A zero-coupon bond is a security that pays no interest, and is therefore bought at a substantial discount from its face value. If the interest rate is 12% with annual compounding how much would you pay today for a zero-coupon bond with a face value of $1,600 that matures in 11 years?

Please round your answer to the nearest hundredth.

To determine the price you would pay today for a zero-coupon bond, we use the formula for the present value (PV) of a single sum, which is:

\[
PV = \frac{FV}{(1 + r)^n}
\]

Where:
- $FV$ is the face value of the bond,
- $r$ is the annual interest rate (as a decimal),
- $n$ is the number of years until maturity.

In this case:
- $FV = 1600$ dollars,
- $r = 0.12$ (12%),
- $n = 11$ years.

Substituting these values into the formula:

\[
PV = \frac{1600}{(1 + 0.12)^{11}}
\]

Now, let's calculate the value.The amount you would pay today for the zero-coupon bond is **$459.96**.

Would you like more details or have any questions? 

Here are some related questions:
1. What is the future value of a different bond if purchased at the same price but with a different interest rate?
2. How does semi-annual compounding affect the price of a zero-coupon bond?
3. What is the yield to maturity for this bond if purchased at the calculated price?
4. How would the bond price change if the maturity period were 15 years instead of 11 years?
5. How do changes in interest rates affect the price of zero-coupon bonds?
6. What are the risks associated with investing in zero-coupon bonds?
7. How would you calculate the price of a zero-coupon bond if interest was compounded monthly?
8. What are the tax implications of investing in zero-coupon bonds?

**Tip:** Zero-coupon bonds are more sensitive to interest rate changes than bonds that pay periodic interest because the entire payment is received at maturity.

Learn how to calculate the price of a zero-coupon bond with a 12% annual interest rate and 11 years until maturity. Understand the formula for present value (PV) and its application in finance. Suitable for advanced high school students and anyone interested in financial calculations.

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