Andrew buys a zero coupon bond with par value of $1,000, yield to maturity of 8%, and maturity of 16 years. How much money does he make if he holds it to maturity? Assume annual compounding.

A zero-coupon bond doesn't pay periodic interest, but instead is sold at a discount and grows to its face value (or par value) at maturity. The amount Andrew pays initially for this bond can be calculated using the present value formula:

\[
\text{Price} = \frac{\text{Par Value}}{(1 + \text{Yield})^{\text{Years}}}
\]

### Given Information:
- Par Value = $1,000
- Yield to Maturity = 8% (0.08 as a decimal)
- Maturity = 16 years

### Calculation:
\[
\text{Price} = \frac{1,000}{(1 + 0.08)^{16}}
\]
\[
\text{Price} = \frac{1,000}{(1.08)^{16}}
\]
Calculating $ (1.08)^{16} $:
\[
(1.08)^{16} \approx 3.5184
\]
\[
\text{Price} \approx \frac{1,000}{3.5184} \approx 284.26
\]

So, Andrew pays approximately $284.26 for the bond.

### Money Made at Maturity:
At maturity, the bond reaches its par value of $1,000, so the profit Andrew makes is:

\[
\text{Profit} = \text{Par Value} - \text{Purchase Price}
\]
\[
\text{Profit} = 1,000 - 284.26 = 715.74
\]

### Answer:
Andrew makes approximately **$715.74** if he holds the bond to maturity.

Would you like more details or have any questions?

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Here are some related questions to deepen your understanding:
1. What would happen to Andrew's profit if the yield to maturity was higher?
2. How does compounding frequency affect the price of a zero-coupon bond?
3. What is the difference in profit if the maturity period is reduced?
4. How would semi-annual compounding change the initial purchase price?
5. What are the risks associated with zero-coupon bonds for investors?

**Tip:** A higher yield decreases the bond's initial purchase price, increasing the potential profit at maturity.

Learn how to calculate the profit on a zero-coupon bond with a par value of $1,000, an 8% yield to maturity, and a 16-year maturity period using the present value formula. This guide covers core finance concepts like yield to maturity, exponential growth, and the compound interest formula. Suitable for high school students in Grades 11-12.

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