00:01
So part of this problem is utilizing compound interest.
00:07
And even though they say t equals 30, and it's compounded monthly, so n equals 12, i'm more concerned about what nt is.
00:17
So 30 times 12 is 360.
00:23
But back to the problem then, i also need the interest rate is 5%, so 0 .05.
00:28
So piecing this together is actually one plus 0 .05 over 12, and it's still 12.
00:39
And what really the theme in this is actually it's a geometric series.
00:46
And the formula of the geometric series is the sum over all 360 terms, 360 deposits, is equal to that first term, which is actually the principal.
00:58
And then one plus, sorry, it's one minus r to the nth power, which is actually nt here, all over one minus r.
01:09
I should probably point out that the r in the problem is actually what i wrote blue here, there and there.
01:17
And i said it, but i just didn't write it.
01:19
It's the principal is 400.
01:20
It's what you deposit each time.
01:23
So the sum after 360 payments looks something like this.
01:28
You might have a different formula, but you should get either the exact same answer or something very similar...