A ten-year zero coupon bond with a face value of $1,000 is currently quoted at $487.20.Assume the bond's yield to maturity (YTM)remains unchanged throughout the bond's term to maturity.What should the bond be sold for three years from now?

Question

Quizplus · Accepted Answer

Since the bond is a zero coupon bond, its yield to maturity is the same as its discount rate. We can use the following formula to calculate the YTM:

PV = FV / (1 + YTM)^n

Where PV is the present value (quoted price) of the bond, FV is the face value of the bond, YTM is the yield to maturity, and n is the number of years to maturity.

Plugging in the given values, we get:

487.20 = 1000 / (1 + YTM)^10

Solving for YTM, we get:

YTM = 7.2%

Now we need to find the present value of the bond three years from now. Since the bond is still a zero coupon bond, we can use the same formula as before, but with n equal to 7 (the remaining term to maturity):

PV = FV / (1 + YTM)^n

PV = 1000 / (1 + 0.072)^7

PV = 604.55

Therefore, the bond should be sold for $604.55 three years from now. Answer choice C is the only option that matches this value.

A Ten-Year Zero Coupon Bond with a Face Value of $1,000