A 15-year zero coupon bond has a yield to maturity of 8 percent and a maturity value of $1,000.What is the amount of tax that an investor in the 30 percent tax bracket would pay during the first year of owning the bond?
A) $7.57
B) $10.41
C) $15.89
D) $20.44
E) $25.22

Question

Quizplus · Accepted Answer

The tax is calculated on the imputed interest, which is the interest that would have been paid during the first year if the bond had paid interest annually. The present value of the bond is calculated using the formula PV = FV / (1 + r)^n, where PV is the present value, FV is the future value ($1,000), r is the yield to maturity (0.08), and n is the number of years (15). This gives PV = $1,000 / (1.08)^15 = $315.24. The interest for the first year is the difference between the present value after one year and the initial present value. After one year, the present value is $315.24 * 1.08 = $340.46. The interest earned in the first year is $340.46 - $315.24 = $25.22. The tax owed on this interest for someone in the 30% tax bracket is $25.22 * 0.30 = $7.57.

A 15-Year Zero Coupon Bond Has a Yield to Maturity