Q:

What exactly is the meaning of future value/present value of an annuity?

We've been dealing with the idea of annuities in a math course I'm taking, and the idea of "present value" and "future value" have come up. So basically, the "value" of an annuity before someone makes any payments is a certain value (why?) and after is another value (obviously because they've been depositing money and that money has been collecting interest as well). So I'm wonder why an annuity account has value before any payments have been made, and what is a way to calculate this? I used the formula R(1-(1+i)^-n)/i, but I'm not sure if this works.
Thank you!

A:

One way to look at it is this: 
Present value: If I were to purchase the annuity today, and take into account all of the future payments and interest, what would I pay? A dollar today is worth what with respect to the value of future payments?  
The account has value today because of the expected payments and expected interest rate.
Future Value: Say I'm making regular payments into a fund over the next 10 years. How much will I have in 10 years? Present Value (again): How much do you need today to be equally well off in 10 years if you don't make any payments?

