What interest rate is implicit in a $1,000 par value zero-coupon bond that matures in 9 years if the current price is $450.

Please specify your answer in decimal terms and round your answer to the nearest thousandth (e.g., enter 12.3 percent as 0.123).

To find the implicit interest rate in a zero-coupon bond, you can rearrange the present value formula:

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

Where:
- $ PV $ is the present value of the bond, which is $450.
- $ FV $ is the face value of the bond, which is $1,000.
- $ r $ is the interest rate (what we're trying to find).
- $ n $ is the number of years until maturity, which is 9.

Rearranging the formula to solve for $ r $:

\[
r = \left(\frac{FV}{PV}\right)^{\frac{1}{n}} - 1
\]

Substituting the values:

\[
r = \left(\frac{1000}{450}\right)^{\frac{1}{9}} - 1
\]

Let's calculate the value:

\[
r = \left(\frac{1000}{450}\right)^{\frac{1}{9}} - 1
\]

\[
r = (2.2222)^{\frac{1}{9}} - 1
\]

\[
r \approx 1.091 - 1
\]

\[
r \approx 0.091
\]

So, the implicit interest rate is approximately **0.091** or **9.1%** when rounded to three decimal places.

Would you like further explanation or have any questions?

Here are some related questions:
1. How would the interest rate change if the bond's current price was $500?
2. What is the relationship between bond price and interest rate?
3. How does the time to maturity affect the implicit interest rate?
4. Can you explain how to calculate the yield to maturity (YTM) for a bond?
5. What are the differences between a zero-coupon bond and a coupon bond in terms of interest rate?
6. How does market interest rate fluctuation impact the price of zero-coupon bonds?
7. What risks are associated with zero-coupon bonds when interest rates rise?
8. How would inflation impact the real return of this bond?

**Tip:** When calculating interest rates for bonds, remember that a higher bond price generally indicates a lower implicit interest rate, and vice versa.

Learn how to calculate the implicit interest rate in a zero-coupon bond with a $1,000 par value that matures in 9 years. Understand the Present Value formula and its application to determine the interest rate from given bond price data. Suitable for advanced high school students and beyond.

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