HW 1.2 Analytic Representations_Equations-Maria Huerta

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1/17/24, 2:12 PM HW 1.2 Analytic Representations/Equations-Maria Huerta https://tdx.acs.pearsonprd.tech/api/v1/print/highered 1/2 Student: Maria Huerta Date: 01/17/24 Instructor: Dania Sinibaldi Course: Quantitative Reasoning O06B SP24 Assignment: HW 1.2 Analytic Representations/Equations Consider a home mortgage of $ at a fixed APR of % for years. 75,000 7.5 20 a. Calculate the monthly payment. b. Determine the total amount paid over the term of the loan. c. Of the total amount paid, what percentage is paid toward the principal and what percentage is paid for interest? a. The monthly payment, PMT, required to repay a loan of P dollars paid n times per year over Y years at an annual rate APR is given by the following formula. PMT = P APR n 1 − 1 + APR n − nY To use the formula to determine the monthly payment, PMT, first identify the values for P, APR, n, and Y. The value of P is $ . 75,000 The value of APR, as a decimal, is . 0.075 The value of n is . 12 The value of Y is years. 20 Now substitute the values of P, APR, n, and Y in the formula. PMT = P APR n 1 − 1 + APR n − nY = $75,000 0.075 12 1 − 1 + 0.075 12 − 12(20) Simplify the numerator. PMT = $75,000 0.075 12 1 − 1 + 0.075 12 − 12(20) = $468.75 1 − 1 + 0.075 12 − 12(20) Next simplify the denominator. PMT = $468.75 1 − 1 + 0.075 12 − 12(20) = $468.75 0.77582582 Finally divide. PMT = $468.75 0.77582582 = $604.19

1/17/24, 2:12 PM HW 1.2 Analytic Representations/Equations-Maria Huerta https://tdx.acs.pearsonprd.tech/api/v1/print/highered 2/2 The monthly payment is $ . 604.19 b. To find the total amount paid over the term of the loan, multiply the monthly payment by the number of months in years. Since there are 12 months in a year, the monthly payment is paid (12)( ) times. 20 20 = 240 Calculate the total amount paid over the term of the loan. $ ( ) $ 604.19 240 = 145,005.60 The total amount paid over the term of the loan is $ . 145,005.60 c. The entire starting loan principal must be repaid over the term of the loan. The amount of the total payment over the term of the loan that goes to principal is P, $75,000. To find the percentage of the total amount paid that goes toward the principal, divide P by total amount paid and multiply by 100, rounding to one decimal place. % 100 $75,000 $145,005.60 51.7 The amount of interest paid is the difference between the total payment and the total amount borrowed. $ $ $ 145,005.60 − 75,000 = 70,005.60 To calculate the percent paid for interest, divide the amount paid for interest by the total amount paid and multiply by 100, rounding to one decimal place. % 100 $70,005.60 $145,005.60 48.3 Therefore, the total amount paid over the length of the loan, % is paid toward the principal and % is paid for interest. 51.7 48.3

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