A Treasury note promises fixed dollar payments on fixed dates. Its market price is whatever makes those payments yield the going rate, so when market yields rise the price has to fall, and when they fall it rises. That inverse link is the most important fact in bond investing, and its size depends mainly on how long the bond has left to run. This page works the arithmetic for new 2-year, 10-year and 30-year Treasuries using the October 30, 2026 par yields of 4.56%, 4.94% and 5.31%, shows how duration turns it into a rule of thumb and how convexity refines it, and explains what holding to maturity does and does not protect. Background on each security is on the US Treasuries hub, and today's yields by maturity are on the Treasury yield curve page.
Why do bond prices fall when rates rise?
Because a bond's coupons are fixed: when new Treasuries pay more, an older bond sells only at a price that gives its buyer the same yield. Nobody pays full price for $49.40 a year when a new note of the same maturity pays $59.40.
Suppose you buy $1,000 of a new 10-year note at par with a 4.94% coupon, which pays $24.70 every six months. A week later, yields on comparable notes jump to 5.94%. A buyer can now get $29.70 every six months from a new note for the same $1,000. Your note will sell only at a price at which its $24.70 coupons, plus the $1,000 at maturity, also yield 5.94%. That price is $925.41: the $74.59 discount makes up, in present-value terms, for the smaller coupons.
The reverse holds when yields fall. Your 4.94% coupons become worth more than the coupons on new notes, so a buyer pays a premium. Either way, the price moves until the old bond's yield matches the market. Investor.gov puts the selling problem directly: to sell an older bond with a lower rate, you might have to sell it at a discount. The coupon itself never changes, as TreasuryDirect's note rules make clear: it is set at the first auction and stays the same until maturity.
How is a Treasury's price calculated?
A Treasury's price is the present value of its remaining coupons plus its face value, each discounted at half the market yield for every six-month period until it is paid. Treasuries pay coupons twice a year, so the formula works in half-years.
Here y is the market yield as a decimal and n is the number of years left. The first term values the stream of coupons; the second values the single repayment of face value at maturity. When y equals the coupon rate, the price is exactly par.
Worked example: Pricing a 4.94% 10-year note after yields rise to 5.94%
- Coupon per half-year: $1,000 × 4.94% ÷ 2 = $24.70, paid 20 times.
- Discount rate per half-year: 5.94% ÷ 2 = 2.97%, and 1.0297 raised to the 20th power is 1.79562.
- Value of the coupons: $24.70 × (1 − 1 ÷ 1.79562) ÷ 0.0297 = $24.70 × 14.9188 = $368.49.
- Value of the face amount: $1,000 ÷ 1.79562 = $556.91.
- Price: $368.49 + $556.91 = $925.41 per $1,000, a fall of 7.46%.
Bills follow a simpler rule because they pay no coupon: their price is face value minus a discount, as T-bill discount rate vs investment rate explains.
How much do 2-, 10- and 30-year Treasury prices change for a 1-point move?
A 1-point move changes the price of a new 2-year note by about 1.9%, a 10-year note by 7.5% to 8.2% and a 30-year bond by 13.4% to 16.8%. The range depends on direction. The table prices each security, bought at par at the October 30, 2026 par yield, after an instant 1-point rise and an instant 1-point fall.
| Treasury | Coupon and yield at purchase | Price after a 1-point rise | Change | Price after a 1-point fall | Change |
|---|---|---|---|---|---|
| 2-year note | 4.56% | $981.32 | -1.87% | $1,019.14 | +1.91% |
| 10-year note | 4.94% | $925.41 | -7.46% | $1,081.99 | +8.20% |
| 30-year bond | 5.31% | $866.10 | -13.39% | $1,167.46 | +16.75% |
Prices are per $1,000 of face value. Two patterns show up. Longer maturities move more, because more of their value sits in payments far in the future, and a change in the discount rate compounds over every period until then. And each security gains more from a fall than it loses from a rise of the same size, an asymmetry explained under convexity below.
Bills sit at the far short end. At the October 30, 2026 discount rates, a 1-point rise would cut the price of a 13-week bill by about 0.26%, a 26-week bill by about 0.52% and a 52-week bill by about 1.06%, because the higher rate applies for only months. That is why bills are the usual home for money with a known spending date; the Treasury bill calculator prices any term at any rate. Per-$10,000 tables for every note and bond maturity are in Treasury notes explained and Treasury bonds explained.
What is duration, and how do you use it as a rule of thumb?
Duration measures how sensitive a bond's price is to yield: multiply modified duration by the change in yield, in points, to estimate the percentage price change.
FINRA states the rule the same way: for every 1-point change in rates, a bond's price moves in the opposite direction by roughly its duration. Macaulay duration, the original measure, is the weighted average time until a bond's payments arrive, with each payment weighted by its present value. Modified duration divides it by one plus the yield per period and is the figure used for price changes.
| Treasury | Macaulay duration, years | Modified duration | Rule of thumb for a 0.25-point rise | Actual | Rule of thumb for a 2-point rise | Actual |
|---|---|---|---|---|---|---|
| 2-year note | 1.93 | 1.89 | -0.47% | -0.47% | -3.78% | -3.69% |
| 10-year note | 8.01 | 7.82 | -1.95% | -1.93% | -15.63% | -14.25% |
| 30-year bond | 15.32 | 14.92 | -3.73% | -3.63% | -29.85% | -24.19% |
For small moves the rule of thumb is close to exact. For a quarter-point rise it misses the 10-year note's actual change by 0.02 point. For a 2-point rise it overstates the 30-year bond's loss by more than 5 points. Duration also explains why maturity is not the whole story. A 30-year bond's duration is about 15 years, not 30, because its coupons return part of the money along the way, and FINRA notes that a higher coupon means a lower duration. A zero-coupon security's duration equals its maturity.
What is convexity, in plain words?
Convexity is the curve in the price-yield relationship: prices rise more when yields fall than they drop when yields rise by the same amount, and duration alone misses that. Duration draws a straight line through today's price; the true price follows a curve that bends upward on both sides of the line.
In practice, convexity works in the holder's favor. As yields rise, a bond's duration shrinks, so each further increase hurts less; as yields fall, duration grows, so each further decrease helps more. Adding a convexity term to the duration estimate fixes most of the error for a 1-point move. With convexities of about 4.6 for the 2-year note, 73.9 for the 10-year and 333.6 for the 30-year, the adjusted estimates for a 1-point rise are -1.87%, -7.45% and -13.26%, within 0.13 point of the actual changes in the table above.
The longer the bond, the more convexity matters, which is why the 30-year bond's gain from a 1-point fall, +16.75%, is so much larger than its 13.39% loss from a 1-point rise. Investors pay for that cushion indirectly: securities with more convexity tend to yield a little less than they otherwise would.
Does holding to maturity remove the risk?
It removes the price risk, because Treasury repays face value at maturity, but not the opportunity cost of earning the old, lower coupon while new bonds pay more. The loss you would take by selling is the same loss you absorb over time by holding.
Worked example: The cost of holding a 4.94% note after yields rise 1 point
- After the rise, a new 10-year note pays $29.70 every six months per $1,000, and yours pays $24.70: $5 less, 20 times.
- The present value of those twenty $5 shortfalls at 2.97% per half-year is $74.59.
- That is exactly the price drop from $1,000 to $925.41: selling locks in the loss at once, holding spreads it over ten years.
- Measured in coupon income, the price drop equals about 1.5 years of the note's $49.40 annual interest; for the 2-year note it is 0.41 year and for the 30-year bond 2.52 years.
Rising rates also have an upside for a holder: each coupon can be reinvested at the higher yield. Over a horizon equal to the Macaulay duration, the two effects roughly cancel. Reinvest every coupon from the 10-year note at the prevailing yield and value the note after 8 years, and $1,000 grows to about $1,477.60 if yields stay at 4.94%, $1,478.10 if they rise to 5.94% and $1,478.40 if they fall to 3.94%. Investors who match the duration of what they own to when they need the money are using this effect.
A real note shows how large the gap between price and promise can get. Treasury sold $38 billion of a 10-year note with a 0.625% coupon on August 12, 2020, at a price of about 99.50 per 100 and a yield of 0.677%. On October 19, 2023, when the 10-year par yield reached 4.98%, a note with that coupon and about 6.8 years left was worth roughly 75 per 100 at the prevailing yield of about 5%, a fall of about a quarter. Held to August 15, 2030, it still repays 100. Selling before maturity, and the tax treatment of a gain or loss, is covered in selling Treasuries before maturity.
What are the risks behind these numbers?
The tables assume an instant, parallel 1-point move in yields, while real curves twist, move gradually and can move much more than 1 point.
- Bigger moves. In 2022 the 10-year par yield rose from 1.63% to 3.88%, more than 2 points in a year; are Treasuries risk-free? works through what that did to a note bought in January.
- Twists. Short and long yields rarely move by the same amount. Late in 2024 bill yields fell while the 10-year rose, so the two ends of a portfolio moved in opposite directions; what moves Treasury yields explains why.
- Funds never mature. A bond fund or ETF keeps a roughly constant duration by replacing bonds as they age, so a price loss is recovered only through higher income or falling yields, never through a maturity date.
- Selling costs. A sale happens at the bid price, and small lots or older issues can trade at a wider gap between bid and ask than the yields above imply.
- Inflation and reinvestment. Holding to maturity protects the dollars, not their purchasing power, and coupons must be reinvested at whatever rate prevails. Short-term vs long-term Treasuries compares how each maturity fares under rising, flat and falling rates.
The full faith and credit of the US government stands behind every coupon and the face value at maturity, not behind the price in between. Prices on this page are calculated from dated yields and are not forecasts; for current bill yields, see today's T-bill rates.