To purchase a new couch that costs 2100 dollars, you set up a store credit card...

To purchase a new couch that costs 2100 dollars, you set up a store credit card that charges interest at 14.7 percent convertible monthly, beginning immediately. Each month that you do not make a payment (starting one month after you purchase the couch), you are charged a 30 dollar fee that is added to your card balance. Due to financial difficulties, you cannot make a payment until 6 months after you purchase the couch. To pay off the card balance, you decide to make 29 monthly payments that increase by 4.6 percent per month. How much is your first payment?

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Expert Solution

Let the first payment be 'x'

Default in Payment - 6 months

Late fee applicable - 5 months = $30*5 = $150

As the late fee is appliacble on payment failure on 1 month after the purchase so failure is of 6 month after the purchase so late fee will be applicable after the first month so for 5 montrhs it will be charged.

Intererst Calculation:

First month = 2100 * 14.7/100/12 = $25.725

Second month = (2100+25.725) *14.7/100/12 = $26.04

Third Month = (2100+25.725+26.04)*14.7/100/12 = $26.359

Fourth Month = (2100+25.725+26.04+26.359)*14.7/100/12 = $26.682

Fifth Month = (2100+25.725+26.04+26.359+26.682)*14.7/100/12 = $27.009

Sixth Month = (2100+25.725+26.04+26.359+26.682+27.009)*14.7/100/12 = $27.340

Total Interest = 25.725+26.04+26.359+26.682+27.009+27.340

= $159.155

Total Dues = 2100+159.155+150 (i.e. Principal + Interest + Late fee)

= $2409.155

Now the payment increases by 4.6% so new payment per month = 1.046x

Therefore,

1.046x*29 = 2409.155

x= 2409.155/1.046/29

= $79.43

Initial First Payment was of $79.43.

ekkarill92 answered 2 years ago

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