1. What is a Zero Coupon Bond?

A zero coupon bond is a debt security that doesn't pay periodic interest but is issued at a discount to its face value. The bond's return comes from the difference between its purchase price and its face value at maturity.

2. How Does the Calculator Work?

The calculator uses the continuous compounding formula:

Where:

• \( PV \) — Present value of the bond ($)
• \( FV \) — Face value of the bond ($)
• \( r \) — Continuous interest rate (as decimal)
• \( n \) — Time to maturity in years
• \( e \) — Euler's number (~2.71828)

Explanation: The formula discounts the future value back to present value using continuous compounding.

3. Importance of Present Value Calculation

Details: Calculating present value helps investors determine the fair price to pay for a zero coupon bond today to achieve a desired return at maturity.

4. Using the Calculator

Tips: Enter face value in dollars, continuous rate as a percentage (e.g., 5 for 5%), and years to maturity. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between zero coupon and regular bonds?
A: Zero coupon bonds don't make periodic interest payments; they're purchased at a discount and pay the full face value at maturity.

Q2: Why use continuous compounding?
A: Continuous compounding provides the most accurate present value calculation and is often used in financial modeling.

Q3: How does the rate affect present value?
A: Higher rates result in lower present values, as future cash flows are discounted more heavily.

Q4: Are zero coupon bonds risk-free?
A: No, they carry interest rate risk and issuer default risk like other bonds.

Q5: What about taxes?
A: In many jurisdictions, imputed interest on zero coupon bonds is taxable annually as it accrues.