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.
| 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 |
Yield to Maturity approximation: YTM = (Coupon + (Face - Price) / Years) / ((Face + Price) / 2)
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.
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.