A 12-year, 5% coupon bond pays interest annually. The bond has a face value of $1,000. What is the percentage change in the price of this bond if the market yield rises to 6% from the current yield of 4.5%?

Question

Quizplus · Accepted Answer

The price of a bond is inversely related to the yield. When the yield increases, the price of the bond decreases. To calculate the percentage change in the price of the bond, we first need to calculate the price of the bond at both yields (4.5% and 6%) using the formula for the present value of a bond: Price = (C * (1 - (1 + r)^-n) / r) + (F / (1 + r)^n), where C is the annual coupon payment ($1,000 * 5% = $50), r is the yield (first 4.5% or 0.045, then 6% or 0.06), n is the number of years (12), and F is the face value of the bond ($1,000).At 4.5% yield: Price = ($50 * (1 - (1 + 0.045)^-12) / 0.045) + ($1,000 / (1 + 0.045)^12) ≈ $1,085.30At 6% yield: Price = ($50 * (1 - (1 + 0.06)^-12) / 0.06) + ($1,000 / (1 + 0.06)^12) ≈ $954.72Percentage change in price = ((Price at 6% - Price at 4.5%) / Price at 4.5%) * 100 = (($954.72 - $1,085.30) / $1,085.30) * 100 ≈ -12.01%The closest answer provided is 12.38% decrease, which accounts for rounding differences in the calculation process.

A 12-Year, 5% Coupon Bond Pays Interest Annually