An annuity is just a stream of payments, like $1000 at the end of every year for 10 years.
The Present Value is the value, found by discounting at some interest rate, at some time before the payments begin.
The Future Value is the accumulated value at some interest rate, at the end of the payments.
You have to be careful when doing the calculations to pay attention to whether the payments are made at the end of the period (that's called, god knows why, an "immediate annuity"), or whether the payments are made at the beginning of the period (called an "annuity due").
Suppose you have a payment of 1 every year for 3 years.
If it's an immediate annuity:
PV = (1+i)^-1 + (1+i)^-2 + (1+i)^-3
since payments are made 1, 2, and 3 years into the future.
And FV = (1+i)^2 + (1+i)^1 + 1
That looks at the situation 3 years later than the PV, and payments were made 2 years ago, 1 year ago, and just now.
If it's an annuity due:
PV = 1 + (1+i)^-1 + (1+i)^-2
FV = (1+i)^3 + (1+i)^2 + (1+i)^1
In both cases, FV = PV times (1+i)^3
That's as simple as I can make it. To work with PV and FV you need to understand those basic concepts completely.
BTW, all the formulas are the sums of a geometric series and so the sums, even for a long annuity, are pretty easy to calculate.
30+ years as an actuary dealing with annuity pricing.
· 7 years ago