Two bonds have a coupon rate of 4.25%, semiannual payments, face values of $1,000, and yields to maturity of 5.1%. Bond D matures in 4 years and bond J matures in 8 years. What is the difference in the current prices of these bonds?

Question

Quizplus · Accepted Answer

The correct answer is A because the difference in the current prices of the two bonds is $24.86. This can be calculated using the following formula:Bond Price = (C / r) * [1 - (1 + r)^-n] + (FV / (1 + r)^n)where:C = coupon paymentr = yield to maturityn = number of periods to maturityFV = face valueFor Bond D:C = $1,000 * 4.25% / 2 = $21.25r = 5.1% / 2 = 2.55%n = 4 * 2 = 8FV = $1,000Bond Price = ($21.25 / 2.55%) * [1 - (1 + 2.55%)^-8] + ($1,000 / (1 + 2.55%)^8)= $955.14For Bond J:C = $1,000 * 4.25% / 2 = $21.25r = 5.1% / 2 = 2.55%n = 8 * 2 = 16FV = $1,000Bond Price = ($21.25 / 2.55%) * [1 - (1 + 2.55%)^-16] + ($1,000 / (1 + 2.55%)^16)= $930.28Therefore, the difference in the current prices of the two bonds is $955.14 - $930.28 = $24.86.

Two Bonds Have a Coupon Rate of 4