00:01
All right, so for this problem, we'll first consider that the total amount repaid s is going to be equal to the sum of the amounts repaid for each period.
00:14
So we know that the amount repay, or let's say that m is going to be the individual monthly repayment amount.
00:21
We'd have that the total repayment value would be m divided by 1 plus the interest rate to the power of 1 over 1 over 1 .5 .5.
00:31
12 plus m over 1 plus the interest rate to the power of 2 over 12 plus m over 1 plus the interest rate to power of 3 over 12 and so on we know that the total number of periods is going to be or the total number of months would be the 12 months per year times 12 the number of years so we'd have 144 periods overall.
01:05
So the last term would be m over 1 plus i to the power of 144 over 12.
01:12
Now what we can do here is first factor out that m value and write this as m times 1 over 1 plus i power of 1 over 12 plus 1 over 1 plus i to the power of 2 over 12 and so on which we should be able to recognize as a geometric series.
01:38
We're taking the sum from j equals 1 up to 144 of 1 over 1 plus i to the power of j over j over 12.
01:53
So using the rules for a geometric series we then have that the s is going to be equal to m over 1 .1, the power of 1 over 12, times 1 minus 1 over 1 .1 to the power of 144 over 12, divided by 1 minus 1 over 1 .1, the power of 1 over 12.
02:27
Let me just double check the values.
02:29
Yes, so i'm using 0 .1 as i, because of the fact that we have 10 % interest.
02:37
And then we have the over 2%.
02:39
12 because we have that the interest is compounded annually...