Treasury Bond Calculator

Treasury Bond Pricing Formula:

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

Face Value (F):

currency units

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 Treasury Bond Pricing Formula?

The Treasury Bond Pricing Formula calculates the present value of a bond by discounting all future cash flows (coupon payments and face value) at the required yield to maturity. It provides the theoretical fair price of a bond in the market.

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

Explanation: The formula calculates the present value of all future cash flows, including regular coupon payments and the final face value payment at maturity.

3. Importance of Bond Pricing

Details: Accurate bond pricing is essential for investors, portfolio managers, and financial institutions to determine fair value, make investment decisions, and assess risk-return profiles.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What is the relationship between bond price and yield?
A: Bond price and yield have an inverse relationship. When yield increases, bond price decreases, and vice versa.

Q2: What happens when coupon rate equals yield?
A: When coupon rate equals yield to maturity, the bond trades at par (price equals face value).

Q3: How does payment frequency affect bond price?
A: More frequent payments generally increase the bond's price slightly due to earlier receipt of cash flows.

Q4: What are zero-coupon bonds?
A: Zero-coupon bonds have no periodic coupon payments. Their price is simply the present value of the face value: \( P = \frac{F}{(1 + r)^n} \).

Q5: How accurate is this pricing model?
A: This is the standard present value model and works well for most bonds, but may need adjustments for bonds with special features like call options or convertible features.