CHAPTER 9 SEC 3

Consumer Loans

What is a consumer loan?

Def. a loan that establishes consumer credit

that is granted for personal use; usually unsecured and based on the borrower's integrity and ability to pay

What is an installment loan?

Def.A loan that is repaid with a fixed number of periodic equal-sized payments.

Loans having a fixed number of payments are called closed-ended credit agreements. Each payment is called an installment. The size of your payments is determined by the amount of your purchase and also by the interest rate that the seller is charging. The interest charged on a loan is called the finance charge.

Add on Interest Method

Def.To determine the payments for an

installment loan, we add the simple interest due on the loan amount and then divide this sum by the number of monthly payments

Formula

Formula for determining the monthly payment of an installment loan.

Monthly payment

P is the principle or the amount of the loan, I is the amount of interest due on the loan, and n is the number or monthly payments.

n

IP

Story

You just bought your first car, for $23,000, which you will pay for in payments. If you take out an add-on loan for 7 years at an annual interest rate of 5.7%, what will be your monthly payments?

First compute the simple interestI =P r tI = 23000*.057*7 = 9177

Next we add the interest to the purchase price.23,000+ 9177=32,177

To find the monthly payments we divide by 84. (Why 84)?

06.38384

177,32

Therefore your monthly payments are $383.06 per month.

On the last problem we were assuming a couple of things.

1) No down payment was put. 2) The rate is set.

Question

How many of you own credit cards?

How much do you use it? Daily? Monthly? Emergency use only?

When using a credit card, you are using open-ended credit.

With open-ended credit the calculations are a bit more complicated.

This is one way credit card companies may compute your finance charge.

Unpaid Balance Method

This method uses the simple interest, but

P = previous month’s balance + finance charge + purchases made – returns – payments.

The variable rate r is the annual rate, and t =

12

1

Assume that the annual interest rate on the your CC is 18.5% and your unpaid balance at the beginning of the month was $670. Since then, you purchased summer clothes of $125 and sent a payment of $230.

A) Using the unpaid balance what is your CC bill this month?

B) What is your finance charge next month?

Make a list of what we know

Previous month balance = $670Purchases made = $125Payments = $230Returns = $0Finance charge on last month = 33.10

12

1185.670

Using the formula;670 + 10.33 + 125 – 230 = 575.33

B) Finance charge for next month575.33*0.185*1/12 =$8.86

You can also use this method to pay off your CC.

Example

You are in debt of $7893.67. You decide that you will pay it off in a certain amount of time. You also decide that you will not use this CC during the pay off. You decide to pay the CC the minimum amount per month of $150.67. What is your balance be at the end of the first month? Assume that the annual interest rate on your card is 17.4% and the CC company is using the unpaid balance to compute the finance charge.

Last month’s balance = $7893.67

Monthly interest rate = 1.45%Payment = $150.67You sent your $150 payment7893.67 - 150.67 = 7,743

Therefore, at the end of the month you still owe

7,743 + (0.0145)(7,743) = 7,855.27

Thus, your $150 payment has reduced your debt by 7893.67 - 7,855.27 =$38.40

Average Daily Balance Method

One of the most common methods used by CC Companies.

1. Add the outstanding balance for your account for each day of the month.

2. Divide the total in step 1 by the number of days in the month to find the average daily balance.

3. To find the finance charge, use the formula I=Prt, where P is the average daily balance found in step 2, r is the annual interest rate, and t is the number of days in the month divided by 365.

Problem

Suppose that you begin the month of January (31 days) with a CC balance of $375.89. Assume that your card has annual interest rate of 19.2% and during January the following adjustments are made on your account.

Jan 7: A payment of $85.89 is credited to your account.

Jan 15: You charged $28.67 for gas.Jan 23: You charged $ 45.56 for going

out with a friend.Use the average daily balance to

compute the finance charge that will appear on you February CC statement.

Day Balance

# of days * balance

1, 2, 3, 4, 5, 6 375.89 6*375.89 = 2255.34

7, 8, 9, 10, 11, 12, 13, 14

290 8*290 = 2320

15, 16, 17, 18, 19, 20, 21, 22

318.67 8*318.67 = 2549.36

23, 24, 25, … 31 364.23 9*364.23 = 3278.07

The average daily balance sum of the last column and divide by # of days in the particular month. As seen above.

# of days * balance6*375.89 = 2255.34

8*290 = 23208*318.67 = 2549.369*364.23 = 3278.07

31

07.327836.2549232034.2255

We next apply the simple interest formula.

Where P = $335.57, r = 0.192, and t =

Therefore I = Prt =

57.335

365

28

94.4365

28)192.0)(57.335(

Therefore your finance charge for February will be $4.94.