I apologize in advance if this reveals my shocking lack of mathematical knowledge!

My husband and I are both public school teachers who plan to retire in our early 50's. At this point, our plans are vague because we each have about 10-15 years to go, and a lot could change between now and then.

The general plan is this: We teach until we have 25-30 years of service credit in our pension system. At that point, we'll be between ages 48 and 56. In order to maximize the pension benefit, we'll hold off on starting the pension payments until we each reach age 60-63. (This is allowed; I checked.) We will use our own savings to support ourselves in the gap years between when we stop working and when we start pulling from the pension system. At that point, the pension payments will fully cover our expenses (with room to spare), so we won't *need* to have our own money left over, but obviously, we would like to keep a generous cushion for anything that might arise.

So, is there an online tool or calculator that will help me figure out roughly how much we need to save for those gap years? Suppose it's 10 years. At first I just multiplied our annual expenses by 10, which yielded a pretty large number. (Duh.) But then I realized that, in year 1, we would take out 1 year's worth of expenses, while the remainder of the stash continues to grow, so it's not just a matter of straight multiplication.

Suggestions?

Thank you!