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The bond calculator above estimates the fair market price of a standard fixed-rate bond: the price at which the bond should trade today given its promised cash flows and the return investors currently demand. It works by discounting every future coupon payment and the final face-value repayment back to the present at the market interest rate you enter. Follow these seven steps to produce an accurate valuation in under a minute.
A useful sanity check is the par test: enter a market rate exactly equal to the coupon rate, and the calculator should return a price equal to the face value. For example, a $1,000 face, 5 percent coupon, 10-year bond priced at a 5 percent market rate is worth exactly $1,000.00. If you do not see par in that scenario, one of the inputs was entered inconsistently. Another check is the direction test: lowering the market rate must always raise the computed price, and raising the market rate must always lower it. Any bond pricing tool that violates this inverse relationship is unreliable.
A bond is a loan made by an investor to a borrower, typically a corporation, a municipality, or a national government. In exchange for the investor cash today, the issuer promises to pay a fixed stream of interest and to return the borrowed principal on a specified future date. The investor who holds the bond is called the bondholder, and the written contract spelling out every promise is the indenture. Because the payments are contractually fixed, bonds are classified as fixed-income securities, and they form the conservative ballast of most diversified portfolios.
Every bond is described by a small set of core terms. The face value, also called par value, is the principal amount repaid at maturity, $1,000 for the typical corporate bond in our examples. The coupon rate is the annual interest rate applied to the face value to determine each year interest; the resulting dollar amount is the coupon payment. The maturity date is the calendar date on which the final coupon and the face value are paid and the bond ceases to exist. The number of years remaining until that date is the term to maturity.
Investors also track several yield concepts. The yield to maturity (YTM) is the single discount rate that equates the bond current price to the present value of all its remaining payments; it is the total annualized return earned by holding the bond to maturity. The current yield is simpler: annual coupon divided by current price, measuring income only. A premium bond trades above face value because its coupon exceeds the market rate; a discount bond trades below face value because its coupon lags the market rate; a par bond trades exactly at face value. Duration, measured in years, quantifies how much the price moves when rates change: a duration of 8 means a one-percentage-point rise in rates cuts the price by roughly 8 percent.
The main bond families differ by issuer and tax treatment. United States Treasury securities, bills, notes, and bonds, carry the full faith and credit of the federal government and are considered free of default risk. Municipal bonds are issued by states, cities, and local authorities, and their interest is frequently exempt from federal income tax and sometimes from state tax. Corporate bonds are issued by companies, pay higher yields to compensate for credit risk (the chance the issuer defaults), and are graded by rating agencies from AAA down to junk status. Zero-coupon bonds pay no periodic interest at all; they are sold at a deep discount and mature at face value, which makes their entire return a capital gain.
Two risks dominate bond investing. Interest-rate risk is the danger that rising market rates depress the value of existing bonds, the effect this calculator demonstrates. Credit risk is the danger that the issuer finances deteriorate, forcing the bond price down even if market rates do not move. Callable bonds add reinvestment risk: the issuer may redeem the bond early when rates fall, leaving the investor to reinvest at lower yields. Understanding these terms turns the calculator from a black box into a genuine valuation instrument.
The price of a fixed-rate bond is the present value of its future cash flows, discounted at the market rate per period. If C is the coupon payment per period, r is the market rate per period, n is the number of periods remaining, and F is the face value, then: Price = C x [1 – (1 + r)^-n] / r + F / (1 + r)^n. The first term values the stream of coupon payments as an ordinary annuity; the second term values the lump-sum principal repaid at maturity. When coupons are annual, r is the annual market rate and n is the number of years. When coupons are semiannual, the market convention for most bonds, r is half the annual market rate and n is twice the number of years, with C equal to half the annual coupon.
Worked example 1, a premium bond. Consider a bond with a $1,000 face value, a 5 percent annual coupon, and 10 years to maturity, while the market rate is 4 percent. The annual coupon is 5 percent of $1,000, which is $50. The annuity factor is [1 – 1.04^-10] / 0.04. Since 1.04^10 equals 1.480244, the factor is [1 – 0.675564] / 0.04 = 8.1109. The present value of the coupons is therefore $50 x 8.1109 = $405.54. The present value of the face value is $1,000 / 1.480244 = $675.56. Adding the two pieces gives a fair price of $405.54 + $675.56 = $1,081.11. Because the 5 percent coupon exceeds the 4 percent market rate, the bond trades at a premium of $81.11 above par. Its current yield is $50 / $1,081.11 = 4.62 percent, below the coupon rate, exactly as theory predicts for a premium bond.
Worked example 2, a discount bond. Now take a bond with a $1,000 face value, a 4 percent annual coupon, and 5 years to maturity, while the market rate is 6 percent. The annual coupon is $40. The annuity factor is [1 – 1.06^-5] / 0.06. Since 1.06^5 equals 1.338226, the factor is [1 – 0.747258] / 0.06 = 4.21236. The present value of the coupons is $40 x 4.21236 = $168.49. The present value of the face value is $1,000 / 1.338226 = $747.26. The fair price is $168.49 + $747.26 = $915.75. Because the 4 percent coupon trails the 6 percent market rate, the bond trades at a discount of $84.25 below par. Its current yield is $40 / $915.75 = 4.37 percent, above the coupon rate, exactly as theory predicts for a discount bond. Notice the symmetry: the premium in example 1 and the discount in example 2 both arise from the two-percentage-point gap between coupon and market rate, and in both cases the current yield lands between the coupon rate and the market rate.
Real-world bonds usually pay interest twice a year, so a careful valuation splits every input into half-year periods. Take a bond with a $1,000 face value, a 6 percent coupon paid semiannually, and 3 years to maturity, while the market rate is 5 percent nominal compounded semiannually. The semiannual coupon is 6 percent / 2 x $1,000 = $30, paid every six months. There are 3 x 2 = 6 periods, and the market rate per period is 5 percent / 2 = 2.5 percent.
The annuity factor is [1 – 1.025^-6] / 0.025. Since 1.025^6 equals 1.159693, the factor is [1 – 0.862297] / 0.025 = 5.5081. The present value of the six $30 coupons is $30 x 5.5081 = $165.24. The present value of the $1,000 face value is $1,000 / 1.159693 = $862.30. The fair price is $165.24 + $862.30 = $1,027.54, a premium of $27.54 because the 6 percent coupon beats the 5 percent market rate.
Compare this with the simpler annual-pay version of the same bond: $60 per year for 3 years discounted at 5 percent gives $60 x 2.7232 + $1,000 / 1.157625 = $163.39 + $863.84 = $1,027.23. The semiannual bond is worth $0.31 more because half of each year interest arrives six months sooner and can be reinvested earlier. The difference is small over three years, but over a 30-year bond the compounding-frequency adjustment becomes material, which is why professional pricing systems always model the actual payment schedule rather than annualizing it. If you use this calculator annual framework for a semiannual bond, halve the coupon and market rates and double the years to keep the valuation honest.
Beginners often treat a bond three yields as interchangeable; they are not. Suppose you buy a bond with a $1,000 face value, a 5 percent coupon ($50 per year), and 10 years to maturity for a market price of $950. The coupon rate is fixed at 5.00 percent; it describes the bond, not your return. The current yield is $50 / $950 = 5.26 percent; it measures this year income against what you paid. The yield to maturity adds the $50 pull-to-par gain ($1,000 received at maturity minus $950 paid today, spread over 10 years, or $5 per year) and comes to approximately 5.64 percent. The standard approximation is [C + (F – P) / n] / [(F + P) / 2] = [$50 + ($1,000 – $950) / 10] / [($1,000 + $950) / 2] = $55 / $975 = 5.64 percent.
Now flip the scenario: you pay $1,080 for the same bond. The coupon rate is still 5.00 percent and the current yield is $50 / $1,080 = 4.63 percent, but the yield to maturity must now absorb an $80 pull-to-par loss ($8 per year): [$50 + ($1,000 – $1,080) / 10] / [($1,000 + $1,080) / 2] = $42 / $1,040 = 4.04 percent. Notice the ordering rule that always holds: for a discount bond, coupon rate is less than current yield is less than yield to maturity (5.00% less than 5.26% less than 5.64%); for a premium bond the order reverses, yield to maturity is less than current yield is less than coupon rate (4.04% less than 4.63% less than 5.00%); and for a par bond all three are equal. If your numbers ever violate this ordering, recheck your inputs before trusting the result.
Bond valuation rarely happens in isolation. Continue your analysis with the CAGR Calculator to convert a bond total return into a smooth annualized growth rate, or browse the full Financial Calculators collection for present-value, investment, and loan tools that complement fixed-income work. Pairing this bond pricer with a compound-growth calculator lets you compare a bond yield to maturity directly against equity-style annualized returns.
This page provides a bond price and yield calculator plus educational reference content. Key facts: bond price equals the present value of coupons plus the present value of face value discounted at the market rate per period; price moves inversely to market rates; a premium bond has coupon rate above market rate and price above face value; a discount bond has coupon rate below market rate and price below face value; current yield equals annual coupon divided by price; yield to maturity is the discount rate equating price to present value of all remaining cash flows; for discount bonds, coupon rate is less than current yield is less than yield to maturity; most bonds pay semiannual coupons, so per-period rate is half the nominal rate and periods are doubled. Worked reference values: $1,000 face, 5 percent coupon, 10 years, 4 percent market rate gives $1,081.11; $1,000 face, 4 percent coupon, 5 years, 6 percent market rate gives $915.75.
Fair price, current yield and premium/discount status — from face value, coupon rate, years and market rate.
Enter the bond’s face value, annual coupon rate, years to maturity and the market rate (yield to maturity). The calculator discounts every coupon payment plus the face value at the market rate to get the fair price, and shows the current yield.
Formula: Price = Σ coupon ÷ (1+r)^t + face ÷ (1+r)^n. Current yield = annual coupon ÷ price. Example: $1,000 face, 5% coupon, 10 years, 4% market rate → price $1,081.11, current yield 4.62%.
Each future payment — the coupons and the face value at maturity — is discounted back to today at the market rate and added up. The calculator above does it instantly.
Existing bonds pay fixed coupons, so when new bonds pay higher rates, the old ones must get cheaper to offer the same yield. Price and yield always move opposite.
The coupon rate is fixed at issue (5% of face = $50/year); the current yield is $50 ÷ the price you actually pay — 4.62% on a $1,081.11 price.
A premium bond costs more than face value (coupon above market rate); a discount bond costs less (coupon below market rate). At par, price equals face value.
The total annualized return if you hold the bond to maturity, including coupons and any price gain or loss. Enter it as the market rate above.
Discount every future cash flow at the market rate: price = annual coupon x [1 – (1 + r)^-n] / r + $1,000 / (1 + r)^n. For a 10-year, 5% ($50 per year) bond when the market rate is 4%, that is $50 x 8.1109 + $1,000 / 1.4802 = $405.54 + $675.56 = $1,081.11, a premium bond because the coupon exceeds the market rate.
It falls. A 10-year, 5% $1,000 bond priced at $1,081.11 at a 4% market rate drops to about $1,000.00 at 5% and roughly $926.40 at 6%. Longer maturities swing more; that sensitivity is measured by duration.
No. Current yield = annual coupon / price; it measures income only. Yield to maturity also includes the pull-to-par gain or loss. For a $950, 10-year, 5% ($50) bond: current yield = $50 / $950 = 5.26%, while YTM is about 5.64%. YTM is the fuller measure of total return.
Cite this page: Sigma Calculator. (2026). Bond Calculator – Price and Yield. https://sigmacalculator.net/financial-calculators/bond-calculator/
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