00:01
So we have a mortgage or a loan amount of $325 ,000 with an interest rate of 4 .2 % compounded monthly, so n is 12, and a term of 30 years.
00:17
Then our monthly interest rate is going to be 0 .042 divided by 12, which is 0 .0035, and the number of payments is going to be n times t, which is 360.
00:40
So our monthly payment is going to be the loan amount times r over n divided by 1 minus 1 plus r over n to the negative nt, which is 325 ,000 times 0 .0035 divided by 1 minus 1 .0035 to the negative 360, which is equal to $1 ,589 .31.
01:27
And then the interest in the first payment is going to be the outstanding balance, which is, of course, 325 ,000 times our monthly interest rate, 0 .035.
01:49
So that then is 325 ,000 times 0 .0035, 1137 .5.
02:03
That means that the principal in the first payment is going to be the payment amount minus the interest in that first payment, which is going to be 1589 .31 minus 1137 .5.
02:26
So that is equal to $451 .81.
02:35
And then for b, if we want the amount of the 181st month's payment, well, let's first calculate the balance after 180 payments.
02:52
That is going to be the loan amount times 1 plus r over n to the 180 minus what we have paid off, which is the payment amount times 1 plus r over n to the 180 minus 1 divided by r over n...