US 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:

Yield to Maturity:

Years to Maturity:

years

Payments per Year (m):

Bond Price (P):

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1. What is the US Treasury Bond Calculator?

The US Treasury Bond Calculator calculates the theoretical price of a US Treasury bond using the standard bond pricing formula. It considers face value, coupon rate, yield to maturity, time to maturity, and payment frequency to determine the bond's present value.

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 bond's yield to maturity.

3. Importance of Bond Price Calculation

Details: Accurate bond pricing is essential for investors, traders, and portfolio managers to determine fair value, make investment decisions, and assess risk-return profiles in fixed income markets.

4. Using the Calculator

Tips: Enter face value in USD, coupon rate and yield as percentages, 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 is the return investors require given current market conditions and risk.

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

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

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

Q5: Are US Treasury bonds risk-free?
A: While considered virtually free of default risk, they still carry interest rate risk, inflation risk, and reinvestment risk.