Price and modified duration of consol bond carrying a yield of 0%

[DexterOnline]

Odd has assigned me to find price and modified duration of a perpetual bond that pays an amount of 1 dollar at the end of each year forever and has a yield to maturity of 0%

I have successfully derived a new pricing formula that resulted in determining the price of the consol bond and its modified duration

a) Finding the price of the bond [V] was akin to finding the result for 1/0 (Division by zero)

b) Finding the modified duration was akin to finding 1st order derivative of 1/i and dividing it by price of the consol bond = -[dV/di]*[1/V] = -[(-1)/(0)^2] / [1/0]

Anyone here has a different view than mine, please let me know

 

[DexterOnline]

Question:
I will take from you a -$1000 bond with annual coupons at 10%;
will you issue me one?

Do you know the formula for Discounted Dollar at an interest rate of i% for 1 period (usually a year) and don't give me the norm bull$hit formula as follows

x = 1+i

D_d = 1/x