Calculate bond prices, yield to maturity, duration, and convexity. Visualize price-yield curves and coupon cash flows.
Bond pricing is present-value arithmetic in reverse: a bond promises fixed coupon payments and a lump-sum principal repayment, and the price is what those promises are worth today at the yield to maturity. This tool takes the coupon rate, maturity, face value, and yield, computes the price, and reverses the calculation to solve for yield when you enter a market price instead. It also reports duration and convexity and draws the price-yield curve and coupon timeline. The recurring surprise: price and yield move in opposite directions, so a coupon above the market yield means a premium price.
A concrete input and expected output from the current implementation.
Input
Face value $1,000; coupon rate 6% paid annually; 5 years to maturity; yield to maturity 5%
Expected output
Price: $1,043.29 per $1,000 face value, a 4.33% premium (coupon above yield). Macaulay duration: 4.48 years; modified duration: 4.26; convexity: 23.4. The curve shows price falling as yield rises, reaching par at a 6% yield.
Each $60 coupon is discounted at 5% per year - the year-5 coupon is worth 60 / 1.05^5 = $47.01 and the principal 1,000 / 1.05^5 = $783.53 - and the discounted stream sums to $1,043.29. Because the coupon rate exceeds the yield, the bond trades at a premium; at a yield equal to the coupon rate it would trade at par.
The price equals the sum of every remaining cash flow discounted at the yield to maturity: a coupon in period t contributes C / (1 + y)^t and the principal repays F / (1 + y)^n. Distant payments are discounted most, which is why long maturities react more to yield changes. Payment frequency and day-count convention change the exact discounting, so the result depends on the bond's convention.
Yield to maturity is the single discount rate that makes present value equal the market price, effectively the bond's internal rate of return. It has no closed-form solution, so the calculator searches for the rate that reproduces the entered price. Duration is the present-value-weighted average time to each cash flow; convexity measures the curvature of the price-yield relationship. Together they estimate how much a yield move changes the price.
Because the price is the present value of fixed cash flows, and a lower discount rate raises present value. That is why prices and yields move in opposite directions and why a bond whose coupon exceeds the current yield trades above its face value. Duration and convexity quantify exactly how sensitive the price is.
Only if you reinvest every coupon at that same yield and the issuer pays everything on schedule. In practice reinvestment rates move, so the realized return differs, and default risk is not captured. Treat YTM as a standardized comparison number, not a forecast.
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