Question

Nash uses a credit card with a 17.8% APR, compounded monthly, to pay for a cruise totaling $1,789.17. He can pay $650 per month on the card. What will the total cost of this purchase be?

A. $1,840.91
B. $2,107.64
C. $1,789.17
D. $2,330.08

Answer 1

Month 1:

Balance Before Interest Is Added: 1789.17 (This is your initial balance)

-----------------------------

Calculate Interest:

I = Prt
I = 1789.17(0.178)(1/12)
I = 26.539355
I = 26.54

The amount of interest alone for month 1 is 26.54. Add this to the balance 1789.17 to get 1789.17 + 26.54 = 1815.71

-----------------------------

Interest has been calculated and has been added on. This is done BEFORE the payment is made. Now you make the payment of 650

Balance before payment: 1815.71
Make payment: 1815.71 - 650 = 1165.71
Balance after payment: 1165.71

================================================================================================================

Month 2:

Balance Before Interest Is Added: 1165.71 (this amount is carried over from last month)

-----------------------------

Calculate Interest:

I = Prt
I = 1165.71(0.178)(1/12)
I = 17.291365
I = 17.29

The amount of interest alone for month 2 is 17.29. Add this to the balance 1165.71 to get 1165.71 + 17.29 = 1183

-----------------------------

Interest has been calculated and has been added on. This is done BEFORE the payment is made. Now you make the payment of 650

Balance before payment: 1183
Make payment: 1183 - 650 = 533
Balance after payment: 533

================================================================================================================

Month 3:

Balance Before Interest Is Added: 533 (this amount is carried over from last month)

-----------------------------

Calculate Interest:

I = Prt
I = 533(0.178)(1/12)
I = 7.90616666666667
I = 7.91

The amount of interest alone for month 3 is 7.91. Add this to the balance 533 to get 533 + 7.91 = 540.91

-----------------------------

Interest has been calculated and has been added on. This is done before the payment is made. Now you make the payment of 540.91

Old Balance (before payment): 540.91
Make payment: 540.91 - 540.91 = 0
Balance after payment: 0

================================================================================================================



The balance is now 0, so you are done. This is assuming that NO additional charges are made to the card.



Here's a summary of what we know and what we figured out (or calculated):



What we know:

Initial Debt (or Initial Balance): 1789.17

APR: 17.8%

Monthly Payments = $650 a month (except for possibly the last payment)

--------------------------------------------------------------------------------------------

What we just found out:

There are 3 payments made total and those payments are: 650, 650, 540.91


Total Cost: 650 + 650 + 540.91 = 1840.91

Total Cost: 1840.91