To calculate the dollar price of a zero-coupon bond, we use the following formula:

$P = \frac{F}{(1 + r)^n}$

Where:

• $P$ = Present value (the price of the bond)
• $F$ = Face value (par value) of the bond
• $r$ = Yield per period (YTM divided by number of compounding periods per year)
• $n$ = Total number of periods (years to maturity multiplied by compounding periods per year)

Given:

• Par value $F = 10,000$
• Yield to maturity (YTM) $= 4.7\%$ per year
• Semiannual compounding: 2 periods per year
• Years to maturity $= 19$

Step-by-step:

1. Calculate the yield per period: $r = \frac{4.7\%}{2} = \frac{0.047}{2} = 0.0235$

2. Calculate the total number of periods: $n = 19 \times 2 = 38$

3. Calculate the price of the bond: $P = \frac{10,000}{(1 + 0.0235)^{38}}$ $P = \frac{10,000}{(1.0235)^{38}}$ $P \approx \frac{10,000}{2.4137} = 4143.48$

Thus, the price of the bond is approximately $4,143.48.

Would you like further explanation on any step, or more details?

Here are five related questions:

1. How would the price change if the yield to maturity were higher?
2. What if the bond compounded annually instead of semiannually?
3. How do you calculate the price for a bond with coupon payments?
4. What is the effect of a shorter time to maturity on bond price?
5. How can you calculate the effective yield for this bond?

Tip: The longer the time to maturity or the higher the yield, the lower the price of a zero-coupon bond.