Bond Calculator

Bond Price 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 Bond Price Formula?

The bond price formula calculates the present value of all future cash flows from a bond, including periodic coupon payments and the final face value payment at maturity. It represents the fair value of a bond in the current 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 discounts all future cash flows back to present value using the required yield as the discount rate.

3. Importance of Bond Pricing

Details: Accurate bond pricing is essential for investors, traders, and financial institutions to determine fair value, make investment decisions, and assess portfolio performance.

4. Using the Calculator

Tips: Enter face value in currency units, coupon rate and yield as decimals (e.g., 5% = 0.05), 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 value (price equals face value).

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

Q4: What is duration and convexity?
A: Duration measures bond price sensitivity to yield changes, while convexity measures how duration changes with yield.

Q5: Are zero-coupon bonds calculated differently?
A: Yes, zero-coupon bonds have no periodic payments, so the price is simply the present value of the face value.