Explanation Given: Consider the first loan option where the principal ( P ) is given as $ 2 , 40 , 000 ,.the interest rate ( r ) is given as 4.250 % and the term ( t )is given as 30 years. Next, consider the second loan option where the principal ( P ) is given as $ 2 , 40 , 000 , the interest rate ( r ) is given as 3.250 % , and the term ( t ) is given as 15 years. Formula used: R = P ( r 12 ) 1 − ( 12 12 + r ) 12 t . Where, R is monthly payment P is the principal and ( r ) is interest rate and t is time. Total payment over life of loan = No . of payments × Total Payment . Total Interest paid over life of loan = Total Payment − Original Payment . Calculation: The interest rate of 4.250 % is not given in the table. Thus, in order to get the payment (R) , the following steps and formulae need to be used: Step 1: Rate is expressed as a decimal. Thus, to convert the rate percent into a decimal, rate percent is divided by 100. r = 4.250 % = 4.250 100 = 0.0425 Step 2: Now, by applying the following formula, the payment is calculated as: R = P ( r 12 ) 1 − ( 12 12 + r ) 12 t = $ 2 , 40 , 000 ( 0.0425 12 ) 1 − ( 12 12 + 0.0425 ) 12 × 30 = $ 2 , 40 , 000 × 0.00354166 1 − ( 12 12.0425 ) 360 = $ 849.9984 1 − ( 0.99647083 ) 360 Further simplified: R = $ 849.9984 1 − 0.28006084 = $ 849.9984 0.71993916 = $ 1 , 180.656 = $ 1 , 180.66 Thus, the payment is $ 1 , 180.66 . The number of payments over life of loan is 360. Thus, the total payment over life of loan is calculated as: Total payment over life of loan = No . of payments × Total Payment = 360 × $ 1 , 180.66 = $ 4 , 25 , 037.60 Thus, the total of payments over life of loans is $ 4 , 25 , 037.60

Mathematical Ideas with Integrated Review and Worksheets plus NEW MyLab Math with Pearson eText -- Access Card Package (Integrated Review Courses in MyLab Math and MyLab Statistics)

1st Edition

ISBN: 9780321977274

Author: Miller, Charles, Heeren, Vern, HORNSBY, John, Christopher

Publisher: PEARSON

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Chapter 13.4, Problem 27E

To determine

To calculate: The better option for a loan if the first loan option where the principal (P) is given as $2,40,000. the interest rate (r) is given as 4.250% and the term (t) is given as 30 years. Next, consider the second loan option where the principal (P) is given as $2,40,000, the interest rate (r) is given as 3.250%, and the term (t) is given as 15 years.

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Chapter 13.4, Problem 26E

Chapter 13.4, Problem 28E

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Chapter 13 Solutions

Mathematical Ideas with Integrated Review and Worksheets plus NEW MyLab Math with Pearson eText -- Access Card Package (Integrated Review Courses in MyLab Math and MyLab Statistics)

Ch. 13.1 - In the following exercises, assume whenever...Ch. 13.1 - In the following exercises, assume whenever...Ch. 13.1 - In the following exercises, assume whenever...Ch. 13.1 - In the following exercises, assume whenever...Ch. 13.1 - In the following exercises, assume whenever...Ch. 13.1 - In the following exercises, assume whenever...Ch. 13.1 - Find the future value of each deposit if the...Ch. 13.1 - Find the future value of each deposit if the...Ch. 13.1 - Find the future value of each deposit if the...Ch. 13.1 - Find the future value of each deposit if the...

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Solution Summary: The author explains that the second loan option is better than the first one, because the total interest paid over the life of loans is 63,553.80.

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