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Mathematical Applications for the ...

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

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BuyFindarrow_forward

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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