term structure of interest rates to calc bond value

Consider a bond that pays an annual coupon of 5 percent and that has three years remaining until maturity. Suppose the term structure of interest rates is flat at 6 percent. How much does the bond price change if the term structure of interest rates shifts down by 1 percent instantaneously.? A) -2.67. B) 2.67. C) 0.00. D) 3.76. I thought this was a duration question and one had to calculate the price increase and decrease resulting from 1% change in interest rate. However Qbank says this value is computed as follows: Bond Price Change = New Price – Old Price = 100 – (5/1.06 + 5/1.062 + 105/1.063) = 2.67. Where in the world does this come from? How would one know the new price is 100?

The new price would be 100 because with a one percent downward shift, the market yield would be 5%, which is the same as your coupon, so the bond would be selling at par.

I think because at interest rates of 5%, the bond is then trading at par (the coupon is 5%). So a shift from 6% to 5% is a shift to par. If it was trading at 6% it would have been trading at a discount prior to the shift.

Thanks for the explanation…it seems obvious now