Explanation Given: Consider the first loan option where the principal ( P ) is given as $ 2 , 40 , 000 , the interest rate ( r ) is given as 3.875 % and the term ( t ) is given as 20 years. Next, consider the second loan option where the principal ( P ) is given as $ 2 , 40 , 000 , the interest rate( r ) is given as 3.000 % , and the term ( t ) is given as 10 years. Formula used: R = P ( r 12 ) 1 − ( 12 12 + r ) 12 t . Where, R is monthly payment and P is the principal and t is time and (r) is interest rate. 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 3.875 % 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 = 3.875 % = 3.875 100 = 0.03875 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 ( 0.03875 12 ) 1 − ( 12 12 + 0.03875 ) 12 × 20 = $ 2 , 40 , 000 × 0.00322916 1 − ( 12 12.03875 ) 240 = $ 774.9984 1 − ( 0.99678122 ) 240 Further simplified: R = $ 774.9984 1 − 0.46127857 = $ 774.9984 0.53872143 = $ 1 , 438.588 = $ 1 , 438.59 Thus, the payment is $ 1 , 438.59 . The number of payments over life of loan is 240. Thus, the total payment over life of loan is calculated as: Total payment over life of loan = No . of payments × Total Payment = 240 × $ 1 , 438

Mathematical Ideas (13th Edition) - Standalone book

13th Edition

ISBN: 9780321977076

Author: Charles D. Miller, Vern E. Heeren, John Hornsby, Christopher Heeren

Publisher: PEARSON

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Chapter 13.4, Problem 28E

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 3.875% and the term (t) is given as 20 years. Next, consider the second loan option where the principal (P) is given as $2,40,000, the interest rate(r) is given as 3.000%, and the term (t) is given as 10 years..

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Chapter 13.4, Problem 27E

Chapter 13.4, Problem 29E

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Chapter 13 Solutions

Mathematical Ideas (13th Edition) - Standalone book

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 36,095.20.

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