Jaime needs to buy a new refrigerator for his apartment. He found what he needed for $1,300 at a well-known appliance store. The store is offering two options for Jaime to finance the appliance:

Option I: A store credit card with a $1,500 limit:

1) The credit card charges 16.5% annual interest rate.

2) The minimum monthly payment is $100 plus the monthly finance charge.

3) No down payment required

4) The loan is expected to be paid off in12 months to avoid additional penalties.

Option II: The appliance store offers an installment loan for his purchase:

1) Loan charges a simple interest rate of 12.5%.

2) Loan must be paid off in 12 equal payments to avoid penalties.

3) A $300 down payment is required.

The annual interest rate on an amount borrowed or a loan is the increment added to the loan at a particular rate over the desired period of time.

The objective of this question is to weigh the two options and determine the best means by which Jamie could get a new refrigerator for his apartment.

Option 1:

The annual interest rate for the first card = $1300 × 16.5%

The annual interest rate = $214.5

The minimum monthly payment is $100 plus the monthly finance charge.

The monthly finance charge on a credit card can be estimated by finding the average daily balance using the Annual interest rate and the days of the billing cycle.

The monthly finance charge [tex]\mathbf{=1300\times \dfrac{0.165}{12}}[/tex]

The monthly finance charge = $17.88

Now,

The minimum monthly payment is $100 + $17.88

The minimum monthly payment for the first month = $117.88

Provided there is no down payment;

In 12 months, Jaime would have paid off the loan with an additional interest of $214.5

Total amount paid = ($117.88 × 12)+$247.5

= $1629.06

Option 2.

The appliance store offers an Installment loan;

The loan charges a simple interest rate of 12.5%;

Using;

[tex]\mathbf{S.I = \dfrac{PRT}{100}}[/tex]

Since the loan must be paid in 12 equal payments, we can say the loan is paid monthly which is equivalent to 1 year.

i.e.

Time (T) = 1 year

[tex]\mathbf{S.I = \dfrac{1300 \times 12.5 \times 1}{100}}[/tex]

S.I = $162.5

Given that;

The down payment = $300

In the total amount of $1300, Jamie has an outstanding amount of $1000 to pay.

Thus, In 12 equal payment times,

Jamie gets to pay = $1000/12

Jamie gets to pay = $83.33 each time.

Total amount paid = $162.5 + 1300

Total amount paid = $1462.5

Therefore, we can conclude that Jamie should accept the second option to buy a new refrigerator for his apartment since the total amount paid in option 2 is lesser than that of option 1.

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