   Chapter 13.II, Problem 54RE ### 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

# a. What is the rebate fraction of a 36-month loan paid off after the 14th payment?b. What is the rebate fraction of a 42-month loan paid off after the 19th payment?

(a)

To determine

To calculate: The rebate fraction for a 36-month loan that is paid after the 14th payment.

Explanation

Given Information:

A loan for 36-month is paid off after the 14th payment.

Formula used:

Follow the steps to compute the rebate fraction:

Sum-of-the-digits formula is computed through the formula,

Sum-of-the-digits=n(n+1)2

Where n represent the number of payments.

Compute the rebate fraction as,

Rebate fraction=Sum of the digits of the number of remaining paymentsSum of the digits of the total number of payments

Calculation:

Consider that a loan for 36-month is paid off after the 14th payment.

Compute the remaining payments by subtracting payment made from total payments.

Payments remaining=3614=22

Hence, the payments remaining are 22.

Compute the sum-of-the-digits of the number of remaining payments by substituting n to 22,

Sum-of-the-digits=n(n+1)2=22(22+1)2=253

Hence, the sum-of-the-digits of the number of remaining payments is 253

(b)

To determine

To calculate: The rebate fraction for a 42-month loan paid off after 19th payment.

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