Here is the original problem and an answer I got by one of the other tutors. Why is this the best formula to use for this problem??

A recent college graduate has taken a new job at Work LLC, and since the company does not offer a traditional pension plan, she plans to take advantage of a tax-free investment account backed by a reputable financial institution that offers a guaranteed 8% annual return for as long as she lives. The graduate plans on working for 45 years before retiring and will save a fixed amount each year until retirement, starting at the end of this year and continuing for all 45 years of work. Once she is retired, she expects to be able to live on the equivalent of $30,000/year in today's terms in addition to expected social security payments. She expects annual inflation to be 4% per year over her life. She doesn't know how long she will live, but knows that with medical advancements, it could be for a very long time. Since one of her great fears is that she will outlive her savings, she plans to arrange retirement funding that will be in place if she were to live "forever" with the understanding that her heirs will inherit the remainder when she dies. If she wants to save a fixed amount each year, starting with one year from now until her 45th work anniversary, how much does she need to save each year?

PV = 30,000 / (0.08 + 0.04) = 250,000

PV above will be the value at 45th year, so this will become FV in calculating the annual savings.

PMT = FV / [((1+rate)n - 1 ) / rate]

PMT = 250,000 / [((1+0.08)45 - 1) / 0.08]

PMT = $646.80 per year

Why is this formula correct? I was using NPV and my calculator but I was told that was incorrect.