Key point
When interest rates rise, existing bonds paying lower rates become less attractive. Their prices fall until their yield matches the new rate. When rates fall, the opposite happens.
Compare
| Scenario | New Bond Yield | Old Bond (5% coupon) | Price Direction |
|---|---|---|---|
| Rates rise to 6% | 6% | 5% is less attractive | Price FALLS below par |
| Rates stay at 5% | 5% | 5% matches market | Price stays near par |
| Rates fall to 4% | 4% | 5% is more attractive | Price RISES above par |
Formula
Yield to Maturity approximation: YTM = (Coupon + (Face - Price) / Years) / ((Face + Price) / 2)
Note
The formula above is the Bogen approximation — convenient for mental math but not exact. The true YTM is the internal rate of return (IRR) of all the bond's cash flows discounted to today's price; a financial calculator or spreadsheet RATE() function solves it iteratively. The gap between the approximation and the true IRR is small for long-maturity bonds near par but can exceed 50 basis points for short maturities (under 3 years) or high-yield bonds (coupon > 8%), where the linear approximation breaks down most severely.
Try it
Key insight
Check-in
Sit with the ideas.
Interest rates in the market rise from 4% to 6%. What happens to the price of an existing bond paying 4%?
Buy a bond ETF after the duration lesson
Pick a Treasury or aggregate bond ETF (e.g., IEF, AGG, BND, TLT). Paper-buy 50 shares. Journal what you expect the position to do if the 10-year yield moves up 100 bps versus down 100 bps.
Open paper portfolio →Practice mode — simulated trades, not investment advice.