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Bond Price Calculator

Find what a bond is worth by valuing its interest payments and face value at the yield you want. Or find the yield to maturity from a quoted price.

Level: Grade 12 to college

  • Common Core standard HSA.SSE.B.4Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems.
Printable worksheet

Bond Price Calculator

Know the answer you need? Pick an input to work backward.

Inputs
Calculate

The market yield, or the return you require, for a bond like this one.

Result

Bond price

$925.61

At a 6% yield, this 5% bond is worth $925.61, a discount to its face value.

Price relative to face value
At a discount
Premium (+) or discount (−) to face value
-$74.39
Current yield
5.402%
Coupon per period
$25.00
Present value of coupons
$371.94
Present value of face value
$553.68
What the price pays for
  • Coupons$371.9440.2%
  • Face value$553.6859.8%

See the step-by-step solution ↓

Step-by-step solution

  1. Find the coupon (C) paid each period: face value × coupon rate, split over 2 payments a year

    C=$1,000.00×0.052=$25.00

  2. Count the coupon periods left (N): 2 per year for 10 years

    N=2×10=20

  3. Split the yearly yield into 2 equal parts, one per coupon period (i)

    i=0.062=0.03

  4. Work out what all the coupons are worth today. Money paid later is worth less than money now

    $25.00×1−(1+0.03)−200.03=$371.94

  5. Work out what the face value (F), paid back at the end, is worth today

    $1,000.00(1+0.03)20=$553.68

  6. Add the two together. That total is the bond's fair price

    $371.94+$553.68=$925.61

  7. Current yield: the annual coupon divided by the price

    $50.00$925.61=5.4018%

  8. Compare the price with the face value

    $925.61−$1,000.00=−$74.39=At a discount

Test yourself

20 quick questions built from this calculator's formula: work out results, predict what happens when an input changes, and work backward from an answer. Every answer comes with the working.

Please note: Results are estimates for planning and comparison. Lenders, banks, and tax authorities may round differently or include fees not modeled here, so confirm figures with your provider before deciding.

What this calculator does

Find out what a bond is worth today, or what return you'd earn at the price you're offered. A plain bond promises two kinds of cash. It pays a fixed interest payment, called the coupon, on a regular schedule. Then it pays back the face value on the maturity (end) date. What the bond is worth today depends on the yield, the yearly return investors want for those payments. When market yields rise above the coupon rate, the price drops below face value. When yields fall below it, the price rises above.

This calculator works both ways. In price mode, enter the yield you want. It values every coupon and the face value in today's dollars to find a fair price. In yield mode, enter the price you're quoted. It finds the yield to maturity: the one yearly rate that makes all the future payments add up to that price. Both modes also show the coupon per period and the current yield.

Where it's used

Why this math matters outside the classroom:

  • Pricing a bond. A $1,000 bond paying a 5% annual coupon for 10 years is worth about $926.40 when similar bonds yield 6%.
  • Premium and discount. When market yields fall below a bond's coupon rate, its price rises above face value, and when yields rise it trades below face value.
  • Yield to maturity. Investors solve for the single rate that makes the present value of the coupons and face value equal the price paid.
  • Finance coursework. Students value a bond as the present value of a level annuity of coupons plus the discounted face value.

Grade level and standards: Grade 12 to college; Common Core State Standards for Mathematics HSA.SSE.B.4. © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.

How to use it

  1. Choose whether to find the price from a yield, or the yield to maturity from a price.
  2. Enter the face value, the yearly coupon rate and the years left until maturity.
  3. Pick how many coupon payments the bond makes each year. Most corporate and government bonds pay twice a year.
  4. Enter the yield you want or the bond's price. Then read the results and the working.

What the inputs mean

Annual coupon rate
The fixed yearly interest rate printed on the bond, applied to the face value. A 5% coupon on a $1,000 bond pays $50 a year.
Years to maturity
Together with the coupon frequency, this must give a whole number of coupon periods. That's because the bond is valued on a coupon date.
Required annual yield
The yearly return the market wants right now for similar bonds, with similar credit quality and time to maturity. It's quoted as a stated yearly rate, compounded as often as the coupons are paid.
Bond price
The price you'd pay for the whole bond, in the same units as the face value. Quotes given as a percentage of par (face value), such as 95, mean $950 on a $1,000 bond.

Formula and method

C = F × c ÷ f;  i = y ÷ f;  N = f × years
Price = C × (1 − (1 + i)^(−N)) ÷ i + F ÷ (1 + i)^N
YTM: solve Price = that sum for i, then YTM = i × f
Current yield = (C × f) ÷ Price

F is the face value and c is the coupon rate. f is the number of coupons per year, and y is the yearly yield. C is the coupon paid each period, i is the yield per period, and N is the number of coupon periods left. YTM is the yield to maturity. The first part of the price formula is what all the coupons are worth today, treated as a series of equal payments. The second part is what the face value, repaid at the end, is worth today.

There's no direct formula for yield to maturity when there are coupons. So the calculator searches for the per-period yield that gives back the price. It keeps narrowing the range until the answer is exact to many decimal places. Current yield ignores the gain or loss at maturity. It only compares the yearly coupon with what you pay.

Worked example

A $1,000 bond pays a 5% coupon twice a year and matures in 10 years. Similar bonds currently yield 6%.

  1. Coupon per period: $1,000 × 0.05 ÷ 2 = $25; periods left: 2 × 10 = 20.
  2. Yield per period: 0.06 ÷ 2 = 0.03.
  3. Coupons: $25 × (1 − 1.03^(−20)) ÷ 0.03 ≈ $371.94.
  4. Face value: $1,000 ÷ 1.03^20 ≈ $553.68.
  5. Price: $371.94 + $553.68 ≈ $925.61, a discount of about $74.39. Current yield: $50 ÷ $925.61 ≈ 5.402%.
  6. In yield mode, the same bond priced at $950 has a yield to maturity of about 5.662%.

Result: At a 6% yield the bond is worth about $925.61. If you can buy it for $950 instead, you'd earn about 5.662% a year by holding it to maturity.

Understanding the result

Say the price you're offered is below the price this calculator gives at your target yield. Then the bond would earn more than you need. If it's above, it would earn less.

Yield to maturity assumes you hold the bond to the end and get every payment on time. It also assumes you can reinvest the coupons at the same yield. It's the standard way to compare bonds with different coupons and prices.

Assumptions and limitations

  • The bond is valued on a coupon date. So there's no accrued (built-up) interest and no day-count adjustment.
  • Every coupon and the face value are paid in full and on time.
  • Yields are stated yearly rates, compounded as often as the coupons are paid (the usual bond-equivalent convention).
  • No rounding, fees or taxes are applied inside the calculation.
  • It doesn't value bonds between coupon dates (dirty and clean prices). It also doesn't handle callable and putable bonds, floating-rate notes or inflation-linked bonds.
  • The risk that the issuer won't pay (default risk) shows up only through the yield you enter.
  • You can't enter a required yield below 0%. But a solved yield to maturity can be negative, when the price is more than every future payment combined.

Frequently asked questions

Why do bond prices fall when interest rates rise?

A bond's coupons are fixed. When new bonds start paying more, an older bond with a lower coupon only appeals at a lower price. The lower price raises its yield to match the market. The reverse happens when rates fall.

What is the difference between current yield and yield to maturity?

Current yield is the yearly coupon divided by the price, so it only counts income. Yield to maturity also counts the gain you make if you buy below face value, or the loss if you buy above it. That gain or loss is spread over the years to maturity.

What does it mean when a bond trades at par, a premium or a discount?

At par, the price equals the face value. That happens when the yield equals the coupon rate. A premium means the price is above face value, because the coupon is higher than market yields. A discount means the price is below face value, because the coupon is lower.

How do I value a zero-coupon bond?

Set the coupon rate to 0%. The price is then just the face value, valued in today's dollars over the full term. Yield mode gives the growth rate from the price to the face value.

How this calculator is checked

Method: Standard bond valuation: present value of a level coupon annuity plus the discounted face value; YTM solved numerically by bisection. The calculation is covered by automated tests with known reference values and edge cases. Last updated 2026-10-18. Found a problem? Tell us.

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