The Bond Calculator estimates a bond’s clean price by discounting remaining coupon payments and face value at the yield to maturity. Enter face value, coupon rate, yield, years to maturity, and coupon frequency, and the Bond Calculator returns the present value of those cash flows exact to the cent for educational pricing.
Bond price moves when yield moves. When yield equals the coupon rate on a coupon date, price sits at par; when yield rises above the coupon, price falls to a discount; when yield falls, price rises to a premium. The Bond Calculator makes that relationship concrete.
*These results are estimates for information only, not investment advice or a trade quote.*
Calculate a bond price with the Bond Calculator
The Bond Calculator prices a bond as the present value of the coupon stream plus the present value of face value, all discounted at the yield. Clean price here means that present value on a coupon date, without accrued interest between payment dates.
Price = Σ (coupon / (1 + y/m)^(k)) + face / (1 + y/m)^(n), where y is annual yield, m is coupons per year, and n is the number of remaining coupon periods. A $1,000 face bond with a 5% annual coupon, 10 years to maturity, and a 6% yield has a clean price of about $926.40. Each $50 coupon and the final $1,000 are worth less today because the market discount rate exceeds the coupon rate.
The Bond Calculator shows that discounted total so price is traceable to the cash flows, not to a black-box quote.
Find the yield to maturity with the Bond Calculator
Yield to maturity is the discount rate that sets the present value of the bond’s remaining cash flows equal to its price. The Bond Calculator uses yield as an input when solving for price, which is the same relationship run in the pricing direction.
If the market price is known and cash flows are known, YTM is the rate that solves Price = PV(coupons + face). When coupon rate equals yield, that price is par. When the entered yield is 6% on a 5% coupon bond, the solved price is the discount figure above. Raising yield further lowers price; lowering yield raises price. The Bond Calculator keeps coupon rate and yield as separate fields so the spread between them is intentional.
YTM is a single constant rate assumption across the remaining life. Real mark-to-market paths vary; the Bond Calculator uses the standard level-yield model for clarity.
Calculate accrued interest with the Bond Calculator
Accrued interest is the portion of the next coupon that has been earned since the last coupon date but not yet paid. The Bond Calculator can prorate that coupon by days elapsed versus days in the coupon period when accrued mode is used.
Accrued ≈ coupon payment × (days since last coupon ÷ days in coupon period). On a $1,000 face, 5% annual coupon paid once a year, the full coupon is $50. Halfway through the year on a simple day-count sketch, accrued interest is about $25. Dirty price is clean price plus accrued; buyers pay dirty, and the accrued portion compensates the seller for the coupon earned so far. The Bond Calculator’s clean-price default omits accrued unless that path is selected.
Between coupon dates, ignoring accrued understates what changes hands in a live trade. The Bond Calculator states which figure it is showing.
Understand premium and discount bonds
A bond trades at a premium when price exceeds face, at a discount when price is below face, and at par when price equals face. The Bond Calculator illustrates all three by changing yield relative to the coupon rate.
On the $1,000, 5% coupon, 10-year annual example: at 5% yield, price is $1,000 (par); at 6% yield, price is about $926.40 (discount); at 4% yield, price is about $1,081.11 (premium).
Investors pay up for a coupon above market yields and demand a discount when the coupon is below market yields. As maturity approaches, price trends toward face if the issuer pays as promised, which compresses premium and discount over time.
The Bond Calculator keeps that coupon-versus-yield story visible whenever the two rates differ.
Coupon frequency changes how often cash arrives and how the periodic discount rate is set. A 5% annual coupon on $1,000 is $50 once a year, or $25 twice a year if paid semi-annually. The Bond Calculator divides the annual yield by the number of coupon periods per year when discounting, matching standard textbook pricing on a coupon date. More frequent coupons slightly change price versus annual payment at the same annual coupon rate because cash arrives sooner. Enter the frequency that matches the bond’s prospectus.
Credit risk, call features, and sinking funds sit outside clean yield-to-maturity pricing on a non-callable fixed coupon. The Bond Calculator assumes the cash flows you imply with face, coupon, and maturity are paid as scheduled. A callable bond needs a different yield measure; do not treat this clean price as a live offer on a complex structure.
Frequently asked questions
How is bond price calculated?
Bond price is calculated as the present value of coupons plus the present value of face value, discounted at the yield. The Bond Calculator applies that discounting model from face, coupon, yield, term, and frequency. A 5% coupon bond at a 6% yield over 10 years prices below par.
What is yield to maturity?
Yield to maturity is the constant annualized discount rate that equates a bond’s price to its remaining cash flows. The Bond Calculator uses yield as the discount rate when computing clean price. When yield equals the coupon rate on a coupon date, price equals face value.
Does the Bond Calculator include accrued interest?
The Bond Calculator returns a clean price by default and can show accrued interest when that mode is used. Clean price excludes the prorated coupon since the last payment date; dirty price adds it. Confirm which figure a broker quote is using before comparing.
Why do bond prices fall when yields rise?
Bond prices fall when yields rise because future coupons and face are discounted more heavily. The Bond Calculator divides each cash flow by a larger factor at a higher yield, which lowers present value. The reverse holds when yields fall.
What is a premium bond?
A premium bond is a bond whose price is above face value, which happens when the coupon rate exceeds the yield used for discounting. The Bond Calculator produces a premium price when the entered yield sits below the coupon rate. The premium is the market’s payment for above-market coupons.
Is the Bond Calculator a live market quote?
The Bond Calculator is not a live market quote. It applies standard present-value math to the inputs entered. Trading decisions need current market data, credit analysis, and professional advice beyond this educational price.
Summary
The Bond Calculator estimates clean bond price by discounting coupons and face at the yield to maturity. When yield equals the coupon rate, price is at par; a $1,000 face, 5% coupon, 10-year bond is worth about $926.40 at a 6% yield and about $1,081.11 at a 4% yield.
Accrued interest prorates the current coupon between payment dates and sits on top of clean price in a dirty quote. Premium and discount labels follow whether price sits above or below face. Figures are for learning, not trade execution or investment advice.