Suppose that you have a liability of $1000 per year in perpetuity and the current interest rate for discounting this perpetuity is 8%. To hedge the value of this perpetuity, you decide to buy a 20-year bond (which also has a discount rate of 8%). How much of a 20-year bond do you need to buy?

I find:

MD20=20/(1+0.08) = 18.5185

Bp= PMT/R = 1000/0.8 = $12,500

Dp= (1+0.08)/0.08= 13.5

MDp=13.5/(1+0.08)=12.408

B20=MDp*Bp/MD20=$8375.408

anything wrong?