Bond Price Calculator

A bond price calculator works out the fair value (present value) of a bond based on its coupon rate, face value, yield to maturity, and time to maturity. It is used by investors valuing fixed-income securities, traders checking whether a bond is priced above or below fair value, and finance students learning about interest rate sensitivity.

How to Use the Bond Price Calculator

1. Enter the bond's face value (par value, typically £100 or $1,000).
2. Enter the annual coupon rate as a percentage.
3. Enter the coupon payment frequency (annual, semi-annual, or quarterly).
4. Enter the yield to maturity (YTM) as a percentage.
5. Enter the number of years (or periods) to maturity.
6. Click calculate to see the bond price and the breakdown of present values.

The Formula

A bond's price is the present value of all future cash flows (coupon payments plus face value at maturity), discounted at the yield to maturity:

Price = sum of (C / (1 + r)^t) + (F / (1 + r)^n)

Where C is the periodic coupon payment, F is the face value, r is the yield per period (YTM / number of payments per year), n is the total number of payment periods, and t is each individual period from 1 to n.

More compactly:

Price = C x (1 - (1 + r)^(-n)) / r + F / (1 + r)^n

Real-World Example

A bond with a face value of £1,000, an annual coupon rate of 5% paid semi-annually, 10 years to maturity, and a yield to maturity of 6%.

• Semi-annual coupon: £1,000 x 5% / 2 = £25
• Semi-annual yield: 6% / 2 = 3% = 0.03
• Number of periods: 10 x 2 = 20

Price = £25 x (1 - (1.03)^(-20)) / 0.03 + £1,000 / (1.03)^20 = £25 x 14.877 + £1,000 / 1.8061 = £371.93 + £553.68 = £925.61

The bond trades at a discount (below par) because the coupon rate (5%) is lower than the current yield (6%). Investors require a lower price to make the bond's yield competitive with current market rates.

The Inverse Relationship Between Bond Prices and Yields

The most important principle in fixed-income investing is that bond prices and yields move in opposite directions. When market interest rates rise, existing bonds become less attractive (their coupons are fixed at a lower rate), so their prices fall until the yield rises to match current market rates. When rates fall, existing bonds become more attractive and prices rise. This sensitivity to rates is measured by duration. Longer-maturity bonds have higher duration and are more sensitive to interest rate changes. A bond with a duration of 7 means that a 1% rise in yields causes its price to fall approximately 7%. Understanding this relationship is essential for managing fixed-income portfolio risk, particularly in rising rate environments.

Frequently Asked Questions

Why does a bond trade at a premium or discount to par? A bond trades at par (face value) when its coupon rate equals the current market yield. It trades at a premium when its coupon rate is higher than the current yield (investors pay more for above-market income), and at a discount when its coupon rate is lower than the current yield (investors pay less because the income is below market). At maturity, the bond always redeems at par regardless of whether it was bought at a premium or discount.

What is the difference between clean price and dirty price for bonds? The clean price (or flat price) is the quoted market price excluding accrued interest. The dirty price (or full price) is the actual amount paid, including accrued interest since the last coupon date. Bond prices in financial markets are almost always quoted as clean prices, but settlement is at the dirty price. This calculator typically computes the clean price; add accrued interest separately to find the purchase cost.

How does callable feature affect bond pricing? A callable bond gives the issuer the right to redeem the bond early, typically at par or a small premium. Issuers call bonds when rates fall, refinancing at lower rates. This limits the price appreciation a buyer can achieve if rates fall, because the bond may be called away. Callable bonds therefore trade at a lower price (higher yield) than equivalent non-callable bonds, with the price difference representing the call option value. The yield to call is a relevant metric alongside yield to maturity for callable bonds.

What is duration and why does it matter? Modified duration measures the percentage change in bond price for a 1% change in yield. It is approximately calculated as: Modified Duration = Macaulay Duration / (1 + r). A bond with modified duration of 8 will lose approximately 8% in price if yields rise by 1%. Duration helps investors and portfolio managers understand and manage interest rate risk. Matching asset duration to liability duration is a common strategy for pension funds and insurance companies.

The same bond at six yields

Hold the £1,000 face value, the 5% coupon paid semi-annually and the ten years to maturity, and move only the yield.

At 5% the price sits exactly at par, which is the check that the formula is aligned: when the coupon rate and the yield are equal, every discounting factor cancels out. The curve either side of par bends rather than running straight. The fall from 6% to 7% is £67.74, a drop of 7.32%, while the rise from 6% to 5% is £74.39, a gain of 8.04%. The same 100 basis point move produces a larger gain than loss, and the asymmetry grows as the move gets larger.

Duration on the same bond

Duration compresses those six prices into one number.

Macaulay duration is the present-value-weighted average time until the cash flows arrive, which lands below the ten-year maturity because the coupons arrive before the principal. Modified duration divides that by one plus the yield per period, and the result of 7.665 says the price should fall about 7.67% for a one point rise in yield. The actual fall is 7.32%, and the 0.35 point difference is curvature the linear measure cannot capture. For larger rate moves the gap widens, which is why bond desks carry a convexity figure alongside duration.

Clean price, accrued interest and the amount paid

A bond bought between coupon dates costs more than its quoted price. Take the same bond at 6%, held 90 days into a 180-day coupon period.

The £25 coupon has half accrued, giving £12.50. The seller receives that £12.50 as part of the settlement because the seller held the bond for the half of the period in which it was earned. The quoted price stays clean across the market so that prices from different dates can be compared, while the cash that changes hands is the dirty price.

What the pricing formula assumes

The formula discounts every cash flow at one rate. It assumes coupon dates fall on an exact grid, that the next coupon arrives one full period from now, that the bond redeems at par at maturity, and that the issuer pays every coupon on time and in full. It produces a clean price, so add accrued interest separately to reach the settlement amount.

It covers plain fixed-rate bonds. Call features, sinking funds, floating coupons, index-linked principal and step-up coupons all change the cash flow list before the formula applies, and each needs its own adjustment. It also assumes a single yield curve point: a bond priced off a full curve with different rates for each cash flow is not what this formula computes.

A note on the discounting convention

The relation between price, coupon and yield is the standard present-value identity for a fixed-rate bond, and it is set out with the duration and convexity measures that extend it in Fabozzi, F. J., "Bond Markets, Analysis and Strategies", which treats each of those measures in a dedicated chapter. One practical difference for UK readers: gilts pay semi-annual coupons on an actual/actual day count, so the period count and the days between payments do not follow the even 180-day grid that the worked example above assumes.

Also try these free tools:

• Bond YTM Calculator
• Bond Equivalent Yield Calculator
• Accrued Interest Calculator