Unit 5 Seminar: Consumer Credit

Installment Loans

Estimated Annual Percentage Rate (APR)

Refund Fractions (when a loan is paid off early)

Open-ended credit

Average Daily Balance

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Consumer credit: a type of credit or loan that is available to individuals or businesses. The loan 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.

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.

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Finance charges or carrying charges: the interest and any fee associated with an installment loan.

Installment loan: a loan that is repaid in regular payments.

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A framing business purchased a mat cutter on an installment plan with a …

$60 down payment. Due at time of purchase when you finance your purchase.

and 12 payments of $45.58. These are installment payments, paid each month to pay the cost of the item plus any finance charges.

The cash price is $500. What you would pay if you paid in full at time of purchase.

The installment price is $606.96 or the sum of the payments plus the down payment. Your total cost for the item. (12 * $45.58) + $60 = $606.96

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Karen purchased a copier on the installment plan with a down payment of $50 and 6 monthly payments of $29.95. Find the installment price.

Use the solution plan. What do you know? What do you need to know?

Installment Price (IP) = total of installment payments + down payment

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We know: Down payment = $50Number of monthly payments = 6Cost of each monthly payment = $29.95

We are looking for:The installment price = IP = ?

Using our formula, substitute the known values.Installment Price (IP) = total of installment payments + down payment

IP = (6* $29.95) + $50IP = $179.70 + $50

IP = $229.70 This is the installment price

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We can find the installment payment if we know the installment price, the down payment and the number of payments.

1. To find the amount financed, subtract the down payment from the installment price.

Amount financed = installment price – down payment

2. Divide the amount financed by the number of installment payments. This is the installment payment.

Installment payment = amount financed number of installment payments

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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.

We know:

Installment Price = $1,220

Down payment = $320

Number of payments = 12 Use the steps to find the installment payment

Find the amount financed:

Installment price – down payment = $1,220 - $320 = $900

Find the installment payment

Amount financed ÷ Number of payments = $900 ÷ 12 = $75

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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 $412.50. What was the installment payment?

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We know:

Installment Price = $412.50

Down payment = $100

Number of payments = 5 Use the steps to find the installment payment

Find the amount financed:

Installment price – down payment = $412.50 - $100 = $312.50

Find the installment payment

Amount financed ÷ Number of payments = $312.50 ÷ 5 = $62.50

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Annual percentage rate (APR):

the true rate of an installment loan that is equivalent to an annual simple interest rate.

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If you borrowed $1,500 for one year and were charged $165 in interest, you would be paying a simple interest rate of 11% annually.

I = PRT $165 = $1,500 * R * 1 (Remember Unit 4)R = $165 ÷ $1,500 = 0.11 = 11% This is the simple interest rate

If you paid the money back in 12 monthly installments of $138.65, you would not have use of the entire $1,500 for a full year.$1,500 + $165 = $1665 $1665 ÷ 12 = $138.65

In effect you would be paying more than the 11% annually. (Actually it’s almost 19.75% APR)

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See lecture notes for full table

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1. Find the interest per $100 financed: divide the total finance charges including interest by the amount financed and multiply by $100.

(Total finance charges ÷ Amount financed)* $100

2. Find the row corresponding to the 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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Lewis Strong 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 = Installment payment * # of payments$142 x 24 = $3,408

Amount financed = installment price - down payment$3,408 - $0 = $3,408

Finance charge = Amount financed – purchase price$3,408 - $3,000 = $408

Calculate the interest per $100 to use the table.

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FinanceCharge $408Interest per $100= $100 $100 $11.97

Amt Financed $3,408

Interest per $100 = $11.97 and number of payments is 24.

Using the table, find the row for 24 monthly payments.

Move across to find the number nearest to $11.97.11.97 – 11.86 = 0.11 12.14 – 11.97 = 0.17 11.86 is closer

Move up to the top of that column to find the APR which is 11%

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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.

What do we know?

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Cost = $1,800 No downpaymentFinance period = 12 months Installment payments = $168

Installment price = Installment payment * # of payments Amount financed = installment price – down payment Finance charge = Amount financed – purchase price Calculate the interest per $100 to use the table.

Using the table, find the row for the number of monthly payments.

Move across to find the number nearest to the interest per $100

Move up to the top of that column to find the APR

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See lecture notes for full table20

Purchase price = $1,800 Down payment = $0Number of payments = 12 Installment payment

= $168.

Installment price = Installment payment * # of payments$168 * 12 = $2,016

Amount financed = installment price – down payment$2,016 – $0 = $2,016

Finance charge = Amount financed – purchase price$2,016 - $1,800 = $216

Calculate the interest per $100 to use the table.($216 ÷ $2,016)*$100 = 0.10714 * $100 = $10.71Number of monthly payments = 12 21

Interest per $100 = $10.71Number of monthly payments = 12

The APR is 19.25%

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Jody’s new laptop cost $1,800 and was financed for 12 months. The monthly payments are $168. We determined that the APR is 19.25%.

After only 6 months, Jody gets a raise at work and wants to pay off the loan.

Does she only pay ½ of the interest she planned to pay?

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If a loan is paid before it is due, some of the interest may be refunded.

It may be less than what you expected.

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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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, you have paid interest for a total of 78 parts: 12 + 11 +10 + 9 + 8 + 7… + 1 = 78

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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 3 + 2 + 1 = 6

Therefore, 6/78 of the total interest must be refunded.

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1. Calculate the refund fraction.

You can use Gauss’ rule to sum consecutive numbers rather than adding by hand:

[(Months remaining) * (Months remaining + 1 )] ÷ 2

Or you can use the Table in the book.

2. Calculate the interest refund

Interest refund = Total interest * Refund Fraction

Total interest can also be called the finance charge.

Sum of digits for number of paymentsRefund Fraction=

Sum of digits for number of payments

remaining

total

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A loan for 12 months with interest of $468.85 is paid in full with five payments remaining. What is the refund fraction for the interest refund?

5 + 4 + 3 + 2 + 1 = 15 (parts) remaining out of 78 (12 months)

15/78 would be applied to the interest to calculate the interest refund.

Using Gauss’ rule:

5 payments remaining: (5*6) ÷ 2 = 15

12 month loan: (12*13) ÷ 2 = 78 Interest Refund: $468.85 * (15/78) = $90.16

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A loan with a total finance charge of $1276.20 for 36 months that was paid in full with 15 payments remaining. What is the refund fraction and interest refund?

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Using Table 2 from the book, the numbers would be:

Sum of digits from 1 to 15 = 120Sum of digits from 1 to 36 = 666

Using Gauss’ rule: Numerator = (15*16) ÷ 2 = 120 Denominator = (36*37) ÷ 2 = 666

Refund fraction = 120/666 = 0.18 Interest refund = $1276.20 * 0.18 = $230

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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

Also known as “line of credit” accounts because you can ADD to the principal by making additional purchases BEFORE paying off the exiting debt.

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Daily Unpaid Balance =

Previous Unpaid Balance

+ total daily purchases made

- total credits for the day

Sum of Daily BalancesAverage Daily Balance =

Number of days

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$5,322.70 ÷ 31 = $171.70$5,322.70 = addition of each day’s ending balance

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Start with the unpaid balance. List purchases and payments by when they were

made, adjusting the balance. Count the number of days that balance was the

same. Multiply the daily unpaid balance by the number of

days that balance was the same. Add up all of those sums to get a total for the month.

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Total of daily sums = $5,322.70 Number of days in this cycle = 31 Average daily balance

= Total of daily sums ÷ Number of cycle days= $5,322.70 ÷ 31= $171.70

Finance charge = Average daily balance * Interest rate per month= $171.70 * 1.5% = $171.70 * 0.015 = $2.57Note: If you have an APR, you must convert that to months, ÷ 12

Reminder of what to complete for Unit 5: Discussion = initial

response to one question + 2 reply posts

MML assignment Instructor graded

assignment (download from doc sharing)

Seminar quiz if you did not attend, came late, or left early

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