Market Price Per 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):

Market Price Per Bond (P):

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1. What Is The Market Price Per Bond?

The market price per bond represents the current value of a bond in the marketplace, calculated as the present value of all future cash flows (coupon payments and face value) discounted at the current market yield.

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:

\( P \) — Market price per bond (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 periodic coupon payments and the final face value repayment.

3. Importance Of Bond Pricing

Details: Accurate bond pricing is essential for investors to determine fair value, make investment decisions, assess risk-return profiles, and for issuers to price new bond offerings appropriately.

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: Why does bond price change inversely with yield?
A: When market interest rates rise, existing bonds with lower coupon rates become less attractive, causing their prices to fall to match the new higher yields.

Q2: What is the relationship between coupon rate and bond price?
A: When coupon rate equals yield, bond trades at par (face value). When coupon rate > yield, bond trades at premium. When coupon rate < yield, bond trades at discount.

Q3: How does time to maturity affect bond price volatility?
A: Longer-term bonds have greater price sensitivity to interest rate changes due to more distant cash flows being discounted over a longer period.

Q4: What are zero-coupon bonds?
A: Zero-coupon bonds pay no periodic interest; they're issued at a deep discount and mature at face value. Their price is simply the present value of the face value.

Q5: How does payment frequency affect bond pricing?
A: More frequent payments (semi-annual vs annual) generally increase the bond's value slightly due to earlier receipt of cash flows and compounding effects.