Quote (Hanako @ Sep 17 2018 06:33pm)
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...
here you calculated the interests on the money that was banked, but you forgot the interests on the interests themselves.
for example in month 2, in your model there is $40+$40 in the bank which makes 80i of interests, but really there's $40*(1+i)+$40 which makes 80i+40i^2
24k+7188k * i is 60k, the result I find is 150k
here's the script I ran (save as somename.html and open with your browser):
<html><script>
increment=40;
interest=0.005;
cycles=12*50;
bank=0;
for (m=0; m<cycles; m++){
bank=bank+increment;
bank=bank+interest*bank;
}
document.write(Math.floor(bank));
</script></html>
This post was edited by lilith0 on Oct 28 2018 05:02pm