Question

You find a zero coupon bond with a par value of $10,000 and 12 years to maturity. The yield to maturity on this bond is 4.9 percent. Assume semiannual compounding periods. What is the dollar price of the bond?(Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

To calculate the price of a zero coupon bond, you can use the present value formula.

Step-by-step explanation:

To calculate the price of a zero coupon bond, you can use the present value formula. The formula for calculating present value is: PV = FV / (1 + r/n)^(n*t), where PV is the present value, FV is the future value or par value of the bond, r is the yield to maturity, n is the number of compounding periods per year, and t is the number of years to maturity. In this case, the par value is $10,000, the yield to maturity is 4.9%, and there are 12 years to maturity with semiannual compounding periods.

Using the formula, the present value of the bond is calculated as: PV = 10000 / (1 + 0.049/2)^(2*12) = $5698.89

Therefore, the dollar price of the bond is $5698.89 (rounded to 2 decimal places).

Answer 2

The dollar price of the zero coupon bond is approximately $5,298.75.

To calculate the dollar price of the zero coupon bond, we need to use the formula for the present value of a bond.

The formula is:

Price = Face Value / (1 + Yield/2)^(2 * Number of Periods)\\

In this case, the face value is $10,000, the yield to maturity is 4.9%, and there are 12 years to maturity with semiannual compounding.

First, let's convert the yield to a decimal by dividing it by 100:
4.9% / 100 = 0.049

Next, we need to calculate the number of periods. Since the bond compounds semiannually, there will be 2 * 12 = 24 periods.

Now we can substitute these values into the formula and calculate the price:

Price = $10,000 / (1 + 0.049/2)^(2 * 12)
= $10,000 / (1 + 0.0245)^(24)
= $10,000 / (1.0245)^(24)
≈ $5,298.75 (rounded to 2 decimal places)