Question

Use the bond term's below to answer the question
Maturity 6 years
Coupon Rate 4%
Face value $1,000
Annual Coupons
Market Interest Rate 6%

Assuming the YTM remains constant throughout the bond's life, what is percentage capital gains/loss between periods 3 and 4 ?

Group of answer choices

1.71%

1.86%

1.77%

1.83%

Answer 1

Annual coupon = 4% of 1000 = 40

Price in year 3 = Coupon * [1 - 1 / (1 + r)^n] / r + FV / (1 + r)^n

Price in year 3 = 40 * [1 - 1 / (1 + 0.06)^3] / 0.06 + 1000 / (1 + 0.06)^3

Price in year 3 = 40 * [1 - 0.839619] / 0.06 + 839.619283

Price in year 3 = 40 * 2.673012 + 839.619283

Price in year 3 = $946.5398

Price in year 4 = Coupon * [1 - 1 / (1 + r)^n] / r + FV / (1 + r)^n

Price in year 4 = 40 * [1 - 1 / (1 + 0.06)^2] / 0.06 + 1000 / (1 + 0.06)^2

Price in year 4 = 40 * [1 - 0.889996] / 0.06 + 889.99644

Price in year 4 = 40 * 1.833393 + 889.99644

Price in year 4 = $963.33215

percentage capital gains/loss = [(963.33215 - 946.5398) / 946.5398] * 100

percentage capital gains/loss = 1.77%