00:01
Hi there, so for this problem, we are given that the james wants to take out a load, and this is going to be for to make monthly payments of $300.
00:18
So that is the ballot that we're going to set to capital b.
00:25
Then the other information that we are given is that this needs to be paid.
00:35
Exactly at 20 years.
00:38
So that will give us, so that will be 20 right there.
00:45
And then, and so the question is, what is the maximum amount that james can afford to borrow? and this with a rate of 8 % compounded monthly.
00:56
So to solve this problem, we are going to use the following formula to find the payment per period of a loan of amount a.
01:06
So that will be that the pavement p is equal to a, this times the rate art, this divided by 1 minus 1 plus the rate art, this elevated to minus n.
01:28
So in here, p is the monthly pavement that we are given, 300, to be made to repeat alone of an amount.
01:37
So what we need to determine in this case is the amount a at a rate period of r and n is the number of payments so the number of payments remember that we have 12 months in one year so that will be since we need to pay this monthly that will be 12 times 20 so that will be 240 so once we know that we substitute the values in here well, we can solve for a quite easy.
02:12
So that will be p times 1 minus 1 plus the rate r, this 2 elevated to minus n, then this divided by the rate art.
02:28
Now, to obtain the rate r, that will be the value that we are given, which is the annual rate of 8%...