Chapter 13.II, Problem 42RE

### Contemporary Mathematics for Busin...

8th Edition
Robert Brechner + 1 other
ISBN: 9781305585447

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 $4,800 36$169.33 27 ____ ____ ____

To determine

To calculate: The rebate fraction, finance charge rebate and loan payoff if amount financed are $4,800, the numbers of payments are 36, monthly payments are$169.33 and payments made are 27.

Explanation

Given Information:

The amount financed is $4,800, the numbers of payments are 36, the monthly payment is$169.33 and payments made are 27.

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 $4,800, the numbers of payments are 36, monthly payments are$169.33 and payments made are 27.

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

Remaining payment=3627=9

Hence, the remaining payments are 9.

Compute the sum of the digits of 9 and 36 months

Sum of the digits of 9=n(n+1)2=9(9+1)2=45

And,

Sum of the digits of 36=n(n+1)2=36(

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