A zero coupon bond is a bond that is sold now at a discount and will pay its face value at some time in the future when it matureslong dashno interest payments are made.
A zero coupon bond with a face value of ​$17 comma 000 matures in 11 years. What should the bond be sold for now if its rate of return is to be 2.6​% compounded semiannually​?


To calculate the current price of a zero-coupon bond, we use the present value (PV) formula, which discounts the future value (FV) back to the present using the rate of return and the number of periods. For this problem, the formula is:

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

Where:
- $PV$ is the present value (the price the bond should be sold for now),
- $FV = 17,000$ is the face value of the bond,
- $r = 0.026$ (2.6%) is the annual interest rate,
- $n = 2$ is the number of compounding periods per year (semiannual compounding),
- $t = 11$ is the number of years until maturity.

Now, let's calculate the present value.The bond should be sold for approximately **$12,795.02** now if its rate of return is to be 2.6% compounded semiannually.

Would you like more details or have any questions?

Here are 5 related questions you might consider:
1. How does changing the compounding frequency affect the price of a bond?
2. What is the relationship between the bond's price and the interest rate?
3. How is the rate of return on a zero-coupon bond calculated?
4. What are the differences between a zero-coupon bond and a coupon bond?
5. How does the time to maturity impact the price of a zero-coupon bond?

**Tip:** The longer the bond's maturity and the higher the interest rate, the lower the bond's current price will be.

A zero coupon bond with a face value of $17,000 matures in 11 years. What should the bond be sold for now if its rate of return is to be 2.6% compounded semiannually?

Learn how to calculate the present value of a zero coupon bond with a face value of $17,000, maturing in 11 years at a 2.6% rate of return compounded semiannually. This problem involves understanding the present value formula for bonds and compound interest, suitable for advanced high school or college-level students.

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