How Bond Prices and Yields Work: YTM, Duration and More
Learn how a bond's price and yield to maturity are linked, why prices fall when rates rise, and what current yield, duration and convexity tell you.
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Free tool: Bond Price CalculatorA bond pays fixed interest, called coupons, and returns its face value at maturity. Its price moves up and down with market interest rates, which changes the return you'd earn by buying it today. This guide explains how bond prices and yields are linked, with worked examples, using the free Bond Price Calculator.
The parts of a bond
- Face value: the amount repaid at maturity, often $1,000.
- Coupon rate: the yearly interest as a share of face value. A 5% coupon on $1,000 pays $50 a year, often as two $25 payments.
- Maturity: when the face value is repaid.
- Price: what the bond trades for today, which can be above or below face value.
Yield to maturity
The yield to maturity (YTM) is the yearly return you'd earn if you buy at today's price, hold to maturity and reinvest the coupons at the same rate. It's the rate that makes the present value of all the coupons and the face value equal to the price.
Example: a $1,000, 5% bond with 10 years left, paying twice a year, trades at $926:
- Yield to maturity: 6.00%
- Current yield (yearly coupon ÷ price): $50 ÷ $926 = 5.40%
Because you pay less than face value, you also gain $74 at maturity, so the YTM is higher than the coupon rate.
Why prices fall when rates rise
A bond's price is its cash flows discounted at the market yield. When yields rise, the same fixed coupons are worth less, so the price falls. The same 5% bond priced at different market yields:
| Market yield | Price | Trades at |
|---|---|---|
| 4% | $1,081.76 | a premium |
| 5% | $1,000.00 | par |
| 6% | $925.61 | a discount |
| 7% | $857.88 | a discount |
Duration and convexity
Duration measures how sensitive the price is to yield changes. The example bond has a Macaulay duration of 7.90 years and a modified duration of 7.67, so a 1-point rise in yields cuts its price by roughly 7.7%. Convexity, 71.8 here, refines that estimate for larger moves: going from 6% to 7% actually lowers the price by about 7.3%.
Longer maturities and lower coupons mean higher duration and more interest rate risk. A 30-year version of the same bond has a modified duration of about 14.3.
Other risks
- Credit risk: the issuer might not pay. Lower-rated bonds pay higher yields to compensate.
- Call risk: some bonds can be repaid early, usually when rates fall.
- Inflation: fixed coupons lose buying power if inflation rises.
For short-term Treasury bills, which pay no coupon, see the T-Bill Calculator.
How to use the Bond Price Calculator
- Open the Bond Price Calculator.
- Choose what to solve for: the yield to maturity from a price, or the price from a market yield.
- Enter the face value, the coupon rate and the current price or market yield.
- Enter the years to maturity and how often coupons are paid.
- Read the results: the yield to maturity or price, the current yield, the duration, the convexity, and the future value and total return if coupons are reinvested at the yield, with growth charts and a yearly table.
Frequently asked questions
How is a bond's price calculated?
By discounting each coupon and the face value at the market yield and adding them up. A 5% 10-year bond priced at a 6% yield is worth about $925.61.
What is the difference between coupon rate and yield?
The coupon rate is fixed when the bond is issued. The yield depends on the price you pay: buy below face value and the yield is higher than the coupon, as with the 6.00% yield on the $926 bond.
What does bond duration mean?
It estimates how much the price changes when yields move. A modified duration of 7.67 means about a 7.7% price change for a 1-point move in yields.