Explanation Given information: Loan amount $ 100 , 050 , payment per month $ 900 , and number of payments 240 Explanation: Let’s assume monthly interest rate is i The general equation for loan payment is P i + R [ ( 1 + i ) − N − 1 ] = 0 , Where P is loan amount, R is the monthly payment and N is the number of periodic payments. Here, P = $ 100050 , R = $ 900 , and N = 240 By substituting these values in the above equation, ⇒ 100050 i + 900 [ ( 1 + i ) − 240 − 1 ] = 0 Let f ( i ) = 100050 i + 900 [ ( 1 + i ) − 240 − 1 ] = 0 Now, roughly graph the function by using the curve-sketching techniques to get value of i 0 By applying the curve-sketching techniques, a rough sketch of the graph of f ( i ) = 100050 i + 900 [ ( 1 + i ) − 240 − 1 ] = 0 is as below. From the graph, it is observed that i − intercept lies in between 0 and 0.01 , so i 0 = 0.01 The formula for the Newton-Raphson algorithm is x new = x old − f ( x old ) f ' ( x old ) So, differentiate f ( i ) with respect to i ⇒ f ' ( i ) = 100050 − 216000 ( 1 + i ) − 241 Substitute the value of i 0 in f ( i ) and f ' ( i ) , and calculate f ( i 0 ) and f ' ( i 0 ) respectively. ⇒ f ( i 0 ) = 100050 ( 0.01 ) + 900 [ ( 1 + ( 0.01 ) ) − 240 − 1 ] = 183.1253 , and ⇒ f ' ( i 0 ) = 100050 − 216000 ( 1 + ( 0

15th Edition

ISBN: 9780137590896

Author: Larry J. Goldstein; David C. Lay; David I. Schneider; Nakhle H. Asmar; William Edward Tavernetti

Publisher: Pearson Education (US)

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Chapter 11.2, Problem 16E

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The monthly rate of interest when a mortgage of $ 100,050 is repaid in 240 monthly payments of $ 900.

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Chapter 11.2, Problem 15E

Chapter 11.2, Problem 17E

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The monthly rate of interest when a mortgage of $ 100 , 050 is repaid in 240 monthly payments of $ 900 .

Solution Summary: The author explains the monthly interest rate for a mortgage of 100,050. The general equation for loan payment is Pi+Rleft, R, and N.

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The monthly rate of interest when a mortgage of $ 100,050 is repaid in 240 monthly payments of $ 900.

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Chapter 11 Solutions