Quote (Taurean @ 17 Sep 2018 18:07)
Oh right. Thanks.
The problem is, when you get interest, you get interest on that sum of money again next time. So it is a cumulative calculation that I don't know how to do. I don't know how often you get interest either. Once a week, month, quarter or year.
Then there's inflation and probably other factors I don't think of.
I assume tax is not relevant with such small sums.
Assuming per month, then let's assume $40 a month with constant interest i (that is, 0.05% interest is i=0.0005). No matter what, you'll be putting 40*12*50=12*2000=24000 on your account.
Assuming you have $40 on month 1, the interest will carry on from month 2 to month 12*50=600, so you get 40*i 599 times (every month except month 1).
Since you put an additional $40 on month 2, you reap the interests associated with them at month 3 until month 600, i.e. 598 times, etc.
At month 599, you reap interests only the 600th month for the additional $40, i.e. one time. The total gain from the interests is then (1+2+3+...+599)*40*i = 1/2*(1+599)*599*40*i = 300*40*599*i =12000*599*i = (7 200 000 - 12 000)*i = 7 188 000 * i
so assuming no mistakes were made, then you'll have in the end, 24 000 + 7 188 000 * i
however this is probably false in practice...