   Chapter 14, Problem 16AT Contemporary Mathematics for Busin...

8th Edition
Robert Brechner + 1 other
ISBN: 9781305585447

Solutions

Chapter
Section Contemporary Mathematics for Busin...

8th Edition
Robert Brechner + 1 other
ISBN: 9781305585447
Textbook Problem

How much more total interest will be paid on a 30-year fixed-rate mortgage for $100,000 at 9.25% compared with a 15-year mortgage at 8.5%? To determine To calculate: The difference in the total interest to be paid on$100,000 when interest rate is 9.25 % for 30 years and when interest rate is 8.5 % for 15 years.

Explanation

Given Information:

Amount financed is $100000, interest rate is 9.25 % for 30 years and the interest rate is 8.5% for 15 years Formula used: The formula for the number of$ 1000 is

Number of $1000s financed = Amount Financed1000 Use the table 14.1 to calculate the table factor. Locate the table factor on the intersection of the number of years column and the interest rate row. The formula for Monthly payment is Monthly Payment = Number of 1000s financed × Table Factor And, Number of payments = Term of loan × 12 Total interest is given by, Total Interest = (Monthly payment × Number of payments) Amount Financed Now, Difference in total interest=total interest for 30yearstotal interest for 15years Calculation: Consider the provided values, Amount Financed=$100,000Interest Rate=9.25%Term of Loan=30years

As, Number of $1000s financed = Amount Financed1000 To calculate number of$ 1000 financed, apply the above formula:

Number of $1000s financed=Amount Financed1000=1000001000=100 Use the table 14.1 for locating the table factor at the intersection of 30 years (column) and 9.25 % interest rate (row). So, the table factor for 30 years at 9.25 % rate of interest is 8.23. As, Monthly Payment = Number of 1000s financed × Table Factor To calculate Monthly Payment, use above formula: Monthly Payment = Number of 1000s financed × Table Factor=100×8.23=$823

As, Number of payments = Term of loan × 12

Use above formula to calculate the number of payments:

Number of payments=Term of loan×12=30×12=360

Then,

Total Interest for 30 years=(Monthly Payment×Number of Payments)Amount Financed=(823×360)100000=$196280 Now consider, Amount Financed=$100,000Interest Rate=8

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