Q: A 30-year semi-annual coupon bond issued today with market rates at 6.75% pays a 6.75% coupon. If the market yield declines by 30 basis points, the price increases to $1,039.59. If the market yield rises by 30 basis points, the price decreases to $962.77. Which of the following choices is closest to the approximate percentage change in price for a 100 basis point change in the market interest rate?
A: Approximate % change in price =
(price if yield down − price if yield up) / (2 × initial price × yield change expressed as a decimal).
Here , the initial price is par, or $1,000 because we are told the bond was issued today at par. So, the calculation is: (1039.59 − 962.77) / (2 × 1000 × 0.003) = 76.82 / 6.00 = 12.80.
I feel like this is a dumb question, but why are we dividing 76.82 by 6 at the end?