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Contemporary Mathematics

for Business and Consumers

Third Edition

By: Robert A. Brechner

Chapter 13Consumer and Business Credit

Copyright © 2003 by South-Western

Chapter 13, Consumer and Business Credit

Section I Open – End Credit – Change Accounts, Credit Cards, and Lines of Credit13-1 Calculating finance charge and new balance by the unpaid or previous month’s balance method.13-2 Calculating finance charge and new balance using the average daily balance method.13-3 Calculating the finance charge and new balance of business and personal lines of credit.

Chapter 13, Consumer and Business Credit (Cont.)

Section II Closed – End Credit Installment Loans13-4 Calculating the total deferred payment price and the amount of the finance charge of an installment loan.13-5 Calculating the amount of the regular monthly payments of an installment loan by formula.13-6 Calculating the annual percentage rate of an installment loan by APR tables and by formula.

Chapter 13, Consumer and Business Credit (Cont.)

Section II Closed – End Credit Installment Loans13-7 Calculating the finance charge and monthly installment loan by using the APR tables installment loan.13-8 Calculating the finance charge rebate and the amount of the payoff when a loan is paid off early by using the sum – of – years – digits method.

Section I, Open – End Credit – Charge Accounts, Credit Cards, and Lines of Credit

Revolving Credit

Interest = Principal x Rate x Time

13-1 Calculating Finance Charge and ?New Balance by the Unpaid or Previous Month’s Balance Method

Steps to Calculate the Finance Charge and new Balance by Using the Unpaid balance Method:Step 1. Divide the annual percentage rate by 12 to find the monthly or periodic interest rate. (Round to the nearest hundredth percent when necessary.

Step 2. Calculate the finance charge by multiplying the previous month’s balance by the periodic interest rate from Step 1.

Periodic rate = Annual percentage rate

12

Finance charge = Previous month’s balance x Periodic rate

13-1 Calculating Finance Charge and New Balance by the Unpaid or Previous Month’s Balance Method (Cont.)

Steps to Calculate the Finance Charge and new Balance by Using the Unpaid balance Method:

Step 3. Total all the purchases and cash advances for the month.Step 4. Total all the payments and credits for the month.Step 5. Use the following formula to determine the new balance:

New Balance = Previous balance + Finance Charge + Purchases and Cash advances - Payments

13-2 Calculating Finance Charge and New Balance by Using the Average Daily Balance Method

Steps to Calculate the Finance Charge and New Balance by Using the Average Daily Balance Method:

Step 1. Starting with the previous month’s balance s the first unpaid balance, multiply each by the number of days that the balance existed, until the next account transaction.Step 2. At the end of the billing cycle, find the sum of all the daily balance figures.Step 3. Find the average daily balance using the formula

Average daily balance = Sum of daily balance

Days in billing cycle

13-2 Calculating Finance Charge and New Balance by Using the Average Daily Balance Method (Cont.)

Steps to Calculate the Finance Charge and New Balance by Using the Average Daily Balance Method:

Step 4. Calculate the finance charge by

Step 5. Compute the new balance as before, using

New balance = Previous balance + finance charge + Purchases and cash advances - Payments

Finance Charge = Average daily balance x Periodic rate

Everybody’s Business

“New Balance” can be calculated by adding the finance charge to the last “Unpaid Balance” of the month.

$427.28 + $3.89 = $431.37

Section II, Closed – End Credit – Installment Loans

13-4 Calculating the Total Deferred Payment Price and the Amount of the Finance Charge of an Installment Loan

Amount Financed = Purchase price – Down payment

Down payment = Purchase price x Down payment percent

Total amount of installment payments = Amount financed + finance charges

Section II, Closed – End Credit – Installment Loans (Cont.)

13-4 Calculating the Total Deferred Payment Price and the Amount of the Finance Charge of an Installment Loan

Finance charge = Total amount of installment payments – Amount financed

Total amount of Installment payment = Monthly payment amount x Number of Monthly payment

Total deferred payment price = Total of installment payments + Down payment

13-5 Calculating the Amount of Regular Monthly Payments of an Installment Loan by adding the Add-on Interest Method

Steps to Calculate the Monthly Payment Using the Add-On Interest:Step 1. Calculate the amount to be financed by subtracting the down payment from the purchase price.

Step 2. Compute the add-on interest charge by using I = PRT.Amount financed = Purchase price (100%) – Down payment percent)

13-5 Calculating the Amount of Regular Monthly Payments of an Installment Loan by adding the Add-on Interest Method (Cont.)

Steps to Calculate the Monthly Payment Using the Add-On Interest:Step 3. Find the Total of installment payments by adding the finance charge to the amount financed.

Step 4. Find the regular payments by dividing the total of installment payments by the number of months of the loan.

Total of installments payments = Amount financed + finance charges

Regular monthly payments = Total of installment payments

Number of months of the loan

Everybody’s Business

As with open-end credit, installment loan consumers are protected by Regulation Z of the Truth in Leading Act.

Advertisers of installment loans such as car dealers and furniture stores, must disclose in the ad and the loan agreement the following information:

Down payment Annual percentage rate

Terms and payments Total payback

13-6 Calculating the Annual Percentage Rate of an Installment Loan by APR Tables and by Formula

Steps to Find the Annual Percentage Rate of an Installment Loan Using APR TablesStep 1. Calculate the finance charge per $100 by

Step 2. From the Table 13-1, scan down the Number of Payments column to the number of payments for the loan in question.Step 3. Scan to the right in that Number of Payments row to the table that most closely corresponds to the finance charge per $100 calculated in Step 1. Step 4. Look to the top of the column containing the finance charge per $100 to find the APR of the loan.

Finance charge per $100 = Finance charge x 100

Amount financed

13-7 Calculating the Finance Charge and Monthly Payment of an Installment Loan by Using the APR Tables

Steps to Find the Finance Charge and Monthly Payment of an Installment Loan by Using the APR TablesStep 1. Using the APR and the number of payments of the loan, locate the table factor at the intersection of the APR column and the number of payments row. This factor represents the finance charge per $100 financed.

Step 2. The total finance charge of the loan can be found by

Step 3. The monthly payment can now be found by

Finance charge = Amount financed x Table factor

100

Monthly payment = Amount financed + finance charge

Number of Months of the Loan

Chapter 13, Consumer and Business Credit

Open – end credit Finance charge

Annual percentage rate (APR Unsecured loan

Secured loan Revolving credit

Billing cycle Average daily balance

Line if credit Prime rate

Install loan Mortgage

Down payment Cash or purchase price

Amount financed Add-on interest

Finance charge rebate Rule of 78

Rebate fraction

Annual percentage rate 12

Finance charge = Previous month’s balance x Periodic rate

Sum of daily balances Days in billing cycle

Finance charge = Average daily balance x Periodic rate

New Previous Finance Purchases and Paymentsbalance balance charge cash advances & credits= + + =

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Periodic rate =

Average daily balance =

Chapter 13

Copyright © 2003 by South-Western

Chapter 13

Amount financed = Purchase price - Down payment

Down payment = Purchase price x Down payment percent

Amount = Purchase price(100% - Down payment %)financed

Total amount of = Amount financed + Finance chargeinstallment payments

Finance charge = Total amount of - Amount financed installment payments

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Chapter 13

Total amount of = Monthly payment x Number of installment payments amount monthly payments

Total deferred pmt. Price = Total of install pmts. + Downpmt.

Interest = Principal x Rate x Time(finance charge) (amount financed)

Regular monthly payments = Total of installment payments Number of months of loan

)1()1(3

72APR

nInP

I

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Chapter 13

Amount financed x APR table factor 100

n(n + 1) 2

Sum of digits of remaining payments Sum of digits of total payments

Finance charge rebate = Rebate fraction x Total finance charge

Loan payoff = (Payments remaining x Pmt amount) - Finance charge rebate

Finance charge =

Sum of digits =

Rebate fraction =