A zero-coupon bond is a security that pays no interest, and is therefore bought at a substantial discount from its face value. If stated interest rates are 6% annually (with quarterly compounding) how much would you pay today for a zero-coupon bond with a face value of $800 that matures in 10 years?

Please round your answer to the nearest hundredth.

To calculate the present value of a zero-coupon bond, you can use the following formula:

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

Where:
- $ PV $ is the present value of the bond (the amount you would pay today).
- $ FV $ is the face value of the bond ($800 in this case).
- $ r $ is the annual interest rate (6% or 0.06).
- $ n $ is the number of compounding periods per year (4 for quarterly compounding).
- $ t $ is the number of years until maturity (10 years).

Let's plug in the values:

\[
PV = \frac{800}{(1 + \frac{0.06}{4})^{4 \times 10}}
\]

First, calculate the quarterly interest rate:

\[
\frac{0.06}{4} = 0.015
\]

Then, compute the total number of compounding periods:

\[
4 \times 10 = 40
\]

Now, calculate the present value:

\[
PV = \frac{800}{(1 + 0.015)^{40}}
\]

\[
PV = \frac{800}{(1.015)^{40}}
\]

\[
PV = \frac{800}{1.8140184} \approx 440.99
\]

So, you would pay **$440.99** today for a zero-coupon bond with a face value of $800 that matures in 10 years with a 6% interest rate compounded quarterly.

Would you like further details or have any questions?

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**Related Questions:**

1. How does the compounding frequency affect the present value of a bond?
2. What would the present value be if the bond matures in 5 years instead of 10?
3. How does changing the interest rate to 5% affect the price of the bond?
4. What would the present value be if the bond compounded annually instead of quarterly?
5. How do you calculate the yield to maturity for a zero-coupon bond?
6. What is the difference between a zero-coupon bond and a regular coupon bond?
7. How would the bond's present value change if the face value were $1,000 instead of $800?
8. What are the tax implications of investing in zero-coupon bonds?

**Tip:** Always remember to adjust the compounding frequency when calculating present value for bonds with different interest compounding periods.

Learn how to calculate the present value of a zero-coupon bond with a 6% annual interest rate compounded quarterly. Example problem: How much would you pay today for a zero-coupon bond with a face value of $800 that matures in 10 years? Detailed step-by-step solution provided.

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