Question

You buy a zero coupon bond at the beginning of the year that has a face value of $1,000, a YTM of 10 percent, and 22 years to maturity. You hold the bond for the entire year. Assume semiannual compounding. How much interest income will you have to declare on your tax return? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

Purchase Price(P0) = Face Value / (1 + r)ⁿ

= $1,000 / [1 + (0.10/2)]^(22*2)

= $1,000 / 8.5572 = $116.86

Price in 1 year(P1) = Face Value / (1 + r)ⁿ

= $1,000 / [1 + (0.10/2)]^(21*2)

= $1,000 / 7.7616 = $128.84

So, the implied interest, which will be taxable as interest income, is:

Implied Interest = P1 - P0

= $128.84 - $116.86 = $11.98