Question

Peyton has a credit card with an annual rate of 24.7% compounded monthly. She used the credit card to purchase cleaning supplies in the amount of $189.56. She can pay up to $72 on the credit card each month. How much total interest will she pay?

$3.90

$7.47

$8.29

Answer 1

This is just not a good question. "up to" That is not meaningful.

If she pays $10 / month, it will be more interest.
If she pays $70 / month, it will be less interest.

How much WILL she pay?

Answer 2

Erm, I'm not sure

Answer 3

I'm so lost D:

Answer 4

Well, as is so often the case, lacking a good problem statement, we have to make a good assumption and solve whatever problem we manage to define.

It is kind of reasonable to suggest that if she CAN pay $72 / month, she WILL pay $72 / month. The problem statement DOES NOT say this. Let's assume it and move on.

i = 0.247 -- Annual Interest Rate to be applied monthly.
j = i/12 = 0.0205833 -- Monthly Interest Rate
r = (1+j) -- Monthly accumulation factor.

Can you accept this one assumption ($72/month) and these three definitions (i, j, r)? I haven't tried to solve the problem, yet. I'm just building the tools!

Answer 5

Yep sounds resonable

Answer 6

The we're ready to roll...

189.56r - 72 = 121.46

Do you believe the state of affairs after one month, having accumulated interest and having made one payment?

Answer 7

Yes

Answer 8

You do month 2. Accrue more interest and make another payment.

Answer 9

What do you mean?

Answer 10

You do for month #2 exactly what I did for month #1. Start with 121.46 and see where it leads.

Answer 11

What did you do for month 1?

Answer 12

You said you believed it.

189.56r - 72 = 121.46

Answer 13

I didn't know the statement related to the problem

Answer 14

I'm not sure what to do

Answer 15

Start with the beginning balance

189.56

Accrue the interest for one month

189.56r

Make a payment

189.56r - 72

Result is the remaining balance after the first month and the first payment.

121.46

Answer 16

Okay, so I don't know what to do for month 2?

Answer 17

EXACTLY the same thing.

Answer 18

Are you saying I plug in 24.7% for r?

Answer 19

No, we defined r up above. That's the deal with these problems. Simply keeping track of everything is the hardest part.

r = 1 + 0.247/12 = 1.020583

It is a monthly accumulation factor. It can be used to calculate the total interest and basis at the end of one month.

Note: I NEVER would say "plug in". There is a principle called "substitution" that would be applicable.

Answer 20

Okay so 2 months would equal 2.002058333

Answer 21

Is there any way we can finish this faster, I wantto go to bed in like 10 minutes and I need to wake up early, this is the last question I have to do x.x

Answer 22

No.

Start with the beginning balance

121.46

Accrue the interest for one month

121.46r

Make a payment

121.46r - 72

Result is the remaining balance after the second month and the second payment.

You tell me what it is...

Answer 23

Is the answer $3.90 ?

Answer 24

At first I got $3.41 but that was wrong

Answer 25

You need to understand the idea of accruing interest and making periodic payments, You will have to tell me how you managed those answers. I do not care about guessing. Show your work and I can see what it is you are doing.

Answer 26

I'd love to but unfortunately I don't have the time now, so I'll go with $3.90, thank you anyways

Answer 27

That's about half the correct answer. When you have the time to learn, feel free to come back.

Answer 28

Keep in mind that it is a horrible problem statement.

Answer 29

Okay I'll come back tomorrow and explain how I got $3.41