Calculate US Treasury Bonds

US Treasury Bond Pricing 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):

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1. What is the US Treasury Bond Pricing Formula?

The US Treasury Bond pricing formula calculates the present value of future cash flows from a bond, including periodic coupon payments and the final face value payment at maturity. It's essential for determining the fair market price of government bonds.

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 discounts all future cash flows (coupon payments and face value) to their present value using the yield to maturity as the discount rate.

3. Importance of Bond Pricing

Details: Accurate bond pricing is crucial for investors, portfolio managers, and financial institutions to determine fair value, assess investment opportunities, and manage interest rate risk in fixed income portfolios.

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 payment frequency. All values must be positive and valid.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between coupon rate and yield?
A: Coupon rate is the fixed interest rate paid on the bond's face value, while yield to maturity is the total return anticipated if the bond is held until maturity, reflecting current market conditions.

Q2: Why does bond price change when yield changes?
A: Bond prices and yields have an inverse relationship. When market interest rates rise, existing bonds with lower coupon rates become less attractive, causing their prices to fall.

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

Q4: How does payment frequency affect bond price?
A: More frequent payments (semi-annual vs annual) generally result in a slightly higher present value due to earlier receipt of cash flows.

Q5: When is a bond priced at par, premium, or discount?
A: Par (price = face value) when coupon rate = yield; premium (price > face) when coupon rate > yield; discount (price < face) when coupon rate < yield.