Bond Price, YTM and Duration — the Investor's Guide to Fixed Income Math
Bonds are simpler than stocks in theory and harder in practice. A bond is a contract: the issuer borrows a fixed principal (face value), pays a fixed coupon on a set schedule, and returns the principal at maturity. If you hold to maturity and the issuer doesn't default, your return is knowable on day one — that's why bonds are called 'fixed income'. The problem is that between issue and maturity, the bond's market price moves with interest rates, credit spreads and time — and understanding that dance is what separates informed investors from yield-chasers.
The single most important number is yield to maturity (YTM). YTM is the internal rate of return you earn if you buy at today's price, receive every coupon on schedule and hold to maturity. It bakes in the pull-to-par (the capital gain or loss you'll realize as the bond's price converges to face value at maturity). Two bonds with identical coupons but different market prices have different YTMs — always compare bonds by YTM, never by coupon rate or current yield alone.
Price and yield move inversely. When the Federal Reserve raises rates, existing bonds paying yesterday's lower coupons become less attractive. Buyers demand a discount to make the math work — price falls until YTM equals the new market rate. A 1% rate rise on a 10-year bond typically drops price 8–9% (that's its 'duration'). This is why long bonds are terrifying in rate-hike cycles and glorious in cutting cycles.
Duration is the risk metric professionals watch. A duration of 7 means a 1% rate change moves price by roughly 7%. Long-maturity, low-coupon bonds have the highest duration. Zero-coupon bonds have duration equal to their maturity — a 20-year zero can move 20% on a 1% rate move. If you can't stomach that, stick to short-duration bonds or bond ladders.
Premium versus discount is not automatically good or bad. A premium bond (price > face) has a coupon above market — you get bigger interest checks but lose principal at maturity. A discount bond (price < face) has a coupon below market — smaller checks but a capital gain at maturity. YTM equalises both scenarios; taxes may not. In taxable accounts, premium bonds can be tax-inefficient because coupon income is ordinary while the capital loss is only recognized at maturity.
This calculator handles both directions — enter YTM to solve for the fair price you should pay, or enter a market price and solve for the YTM you'd earn. Combine it with our Dividend Calculator for a full income-portfolio view, and always cross-check against a broker's screen before placing an order. Corporate and municipal bonds trade with wide bid-ask spreads; a quoted YTM in a broker screen may hide 20–50 basis points of markup versus institutional pricing.