   Chapter 13.II, Problem 41RE ### 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

# You are the loan department supervisor for the Pacific National Bank. The following installment loans are being paid off early, and it is your task to calculate the rebate fraction, the finance charge rebate, and the payoff for each loan. Amount Number of Monthly Payments Rebate FinanceCharge Loan Financed Payments Payment Made Fraction Rebate Payoff $9,500 48$267.00 36 ____ ____ ____

To determine

To calculate: The rebate fraction, finance charge rebate and loan payoff if amount financed is $9,500, the number of payments are 48, monthly payments are$267.00 and payments made are 36.

Explanation

Given Information:

The amount financed is $9,500, the numbers of payments are 48, monthly payments are$267.00 and payments made are 36.

Formula used:

Follow the steps to compute the finance charge rebate and loan payoff.

Step 1: Compute the rebate fraction.

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

Step 2: Identify the finance charge rebate.

Finance charge rebate=Rebate fraction×Total finance charge

Where total finance charge can be computed as:

Finance Charge=Monthly payment×Number of month of the loanAmount financed

Step 3: Compute loan payoff.

Loan payoff=(Payment remaining×Payments amount)Finance charge rebate

Calculation:

Consider the amount financed is $9,500, the numbers of payments are 48, monthly payments are$267.00 and payments made are 36.

Compute the remaining number of payment by subtracting payment made from the number of payment.

Remaining payment=4836=12

Hence, the remaining payments are 12.

Compute the sum of the digits of 12 and 48 months.

Sum of the digits of 12=n(n+1)2=12(12+1)2=78

And,

Sum of the digits of 48=n(n+1)2=48(

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