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?

$1,840.91

$2,107.64

$1,789.17

$2,330.08

Answer 1

were you able to get anywhere with this one?

Answer 2

no

Answer 3

Ok the basic steps are this

Step 1) Calculate interest
Step 2) Add the interest onto the balance
Step 3) Subtract the monthly payment (of $650 or less)

You follow these steps until the balance is $0

During these steps, you keep track of how many payments are made and how much is made for each payment. Then you add up those payments to get the total cost.

Answer 4

Does that help or did you need me to go into further detail?

Answer 5

I think I could do that

Answer 6

ok tell me what you get so I can check it

Answer 7

actually could you go into further detail lol

Answer 8

Sure thing, hopefully this isn't too much, but this is how you completely break it down

Answer 9

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

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

Answer 10

thank you very much. I understand how to do it now :)

Answer 11

ok great, glad it's making sense now