3 if you plan to purchase a home and your bank is ready to...

3. If you plan to purchase a home and your bank is ready to offer you a $200,000 mortgage loan for 10 years. The loan bears a compound annual interest rate of 24 percent (6% per quarter) and calls for equal quarterly installment payments at the end of each quarter for the next 10 years. a) What is the amount of the quarterly payment that you have to pay the bank? (6 points) b) Establish loan amortization schedules for the first 4 quarters only? (8 points) c) What is the total amount that will be paid at the end of 10th year?(3 points) d) What is the amount of total interest that will be paid after 10 years?(3 points)

Transcript

00:01 You want to purchase a home with a mortgage or loan amount of $200 ,000.

00:06 You are offered a mortgage with a term of 10 years with quarterly payments and quarterly interest compounding.

00:19 So n is equal to four, four quarters per year.

00:22 Your annual interest rate, r, is 24 percent and that is equal to six percent per quarter.

00:35 So r over n is six percent which is 0 .06.

00:41 And let's see here, we want to know then what the quarterly payment is.

00:48 Well that is going to be the loan amount times r over n divided by one minus one plus r over n to the negative nt.

01:00 That is the formula.

01:01 So we get 200 ,000 times 0 .06 divided by one minus 1 .06 to the negative 40.

01:15 And that then is equal to, let's see here, 200 ,000 times 0 .06 and divided by in parentheses one minus 1 .06 to the negative 40.

01:31 Close your parentheses.

01:34 13292 .31.

01:38 So this is your monthly payment.

01:41 And then for part b, we want to establish a loan amortization schedule for the first four quarters only.

01:51 Well your balance at time zero is the loan amount of 200 ,000.

02:02 So let me line that up properly.

02:06 Okay so we have time, we have our payment, we have our principal, we have our interest, and we have the new balance.

02:27 So we start with a balance of 200 ,000.

02:32 Then our interest for period one is going to be the interest rate of 0 .06 times the balance the time before.

02:46 So that is going to be 0 .06 times 200 ,000.

02:54 12 ,000.

02:59 And our payment was 13 ,292 .31.

03:06 So then your principal will be the payment minus the interest which is 12 ,092 .31.

03:17 And that is the reduction in your balance.

03:21 So this is payment minus the interest and this is the previous balance t minus one minus the principal paid.

03:38 So this then is 198707 .69.

03:47 And then for your second quarter you're again going to have the same payment.

03:54 Your principal now is going to be 0 .06 times this amount.

04:00 So that is 11922 .46...

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