Confused about the annuity formula?

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Hi I'm trying to understand the formula for calculating the present value of annuity (or perpetuity) but I just can't really visualise where each term has come from. For compound interest with just one original cash payment I understand that: FV = PV (1 + i)^n Where FV is the future value, PV the present value, i the decimal interest rate and n the number of periods over which the interest is compounded. This formula makes good sense to me but when regular reinvestments are made during the time over which the interest is calculated I really struggle. I've read that if we make a regular cash payment of C at every compound period then the present value is: PV = C/(1+i) + C/(1+i)^2 + C/(1+i)^3 + ... For a perpetuity, i.e. the cash payments are unending. I'm probably just being stupid but where does this formula come from? I mean I don't understand why the powers increment as they do. Also if I took that perpetuity and just considered the first two years, so I consider a 2 year annuity, I would have: PV = C/(1+i) + C/(1+i)^2 Wouldn't I? But the present value can't change just because I consider a shorter period of time; the present value is just the money I start with so how can that be altered by shortening the interest period. I think I must be misunderstanding the term 'present value' as well in that case. Can anyone help me?