Question

Use the bond term's below to answer the question
Maturity 7 years
Coupon Rate 4%
Face value $1,000
Annual Coupons
YTM 5%

Assuming the YTM remains constant throughout the bond's life, what is percentage capital gains/loss between periods 2 and 3 ?

A. 0.8190%

B. 0.8436%

C. 0.7875%

D. 0.8269%

Answer 1

Coupon = 4% of 1000 = 40

Number of period remaining = 5

Price = Coupon * [1 - 1 / (1 + r)ⁿ] / r + FV / (1 + r)ⁿ

Price = 40 * [1 - 1 / (1 + 0.05)⁵] / 0.05 + 1000 / (1 + 0.05)⁵

Price = 40 * [1 - 0.783526] / 0.05 + 783.526166

Price = 40 * 4.329477 + 783.526166

Price = $956.705233

Number of period remaining = 4

Price = Coupon * [1 - 1 / (1 + r)ⁿ] / r + FV / (1 + r)ⁿ

Price = 40 * [1 - 1 / (1 + 0.05)⁴] / 0.05 + 1000 / (1 + 0.05)⁴

Price = 40 * [1 - 0.822702] / 0.05 + 822.702475

Price = 40 * 3.545951 + 822.702475

Price = $964.540495

Capital gain/loss = [(964.540495 - 956.705233) / 956.705233] * 100

Capital gain/loss = 0.8190%