   Chapter 6.5, Problem 29E Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781337625340

Solutions

Chapter
Section Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781337625340
Textbook Problem

A recent college graduate buys a new car by borrowing $18,000 at 8.4% compounded monthly for 5 years. She decides to pay$384 instead of the monthly payment required by the loan.(a) What is the monthly payment required by the loan, and how much extra did she pay per month?(b) How many $384 payments will she make to pay off the loan?(c) How much will she save by paying$384 per month rather than the required payment?

(a)

To determine

To calculate: The monthly payment on the loan and the extra amount paid per month if the amount $18,000 is borrowed by a college graduate at 8.4% compounded monthly for 5 years for buying a new car Explanation Given Information: The amount$18,000 is borrowed by a college graduate at 8.4% compounded monthly for 5 years for buying a new car. Instead of monthly payments required she pays $384. Formula used: If a debt of$An, with interest at a rate of i per period, is amortized by n equal periodic payments, the size of each payment is:

R=An[i1(1+i)n]

Calculations:

Consider the provided information:

The amount $18,000 is borrowed by a college graduate at 8.4% compounded monthly for 5 years for buying a new car. Instead of monthly payments required she pays$384.

Since, according to the given information,

The amount $18,000 is borrowed by a college graduate. Therefore, An=18,000 They refinance at 8.4% compounded monthly for 5 years. Therefore, n=5×12=60 And, i=8.4100×112=0.007 The size of each payment is: R=An[i1(1+i)n] Substitute 18,000 for An, 0.007 for i and 60 for n in R=An[i1(1+i)n] (b) To determine To calculate: The number of payments of$384 she would make to pay off the loan if the amount $18,000 is borrowed by a college graduate at 8.4% compounded monthly for 5 years for buying a new car. (c) To determine To calculate: The amount saved by her by paying$384 per month instead of the required payment if the amount \$18,000 is borrowed by a college graduate at 8.4% compounded monthly for 5 years for buying a new car.

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