# Credit cards: How long to pay off balance, assuming that....

#### Btoepp

##### New member
Okay, this problem is kickin me around somethin fierce, please help!

Joe College decides he wants to buy a top of the line entertainment system. The only problem is he can’t afford the $5,000 it will cost him. He decides to put it on his credit card. His card currently charges him 0.75% using the daily average balance on purchases and he can afford to spend$300 per billing cycle making payments.

Part 1: Figure out how long it will take Joe to pay off the credit card if his Original purchase is on the tenth day of the first billing cycle and his 300 payments are made on the 12th of each subsequent 30 day billing cycle. Determine how much his endeavor really costs him and how much interest he pays.

#### stapel

##### Super Moderator
Staff member
What formulas have they given you to work with (and how are their variables defined)? How far have you gotten in applying these formulas?

Please be complete. Thank you!

Eliz.

#### Btoepp

##### New member
Average daily balance is found by adding the unpaid balances for each day of the billing period and dividing by the number of days in the billing period.

I= Prt r=mo rate t one month

#### Btoepp

##### New member
Does that mean that i don't count the payments until the next month? If it says his original payment was on the 10th and each payment is due on the 12 of each subsequent billing cycle then i wouldn't count this time?

#### stapel

##### Super Moderator
Staff member
stapel said:
What formulas have they given you to work with (and how are their variables defined)?
Btoepp said:
I= Prt r=mo rate t one month
All you've been given to work with is just the simple-interest formula? :shock:

I mean, you can probably do it this way... eventually.... But considering that you'd have to work with daily interest charges and three hundred payments, I can only imagine how long this would take! :?

You've got to have something better to work with: annuity formulas, compound-interest formulas, something! Please consult with your instructor regarding better methods and/or formulas. :idea:

Eliz.

#### Btoepp

not 300 payments. $300 payments #### stapel ##### Super Moderator Staff member Part 1: Figure out how long it will take Joe to pay off the credit card if...his 300 payments are made on the 12th of each subsequent 30 day billing cycle. Btoepp said: not 300 payments.$300 payments
Ah. Another typo. Still, that doesn't change the basic fact that, lacking any proper tools for dealing with this, you're in for a very long slog. I don't envy you! :shock:

Eliz.

#### Btoepp

##### New member
Well, if anyone wants to take a shot at it, here's my understanding

5000(1)+ 4700(30)
30

= 4866.67

I=Prt
I= 4866.67(.0075)(1)
I=36.50

What do I do with this afterward? Do I subtract it from his monthly payment on the creadit card?