Question

Peter buys ten zero-coupon bonds with a maturity of 30 years for a total of $4,119.87. Assume he buys the bonds on June 30th. How much interest will he have to report for tax purposes for the first year? Assume annual compounding for simplicity.

		a. $0 because it is a zero-coupon bond.
		b. $61.80.
		c. $123.60.
		d. $300.00.

Answer 1

For zero-coupon bonds there is no annual interest but annual price appreciation is considered for tax purposes.

Present value of a bond = $ 4,119.87/10 = $ 411.987

Future value of bond on maturity = $ 1,000

Number of years to maturity, n = 30

Rate of interest = (FV/PV)^1/n – 1

                         = ($ 1,000/$ 411.987) ^1/30 – 1

                         = (2.42726105435366)^{0.03333333333} – 1

                         = 1.02999997995598 – 1

                         = 0.02999997995598 or 3 %

Price of a bond after one year = $ 411.987 x 1.03 = $ 424.34661

Price of 10 bond after one year = $ 424.34661 x 10 = $ 4,243.4661

Interest for tax purpose = $ 4,243.4661 - $ 4,119.87

                                      = $ 123.5961

Semi-annual Interest (from 1^st July to Dec 31) = $ 123.5961/2 = $ 61.79805 or $ 61.80

Hence option “b. $ 61.80” is correct answer.