US Treasury Bond Value Calculator

US Treasury Bond Value 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 Value Formula?

The US Treasury Bond Value formula calculates the present value of a bond by summing the present values of all future coupon payments and the face value payment at maturity. This formula is essential for bond pricing and investment analysis.

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 Valuation

Details: Accurate bond valuation is crucial for investors to determine fair prices, assess investment opportunities, and manage fixed-income portfolios. It helps in comparing different bond investments and making informed decisions.

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.

Q2: Why does bond price change when yield changes?
A: Bond price and yield 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 typically have maturities of 10 to 30 years, while Treasury notes have 2 to 10 years, and Treasury bills have less than 1 year.

Q4: How does payment frequency affect bond value?
A: More frequent payments generally increase the bond's value slightly due to earlier receipt of cash flows, though the effect is usually small.

Q5: What happens if yield equals coupon rate?
A: When yield to maturity equals the coupon rate, the bond typically trades at par value (face value).