00:01
So in this problem, we're given the pmt formula, which represents how much the payment amount would be.
00:06
Pmt represents the payment amount, which is either yearly or monthly.
00:10
P is how much the loan is.
00:12
R is the interest rate.
00:13
N is the number of payments per year.
00:15
And t is the number of years.
00:17
So in number three, we're told to calculate the monthly payment for a car loan.
00:21
That's $20 ,000, so that would be our p value, over a length of five years, so that's t.
00:28
The interest rate is 7 .9%, and it's going to be compounded yearly.
00:32
So in this case, because it's compounded yearly, n would equal to 1, and therefore we can keep t in terms of years, because it's only going to be paid per year.
00:40
So now we can go ahead and substitute these values into our expression.
00:44
So the payment would equal to p, which is $20 ,000.
00:49
Now the one thing i will do is i'm going to put this over 1, which means p can actually go in our numerator.
00:55
So then i'm going to multiply it by r.
00:57
Now keep in mind, r is given as a percent.
00:59
We have to convert it to a decimal by dividing by 100.
01:02
So i'm going to move the decimal point two places to the left.
01:05
So r that we're putting in our formula will be 0 .079.
01:10
Now it's getting divided by n, which is simply just 1, times 1 plus r, 0 .079, all over n, which is 1.
01:18
And for the exponent, it would be 1 times 5.
01:21
That's our t value.
01:22
For our denominator, we're going to have 1 plus r, 0 .079, divided by n, which is 1, all raised to the 1 times 5 power, and then minus 1.
01:33
Now, because many of our denominators is equal to 1, we can go ahead and simplify to start with.
01:38
So our numerator would just be 20 ,000 times 0 .079, times 1 plus 0 .079 to the 5th power, all getting divided by 1 plus 0 .079 to the 5th power, minus 1.
01:56
So now we can go ahead and punch this into our calculator...