield conventions decide the inputs. This page uses annual compounding with whole years. Semiannual bonds need halved yield, halved coupon, and doubled periods before comparing. Callable, floating, and inflation linked bonds need their own terms.
This page values fixed cash flows only. It does not model default, taxes, or rate paths. For a buy choice, compare yield to maturity against holding time and tax status.
How to use
- Enter the face value in dollars.
- Enter the annual coupon percent.
- Enter the yield to maturity percent.
- Enter whole years to maturity.
- Read price first, then annual coupon.
- Read premium or discount against face.
Formula
- F
- Redeemed amount at maturity, in dollars.
- C
- Yearly coupon dollars, face times coupon percent.
- y
- Yield to maturity per year as a decimal.
Annual coupon bond with fixed yield to maturity. At zero yield there is no discounting, and at zero coupon only face discounts. Taxes, calls, and credit moves sit outside this math.
Worked example
Example: 5% bond at 6% yield
Defaults: $1,000 face with 5% coupon at 6% yield for 10 years, annual coupons.
- Inputs: $1,000 face, 5% coupon, 6% yield, 10 years.
- Coupon: 1000 times 0.05 is $50.00 a year.
- Discount factor: 1.06 to the minus 10 is 0.558395.
- Annuity: (1 minus 0.558395) / 0.06 is 7.360087.
- Price: 50 times 7.360087 plus 1000 times 0.558395 is $926.40, a -$73.60 discount. Tool shows the same.
Reference table
| Coupon and yield | Price | Against face |
|---|---|---|
| 5% at 6%, 10 yr | $926.40 | -$73.60 discount |
| 4% at 4%, 5 yr | $1,000.00 | +$0.00 premium |
| 0% at 5%, 10 yr | $613.91 | -$386.09 discount |
| 6% at 4%, 10 yr | $1,162.22 | +$162.22 premium |
| 3% at 7%, 20 yr | $576.24 | -$423.76 discount |
Limits
- Annual fixed coupons only. Semiannual needs conversion.
- Fixed yield assumed. Rate moves reprice instantly.
- No credit, call, or tax layers.
- Whole years only. Odd first coupons need day counts.
Common mistakes
- Using coupon rate as yield.
- Pricing semiannual bonds with annual periods.
- Reading discount as loss without yield context.
- Ignoring taxes on coupons and gains.
- Comparing nominal yields across maturities as if equal risk.
Try it yourself
Quick checks. Answers sit tucked under each question.
$1,000 face, 4% coupon, 4% yield, 5 years?
Coupon equals yield, so price is face: $1,000.00 with $40.00 coupon and +$0.00 premium.
Zero coupon, 5% yield, 10 years?
Zero coupon discounts face only: 1000 / 1.05^10 is $613.91, a -$386.09 discount.
Questions
What is the bond price formula?
Price = C times (1 minus (1+y) to the minus n) / y plus F /(1+y)^n. Here $926.40.
What is a premium?
Price above face. Yield below coupon means premium.
What is a discount?
Price below face. Yield above coupon means discount, here -$73.60 discount.
What if coupon equals yield?
At equal rates price is face. Here 4% on 4% for 5 years is $1,000.00.
What happens at zero yield or zero coupon?
Price is face plus coupons undiscounted. A zero at 5% for 10 years is $613.91.
Does this handle semiannual coupons?
No. Annual periods here. Semiannual needs halved rates and doubled periods.