Is there a particular forumla or calculator for incremental growth over a number of time(s)?

It's basically an arithmetic sequence and there are formulas for that.

An arithmetic sequence has a starting value which is 8 in your case:
a = 8

And it has a common difference between terms. In your case you add 2 each time.
d = 2

Let n be the count of which 180 period you are in.
n = 1 represents the first period ($8)
n = 2 represents the second period ($10)
etc.

The formula for how much you are saving for period 'n' is:
a[n] = a + d(n - 1)

For example:
a[1] = 8 + 2(1 - 1) = 8 + 2*0 = 8
a[2] = 8 + 2(2 - 1) = 8 + 2*1 = 10
a[3] = 8 + 2(3 - 1) = 8 + 2*2 = 12
etc.

Next, if you wanted the sum of the contributions for all those periods:
S[n] = (a + a[n]) * n/2

So for 1 period:
S[1] = (8 + 8) * 1/2 = 16/2 = 8
S[2] = (8 + 10) * 2/2 = 18 * 1 = 18
S[3] = (8 + 12) * 3/2 = 20 * 3/2 = 30
etc.

The only issue is that's assuming each period counts as 1, but in your case, you are contributing for 180 days. So multiply that by 180.

We can put that all together into the following formula:
T[n] = 90 * (2a + d(n - 1)) * n

We can simplify that further by plugging in your values of a and d.
T[n] = 90 * (16 + 2(n - 1)) * n
T[n] = 90 * (16 + 2n - 2) * n
T[n] = 90 * (14 + 2n) * n
T[n] = 180 * (n + 7) * n

So after 1 period, you would have:
T[1] = 180 * 8 * 1
= 1440

And after 2 periods, you would have:
T[2] = 180 * 9 * 2
= 180 * 18
= 3240

And after 3 periods, you would have:
T[3] = 180 * 10 * 3
= 180 * 30
= 5400

Make sense?

180(8+10+12+14+16)= $10,800