# duration problem

Here is a problem from QBank: A \$1,000.00 face value, 15-year semi-annual coupon bond pays a 7.25 percent coupon. The current market price is \$1,046.71 at market rates of 6.75 percent. If the market yield declines by 75 basis points, the price increases to \$1,122.50. If the market yield rises by 75 basis points, the price decreases to \$977.71. 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? Can someone solve this?

The first part “A \$1,000.00 face value, 15-year semi-annual coupon bond pays a 7.25 percent coupon. The current market price is \$1,046.71 at market rates of 6.75 percent” is just enabling you to get to the current price of the Bond and duration = (P_ - P+) / (2 * P * delta r) (1122.5 - 977.71) / (2 * 1046.71 * .0075) = 9.22

I thought the formula was Duration = percentage change in bond price / yield change in percent Why didn’t you use percent changes? What am I missing here?

Looks like there might be a couple of different ways of getting duration. cpk is (correctly) figuring out something like “effective duration”. So from cpk’s answer can you complete the problem when you combine it with your formula for duration?