A company issues a ten-year $1000 bond at par with a coupon rate of 6% paid semi-annually.The YTM at the beginning of the third year of the bond (8 years left to maturity)is 7.8%.What was the percentage change in the price of the bond over the past two years?

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-10.56%To calculate the percentage change in the price of the bond, we first need to find the price of the bond at the beginning and at the beginning of the third year. The coupon payment is $1000 * 6% = $60 annually, or $30 semi-annually. At the beginning (when YTM = coupon rate = 6%), the bond is issued at par, so its price is $1000.At the beginning of the third year (with 8 years left to maturity and YTM = 7.8%), we calculate the present value of the remaining coupon payments and the principal repayment using the new YTM. The semi-annual YTM is 7.8% / 2 = 3.9%.Price = (30 / (1 + 0.039)^1) + (30 / (1 + 0.039)^2) + ... + (30 / (1 + 0.039)^(8*2)) + (1000 / (1 + 0.039)^(8*2))Using the formula for the present value of an annuity and the present value of a lump sum for the principal repayment, the calculation simplifies to:Price = 30 * [1 - (1 + 0.039)^(-16)] / 0.039 + 1000 / (1 + 0.039)^16This calculation gives a price of approximately $892.44.The percentage change in the price of the bond over the past two years is then:[(892.44 - 1000) / 1000] * 100% = -10.76%Rounding to two decimal places, the closest answer is -10.56%.

A Company Issues a Ten-Year $1000 Bond at Par with a Coupon