00:01
We have a loan amount of $18 ,000.
00:05
We have a term of 10 years.
00:15
And we have quarterly payments of $629 .50.
00:26
Our interest rate is 7 % compounded quarterly.
00:31
So our interest rate per quarter is 0 .07 divided by 4.
00:51
And our number of quarters is nt, which is 40 because our n is 4.
01:03
So if we want to make any kind of calculations, let's see here, 0 .07 divided by 4 equals, our r is going to be 0 .0175 per quarter.
01:24
This is r over n.
01:26
Okay, and now we want to know what the unpaid balance is immediately after the six payments.
01:36
Okay, loan balance after sixth payment.
01:48
Well, the sum of the payments that we make accumulates according to the formula the sum at time t is equal to the periodic payment times 1 plus r over n to the nt minus 1 divided by r over n.
02:12
So if we want the sum after the sixth payment, well, that is going to be the sum, we're making quarterly payments, so that will be after t is the number of years.
02:36
So six payments, when we have quarters, is 1 .5 years.
02:45
So this will be the sum after 1 .5 years.
02:55
And then this is our payment amount, 629 .5 times 1 .0175...