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**12.1 Installment Loans and Closed-end Credit**

Find the amount financed, the installment price and the finance charge of an installment loan. Find the installment payment of an installment loan. Find the estimated annual percentage rate (APR) using a table.

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Key Terms Consumer credit: a type of credit or loan that is available to individuals or businesses. The loan is repaid in regular payments. Installment loan: a loan that is repaid in regular payments. Closed-end credit: a type of installment loan in which the amount borrowed and the interest is repaid in a specific number of equal payments.

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Key Terms Open-end credit: a type of installment loan in which there is no fixed amount borrowed or number of payments. Regular payments are made until the loan is paid off. Finance charges or carrying charges: the interest and any fee associated with an installment loan.

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**12.1.1 Find the Amount Financed, the Installment Price and the Finance Charge of an Installment Loan**

Cash price: paid all at once at time of purchase Down payment: partial payment Amount financed: total amount paid in regular payments to pay off the balance Installment price: includes all installment payments, finance charges and down payment

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Look at this example The 7th Inning purchased a mat cutter for the framing department on the installment plan with a $60 down payment and 12 payments of $ Find the installment price of the mat cutter. Installment Price (IP) = total of installment payments + down payment IP = (12 x $45.58) + $60 IP = $ = $606.96

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Try this example Karen purchased a copier on the installment plan with a down payment of $50 and 6 monthly payments of $ Find the installment price. $229.70

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**12.1.2 Find the Installment Payment of an Installment Loan**

We can find the installment payment if we know the installment price, the down payment and the number of payments. Find the amount financed; subtract the down payment from the installment price. Divide the amount financed by the number of installment payments.

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Look at this example The installment price of a pool table was $1,220 for a 12-month loan. If a $320 down payment was made, find the installment payment. Installment Price = $1,220 $1,220 - $320 = $ [$320 is the down payment.] $900 ÷ 12 = $75 The installment payment is $75

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Try this example Peggy bought a new dryer on an installment plan. She made a down payment of $100. The installment price for a five month loan was $ What was the installment payment? $62.50

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**12.1.3 Find the Estimated APR Using a Table**

Annual percentage rate (APR): the true rate of an installment loan that is equivalent to an annual simple interest rate. Truth in Lending Act: passed in 1969 by the federal government, it requires a lending institution to tell the borrower in writing what the APR actually is.

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**Annual Simple Interest Rate Equivalent**

Example: If you borrowed $1,500 for one year and were charged $165 in interest, you would be paying an interest rate of 11% annually. $165 ÷ $1,500 = 0.11 = 11% If you paid the money back in 12 monthly installments of $138.75, you would not have use of the entire $1,500 for a full year. In effect you would be paying more than the 11% annually.

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**Percentage rate tables**

The APR can be determined using a government-issued table. APR rates are within ¼ % which is the federal standard. A portion of one of these tables based on the number of monthly payments is shown in your text in Table 12-1.

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**Using a per $100 of amount financed table**

1. Find the interest per $100 financed; divide the finance charges including interest by the amount financed and multiply by $100. 2. Find the row corresponding to number of monthly payments. Move across the row to find the number closest to the value from step 1. Read up the column to find the APR for that column.

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Look at this example Lewis Strang bought a motorcycle for $3,000, which was financed at $142 per month for 24 months. There was no down payment. Find the APR. Installment price = $142 x 24 = $3,408 Finance charge = $3,408 - $3,000 = $408

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**Find the APR using the table**

Interest per $100 = finance charge x $100 = amount financed $408 $3,408 x $100 = $11.97 Find the row for 24 monthly payments. Move across to find the number nearest to $11.97. Move up to the top of that column to find the APR which is 11%

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Try this example Find the APR for Jody’s new laptop which cost $1,800 and was financed for 12 months. There was no down payment. The monthly payments were $168. Answer: Installment price = $168 x 12 = $2,016 Finance charge = $2,016 - $1,800 = $216 $216/$2016 = x100 = $10.71 The APR is 19.25%

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**12.2 Paying a Loan Before it is Due**

If a loan is paid before it is due, some of the interest may be refunded. It may be less than what you expected. Find the interest refund using the rule of 78: A method for the amount of refund of finance charge for an installment loan that is paid before it is due.

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**How to find the refund fraction**

In a twelve-month loan: Month 1: Interest accrues on 12 parts of the principal. Month 2: Interest accrues on 11 part of the principal Month 3: Interest accrues on 10 parts of the loan and so on. At the end of 12 months, there is a total of 78 parts: … + 1 = 78

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**Example: the loan is paid off at the end of month 9**

Month 10: interest is accrued on 3 parts of the principal. Month 11: interest is accrued on 2 parts of the principal. Month 12: interest is accrued on 1 part of the principal. The sum is = 6 Therefore, 6/78 of the total interest must be refunded.

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Look at this example A loan for 12 months with interest of $ is paid in full with five payments remaining. What is the refund fraction for the interest refund? = 15 (parts) remaining out of 78 15/78 would be applied to the interest to calculate the interest refund.

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Try this example A loan of 12 months with interest of $224 is paid in full with four payments remaining. Find the refund fraction for the interest refund. Then, find the interest refund. = 10 The fraction is 10/78. $224 x 10/78 = $28.72. The amount to be refunded is $28.72

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**Find any refund fraction for the interest refund**

The numerator is the sum of the digits from 1 through the number of months remaining of a loan paid off before it was due. The denominator is the sum of the digits from 1 through the original number of months of the loan. Use the sum of digits table (Table 12-2)

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**The sum of the digits for total number of payments**

Look at this example Refund fraction = The sum of digits for number of payments remaining The sum of the digits for total number of payments Example: A loan for 36 months that was paid in full with15 payments remaining would have a refund fraction as follows: Sum of digits from 1 to 15 Sum of digits from 1 to 36

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**So, the refund fraction is…**

Using the Table 12-2, the numbers would be: Sum of numbers from = 120 Sum of numbers from = 666 120/666= 20/111 Multiply the total finance charge by the refund fraction to determine the refund amount.

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Try this example Using the fraction from the previous slide, (20/111), find the refund amount on total finance charge of $1, Answer: $230

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Try this example Ruth Miller paid off a 18-month loan with 6 months remaining. The total finance charge was $342. Find the refund fraction and the amount of the refund. The refund fraction is 21/171 The refund amount is $42

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12.3 Open-End Credit Find the finance charge and the new balance using the average daily balance method.

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**Open-End Credit Also known as “line of credit” accounts.**

Adding to an existing loan happens when a person or company, Makes additional purchases before paying off existing debt. Makes the minimum payment, adding to finance charges Takes cash advances, incurring interest charges Adds additional debit obligations

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**When does the balance change?**

In most cases, if a transaction reaches a financial institution at any time during the day, the transaction is posted and the balance is updated at the end of the business day. Calculations on the day’s unpaid balance are made on the end-of-day amount (same as the beginning of the next day.)

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**Find the Average Daily Balance**

Daily unpaid balance = previous daily unpaid balance + total purchases and cash advances for the day – total credits for the day. Average daily balance = Sum of unpaid balances Number of days in a billing cycle

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Look at this example

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Hodge’s Tax Service

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Hodge’s Tax Service

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Tip! The unpaid balance on an account for a billing cycle is the unpaid daily balance for the last day of the billing cycle. The beginning balance for the next cycle is the unpaid balance for the previous cycle.

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Math in Our World Section 8.4 Installment Buying.

Math in Our World Section 8.4 Installment Buying.

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