00:01
Being told that maggie invests 150 pounds every month for six years at a 6 % interest rate.
00:09
So i've drawn a little timeline here.
00:15
If she deposited $150 now at time zero or month zero, then same thing would happen next month after one month, $150, after two months and so on.
00:28
And we're doing this for a full six years.
00:31
So if you multiply six by 12 months, that'll be 72 payments altogether.
00:38
So because we started at zero, our last payment is going to be at month 71.
00:46
So now notice that each of these deposits is going to earn a different amount of interest because this first one is going to earn the full 72 months of interest, whereas this last one is only going to earn one month of interest.
01:08
So what we need to do is model what the rates are going to look like.
01:14
So the first one would be 150 times r to the 72.
01:23
Whatever the rate is, the power of 72.
01:27
Plus the next one would be 150 r to the power of 71 plus 150 r to the 70 and then all the way at the end we have 150 r to the power of 1 and recognize here that we can take out 150 r as a common factor then we're left with r to 71 plus r70 plus r 69 plus r to the power of zero or we can just call it one.
02:12
So what we have, 150r, this is a geometric sequence or geometric series with first term.
02:25
It's actually easier if we do this in the reverse order.
02:28
So i'm going to rewrite this, 1 plus r plus r squared plus dot dot dot plus r 71.
02:37
So now we can see that our first term is 1 and the common ratio is r.
02:43
It would have worked the other way, but i want to avoid the exponent work...