What is the logic of perpetuities present value calculation?

So you can see how much money you have!!. Suppose somebody leaves you an inheritance, and they stipulate that you should recieve an annual payment of $100,000 for your natural life. Now, you don't really know how much money you have. But, if you can find out what interest rate you get on your Trust Fund, then you can easily figure out how much money you have. So, if you knew you were getting 6% annual interest on your Fund, then you would divide your $100,000 by 6% =100,000 / .06 =$1,666,667.00.

That would be the PV of your Perpetual Annuity.

You use present value if you are going to get a set regular value for a period of time and at the end you will have nothing left.

The present value is how much money initial money is needed if you are going to get this regular payment, it takes into account that you are going to be getting interest along the way.

So you use present value if you have 0 left at the end

and 

you use future value if you have 0 at the beginning

A PERPETUITY is an annuity that has no end, or a stream of cash payments that continues forever.