US Government Treasury Bond Calculator

Bond Price Formula:

\[ P = \sum_{t=1}^{n} \frac{C}{(1 + r)^t} + \frac{F}{(1 + r)^n} \]

Face Value (F):

USD

Coupon Rate:

decimal

Yield to Maturity:

decimal

Years to Maturity:

years

Payments per Year (m):

Bond Price (P):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the US Government Treasury Bond Calculator?

The US Government Treasury Bond Calculator calculates the theoretical price of US government bonds using the standard bond pricing formula. It helps investors determine the fair value of treasury bonds based on current market conditions.

2. How Does the Calculator Work?

The calculator uses the bond pricing formula:

\[ P = \sum_{t=1}^{n} \frac{C}{(1 + r)^t} + \frac{F}{(1 + r)^n} \]

Where:

\( P \) — Bond price (USD)
\( C \) — Periodic coupon payment = (coupon rate × F) ÷ m (USD)
\( r \) — Periodic yield to maturity = yield ÷ m (decimal)
\( t \) — Period number (unitless)
\( F \) — Face value (USD)
\( n \) — Total number of periods = years × m (unitless)
\( m \) — Payments per year (unitless)

Explanation: The formula calculates the present value of all future cash flows (coupon payments and face value) discounted at the required yield to maturity.

3. Importance of Bond Price Calculation

Details: Accurate bond pricing is essential for investors to make informed decisions, assess investment opportunities, and manage fixed-income portfolios effectively.

4. Using the Calculator

Tips: Enter face value in USD, coupon rate and yield as decimals (e.g., 0.05 for 5%), years to maturity, and select the payment frequency. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between coupon rate and yield?
A: Coupon rate is the fixed interest rate paid by the bond, while yield reflects the current market return required by investors.

Q2: Why does bond price change when yield changes?
A: Bond prices and yields have an inverse relationship. When market yields rise, existing bond prices fall to make them competitive with new bonds.

Q3: What are typical US Treasury bond maturities?
A: Treasury bonds have maturities of 20-30 years, while notes are 2-10 years, and bills are up to 1 year.

Q4: How does payment frequency affect bond price?
A: More frequent payments generally increase the bond's value due to earlier receipt of cash flows.

Q5: Are US Treasury bonds risk-free?
A: US Treasury bonds are considered virtually risk-free in terms of default risk, but they still carry interest rate risk.