Bond Selling Price Calculator

Bond Selling Price Formula:

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

Face Value (F):

currency units

Coupon Rate:

decimal

Yield to Maturity:

decimal

Years to Maturity:

years

Payments per Year (m):

Selling Price:

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1. What is the Bond Selling Price Formula?

The bond selling price formula calculates the present value of all future cash flows from a bond, including coupon payments and the face value repayment at maturity. It determines the fair market price of a bond based on current market conditions.

2. How Does the Calculator Work?

The calculator uses the bond pricing formula:

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

Where:

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

Explanation: The formula discounts all future cash flows (coupon payments and principal repayment) to their 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 in fixed income markets.

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 the payment frequency. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is the relationship between yield and bond price?
A: Bond prices and yields have an inverse relationship. When market yields rise, bond prices fall, and vice versa.

Q2: How does coupon rate affect bond price?
A: Bonds with higher coupon rates typically trade at higher prices than similar bonds with lower coupon rates, all else being equal.

Q3: What happens when a bond is priced at a discount or premium?
A: A bond trades at a discount when its price is below face value (yield > coupon rate), and at a premium when above face value (yield < coupon rate).

Q4: How does time to maturity affect bond price volatility?
A: Longer-term bonds are more sensitive to interest rate changes and exhibit greater price volatility than shorter-term bonds.

Q5: What are zero-coupon bonds?
A: Zero-coupon bonds don't pay periodic coupons. Their price is simply the present value of the face value: Price = F / (1 + r)^n.