The formula
How it works
Work out what a bond is worth from its coupon, its yield and its time to maturity. Enter the face value, coupon rate, yield to maturity and term to get the price, and see whether it trades at a premium or a discount.
FAQ
Why does the price differ from the face value?
A bond’s price moves opposite to yields. If the market yield is above the coupon rate, the bond is worth less than face value (a discount); if the yield is below the coupon, it is worth more (a premium). Only when yield equals the coupon does the price equal the face value.
What is yield to maturity?
Yield to maturity (YTM) is the single rate that makes the present value of all the bond’s future coupons and its final face value equal to its price. It represents the total return you would earn holding the bond to maturity, and is the rate the calculator discounts the cash flows at.
Does the coupon payment frequency matter?
Yes — paying coupons semi-annually or quarterly instead of annually splits both the coupon and the yield into smaller per-period amounts but compounds them more often, which slightly raises the price compared with an annual-pay bond at the same stated rates. That’s why the frequency input changes the result even when the annual coupon and yield stay the same.
What is the difference between this price and the “clean” or “dirty” price quoted in the market?
This calculator gives the clean price, which assumes you buy right on a coupon date. In practice, buying between coupon dates also means paying the seller accrued interest for the days since the last payment, so the dirty price you actually settle is the clean price plus that accrued amount.
Why do bond prices fall when interest rates rise?
A bond’s coupon is fixed when it is issued, so when new bonds start offering higher yields, an older bond with a lower coupon must sell for less to offer a competitive return — the discounting in the formula pushes its present value down as \(y\) rises. Longer-maturity bonds feel this effect more than short ones because more cash flows are pushed further into the future.
What happens to the price as the bond gets closer to maturity?
As the years to maturity shrink, fewer coupons remain to discount and the present value converges toward the face value, so a premium or discount gradually shrinks to zero by the maturity date, assuming the yield doesn’t change.
Does this calculator account for credit risk or call features?
No — it prices a plain, non-callable bond purely from its stated coupon, yield and maturity, assuming all payments are made in full and on time. Callable bonds, credit spreads and default risk all affect real-world pricing but aren’t modelled here; the yield to maturity you enter should already reflect the market’s view of that risk.
About the bond calculator
This calculator prices a bond by discounting its future cash flows — the regular coupon payments and the face value repaid at maturity — back to today at the yield to maturity. It is the standard way to value a fixed-income security, and it makes clear the inverse relationship between yields and prices that drives the bond market. The result also shows whether the bond trades above or below its face value.
How to use it
Enter the bond’s face value, its coupon rate, the current yield to maturity, the years remaining and how many coupons it pays a year. The calculator returns the price, the current yield and the premium or discount to face value. For example, a $1,000 bond paying a 5% coupon with a 6% yield over 10 years, paid semi-annually, is worth about $926 — a discount, because its yield exceeds its coupon.
The formula
The price is the present value of every cash flow, , where is the coupon per period, the yield per period, the number of periods and the face value. The coupon and yield are divided by the number of payments per year, so a semi-annual bond uses half the annual coupon and half the annual yield across twice as many periods.
Where it is used
Investors use it to decide whether a bond is fairly priced given prevailing yields, and to see how sensitive its price is to interest-rate changes. Students of finance use it to learn the core of fixed-income valuation, and portfolio managers use the same discounting to mark bonds to market. Because it lays out price, coupon and yield together, it also clarifies why rising rates push existing bond prices down.