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39. Suppose Ms. Lee is buying a new house and must borrow $150,000. She wants a 30-ycar mortgage and she has two choices. She can either borrow money at 7% per year with no points, or she can borrow the money at 6.5% per year with a charge of 3 points. (A "point" is a fee of 1% of the loan amount that the borrower pays the lender at the beginning of the loan. For example, a mortgage with 3 points requires Ms. Lee to pay $4,500 extra to get the loan.) As an approximation, we assume that interest is compounded and payments are made continuously. Let M(t) = amount owed at time t (measured in years), r = annual interest rate, and p = annual payment. Then the model for the amount owed is dM = rM – p. dt (a) How much does Ms. Lee pay in each case? (b) Which is a better deal over the entire time of the loan (assuming Ms. Lee does not invest the money she would have paid in points)? (c) If Ms. Lee can invest the $4,500 she would have paid in points for the second mortgage at 5% compounded continuously, which is the better deal?

39. Suppose Ms. Lee is buying a new house and must borrow $150,000. She wants a 30-ycar mortgage and she has two choices. She can either borrow money at 7% per year with no points, or she can borrow the money at 6.5% per year with a charge of 3 points. (A "point" is a fee of 1% of the loan amount that the borrower pays the lender at the beginning of the loan. For example, a mortgage with 3 points requires Ms. Lee to pay $4,500 extra to get the loan.) As an approximation, we assume that interest is compounded and payments are made continuously. Let M(t) = amount owed at time t (measured in years), r = annual interest rate, and p = annual payment. Then the model for the amount owed is dM = rM – p. dt (a) How much does Ms. Lee pay in each case? (b) Which is a better deal over the entire time of the loan (assuming Ms. Lee does not invest the money she would have paid in points)? (c) If Ms. Lee can invest the $4,500 she would have paid in points for the second mortgage at 5% compounded continuously, which is the better deal?

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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39. Suppose Ms. Lee is buying a new house and must borrow $150,000. She wants a 30-ycar mortgage and she has two choices. She can either borrow money at 7% per year with no points, or she can borrow the money at 6.5% per year with a charge of 3 points. (A "point" is a fee of 1% of the loan amount that the borrower pays the lender at the beginning of the loan. For example, a mortgage with 3 points requires Ms. Lee to pay $4,500 extra to get the loan.) As an approximation, we assume that interest is compounded and payments are made continuously. Let M(t) = amount owed at time t (measured in years), r = annual interest rate, and p = annual payment. Then the model for the amount owed is dM = rM – p. dt (a) How much does Ms. Lee pay in each case? (b) Which is a better deal over the entire time of the loan (assuming Ms. Lee does not invest the money she would have paid in points)? (c) If Ms. Lee can invest the $4,500 she would have paid in points for the second mortgage at 5% compounded continuously, which is the better deal?
Transcribed Image Text:39. Suppose Ms. Lee is buying a new house and must borrow $150,000. She wants a 30-ycar mortgage and she has two choices. She can either borrow money at 7% per year with no points, or she can borrow the money at 6.5% per year with a charge of 3 points. (A "point" is a fee of 1% of the loan amount that the borrower pays the lender at the beginning of the loan. For example, a mortgage with 3 points requires Ms. Lee to pay $4,500 extra to get the loan.) As an approximation, we assume that interest is compounded and payments are made continuously. Let M(t) = amount owed at time t (measured in years), r = annual interest rate, and p = annual payment. Then the model for the amount owed is dM = rM – p. dt (a) How much does Ms. Lee pay in each case? (b) Which is a better deal over the entire time of the loan (assuming Ms. Lee does not invest the money she would have paid in points)? (c) If Ms. Lee can invest the $4,500 she would have paid in points for the second mortgage at 5% compounded continuously, which is the better deal?
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