Question

There are zero coupon bonds outstanding that have a YTM of 5.73 percent and mature in 23 years. The bonds have a par value of $10,000. If we assume semiannual compounding, what is the price of the bonds?

Answer 1

To calculate the price of the zero coupon bond with a par value of $10,000, a YTM of 5.73%, and semiannual compounding for a 23-year maturity, the present value formula yields a bond price of $2,030.88.

Step-by-step explanation:

To calculate the price of a zero coupon bond, we need to discount the par value of the bond to the present using the yield to maturity (YTM). The formula to find the present value (PV) of a zero coupon bond is PV = F / (1 + r/n)^(n*t), where F is the par value of the bond, r is the YTM, n is the number of times interest is compounded per year, and t is the number of years until maturity.

Given the par value (F) of $10,000, a YTM (r) of 5.73%, semiannual compounding (n = 2), and a maturity of 23 years (t = 23), the calculation is as follows:

PV = $10,000 / (1 + 0.0573/2)^(2*23)

PV = $10,000 / (1.02865)^(46)

PV = $10,000 / (4.9244)

PV = $2,030.88

The price of the bond is $2,030.88 when assuming semiannual compounding at a YTM of 5.73 percent for a 23-year maturity.

Answer 2

Given

There are zero coupon bonds outstanding that have a YTM of 5.73 %

The bonds have a par value of $10,000

Now , If we assume semiannual compounding, what is the price of the bonds :

P = $10,000 (PVIF 5.73 %,60)

P = $2,143.67