Explanation Given information: Principal = P =$100,000.00 APR =6% Loan term = Y = 20 years. Formula used: The fixed monthly payment PMT is given by P M T = P × ( A P R n ) [ 1 − ( 1 + A P R n ) − n Y ] Calculation: (a) The fixed monthly payment for the loan principal of $100,000 at a rate of 6% for 20 years is calculated by substituting the values in the formula. P M T = P × ( A P R n ) [ 1 − ( 1 + A P R n ) − n Y ] = $ 100 , 000 × ( 0.06 12 ) [ 1 − ( 1 + 0.06 12 ) − 12 × 20 ] = $ 500 [ 1 − ( 1.005 ) − 240 ] = $ 500 0.6979 = $ 716.43 The fixed monthly payment every month is $716.43 . (b) If an additional payment (13 th instalment) is made every year, the loan term in years is calculated by rearranging the expression for PMT as follows: P M T = P × ( A P R n ) [ 1 − ( 1 + A P R n ) − n Y ] 1 − ( 1 + A P R n ) − n Y = P × ( A P R n ) P M T ( 1 + A P R n ) − n Y = 1 − [ P × ( A P R n ) P M T ] Taking logarithm on both sides, log [

Using and Understanding Mathematics: A Quantitative Reasoning Approach (6th Edition)

6th Edition

ISBN: 9780321914620

Author: Jeffrey O. Bennett, William L. Briggs

Publisher: PEARSON

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Chapter 4.D, Problem 54E

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(a) The payment to be per month on a loan of $100,000 at APR 6%for a loan period of 20 years.

(b) The period of the loan if a 13^th instalment is made every year.

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Chapter 4.D, Problem 53E

Chapter 4.D, Problem 55E

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Chapter 4 Solutions

Using and Understanding Mathematics: A Quantitative Reasoning Approach (6th Edition)

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(a) The payment to be per month on a loan of $100,000 at APR 6%for a loan period of 20 years. (b) The period of the loan if a 13 th instalment is made every year.

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(a) The payment to be per month on a loan of $100,000 at APR 6%for a loan period of 20 years. (b) The period of the loan if a 13th instalment is made every year.

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(a) The payment to be per month on a loan of $100,000 at APR 6%for a loan period of 20 years.

(b) The period of the loan if a 13^th instalment is made every year.