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This problem is on Calculation of monthly mortgage payment. Suppose a loan of A dollars is amortized over n years at an annual interest rate r compounded monthly. Let i =r/12, be the equivalent monthly rate of interest. the equivalent monthly rate of interest. Then the monthly payments will be M dollars, where M(A, n, i) = Ai / (1-(1+i)^-12n) (a) Allison has a home mortgage of $250,000 at the fixed rate of 5.2% per year for 15 years. What are her monthly payments? How much total interest does she pay for the loan. (b) Nathan also has a mortgage of $250,000 but at the fixed rate of 5.6% per year for 30 years. What are his monthly payments? How much total interest does he pay for the loan?

          This problem is on Calculation of monthly mortgage payment.

Suppose a loan of A dollars is amortized over n years at an annual

interest rate r compounded monthly. Let i =r/12, be the equivalent monthly rate of interest.

the equivalent monthly rate of interest. Then the monthly payments will be M dollars, where

M(A, n, i) = Ai / (1-(1+i)^-12n)

(a) Allison has a home mortgage of $250,000 at the fixed rate of 5.2% per year for 15 years. What are her monthly payments? How much total interest does she pay for the loan.

(b) Nathan also has a mortgage of $250,000 but at the fixed rate of 5.6% per year for 30 years. What are his monthly payments? How much total interest does he pay for the loan?
        
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This problem is on Calculation of monthly mortgage payment.

Suppose a loan of A dollars is amortized over n years at an annual

interest rate r compounded monthly. Let i =r/12, be the equivalent monthly rate of interest.

the equivalent monthly rate of interest. Then the monthly payments will be M dollars, where

M(A, n, i) = Ai / (1-(1+i)^-12n)

(a) Allison has a home mortgage of 250,000 at the fixed rate of 5.2% per year for 15 years. What are her monthly payments? How much total interest does she pay for the loan.

(b) Nathan also has a mortgage of250,000 but at the fixed rate of 5.6% per year for 30 years. What are his monthly payments? How much total interest does he pay for the loan?

Added by Christopher M.

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Calculus: Early Transcendentals
Calculus: Early Transcendentals
James Stewart 8th Edition
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This problem is on Calculation of monthly mortgage payment. Suppose a loan of A dollars is amortized over n years at an annual interest rate r compounded monthly. Let i =r/12, be the equivalent monthly rate of interest. Then the monthly payments will be M dollars, where M(A, n, i) = Ai / (1 - (1+i)^-12n). (a) Allison has a home mortgage of $250,000 at the fixed rate of 5.2% per year for 15 years. What are her monthly payments? How much total interest does she pay for the loan? (b) Nathan also has a mortgage of $250,000 but at the fixed rate of 5.6% per year for 30 years. What are his monthly payments? How much total interest does he pay for the loan?
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Transcript

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00:01 To give us a formula for monthly payments and dollars that depends upon the amount of your loan, which is a, your interest rate, which is i, and i in this case is going to be the same as r over 12, and then n would be the number of payments that you're going to make.
00:21 So n is going to be the number of payments.
00:29 I'm sorry, it's going to be the number of years in this case, number of years.
00:33 I had to go back and reread.
00:34 I just did a different problem.
00:35 So n is a number of years.
00:37 So we're going to come up here and look at allison, and we're going to say her monthly payment, i'm going to put m, it's going to be $250 ,000 for her month for the financing at a rate of 5 .2 % per year.
00:50 So we're going to put 0 .052 over 12, and then we're going to put that as 1 minus 1 plus .052 over 12 to the negative 12, and she's going to do this for 15 years.
01:05 And then we're going to do the same thing for nathan.
01:08 We'll go to our calculator in a minute.
01:10 And he's going to get $250 ,000, the same amount.
01:14 He's going to have 5 .6%.
01:17 So we're going to put 056 over 12, and then we'll go 1 minus 1 plus 0 .056 over 12 to the negative 12.
01:27 And he's going to do this for 30 years.
01:30 So let's see what their monthly payments are going to be.
01:32 And then they want to know how much interest they're going to pay.
01:35 So let's go to our calculator real quick, and i'm going to go $250 ,000.
01:39 I'm bad about that.
01:41 Okay.
01:43 Parentheses, 0 .052 divided by 12.
01:47 And then i'm going to divide that by, and i'm going to open another parenthesis for the denominator.
01:53 1 minus, parentheses, 1 plus .052 divided by 12.
01:59 And i'm going to raise that to parentheses, negative 12 times 15...
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