Everyone is kinda right.
For an annuity, the PRESENT VALUE is the amount you need to invest NOW AS A SINGLE LUMP SUM to reach a certain goal in the future.
The formula with the A in it is used if you know what that financial goal is. A is the "future value". For example, how much would I need to invest NOW AS A SINGLE LUMP SUM to reach get $30000 in three years. It's actually just the compound interest formula with the subject changed.
The formula with the M in it is more complicated and is used for a more complicated situation, where you know what the equivalent monthly payment is, and you don't necessarily need to know that final goal. The M is the "monthly payment". For example, how much would I need to invest NOW AS A SINGLE LUMP SUM to reach the SAME goal as I would if I invested $30 per month for 3 years.