Question

Cherie owes $6,230 on her Electronics Boutique credit card with a 20.4% interest rate. She owes $2,960 on her Miscellaneous Goods credit cards which has a 28.1% interest rate. What is the total monthly payment needed to pay off both cards in three years, assuming she makes fixed payments and does not charge any more purchases with the card?

$255.28

$355.40

$380.63

$343.41

Answer 1

What's your plan for this? You'll need to calculate each separately.

Fixed Payments
End of the Period (Month)
36 Months

Go!

Answer 2

m = b*i(1+i)^nt/(1+i)^nt-1

Answer 3

With that I got $355.40
, but i'm unsure of my answer.

Answer 4

Okay, tell me what that is supposed to be.

b = ??
i = ??
n = ??
m = ??
t = ??

This accomplishes two things:

1) It tells me you either know or don't know that you have the right idea.
2) It helps me make sure we are speaking the same language. Not all authors use the same notation.

And what was $355.40 supposed to be. It that the whole problem solution or just one of the pieces.

Answer 5

M is the monthly payment amount, B is the balance of the loan, i is the periodic interest rate, n is the number of payments per year, and t is the number of years of the loan.

Answer 6

i can be found by dividing the APR by the number of periods.

Answer 7

Just to be clear:

b = Balance = 6230
i = Periodic Interest = 0.2040/12 = 0.017
n = Payments per Year = 12
m = Monthly Payment Amount -- The thing we seek (Don't change notation. M and m should not mean the same thing!)
t = Loan Years = 3

Do we have an agreement?

We're doing only the first piece, right?

Answer 8

yes

Answer 9

Okay, let's have a look at that formula.

I evaluate your formula to give the correct answer, but there are two things wrong.

1) You appear not to have waded through it very well. Are you sure you have the denominator as \((1+i)^{nt} - 1\;rather\;than\;(1+i)^{nt - 1}\)?

2) What a silly formula. Why would calculate the accumulated value of payments to match the accumulated value of the original balance? It's a WHOLE LOT simpler to use the Present Value for such things.

Answer 10

Yes, it's (1+i)^nt -1, I actually got everything I just said from the lesson.. I really don't like it either. A lot of these equations and problems they give me are very vague and generic :/

Answer 11

That's okay. We don't have to panic unless you don't understand how to find the right formula. Since you DID find the right formula, we should be fine.

m = b*i(1+i)^nt/(1+i)^nt-1

nt = 36

(1.017)^36 = 1.8346545623617017467389184571245

(1+i)^36/[(1+i)^36-1] = 2.1981004419007117071215894065671

2.1981*0.017*6230 = 232.8008178

So, where did you go wrong?

Answer 12

I have no idea,232 isn't an answer choice though. This is all so confusing.

Answer 13

If I were writing the test, I would put it in the answer choices. Everyone who marked it would have worked only half the problem and gotten it wrong!!

Don't forget, we're doing only the Electronics Boutique credit card! We should not yet be looking for answers! Now, we have to do the other card!

b = Balance = 2960
i = Periodic Interest = 0.2810/12 = 0.02341666666666666666666666666667
n = Payments per Year = 12
m = Monthly Payment Amount -- The thing we seek
t = Loan Years = 3

Let's see what you get for this card.

Answer 14

There were answer choices, I wrote them with the problem
$255.28

$355.40

$380.63

$343.41

Answer 15

But with that I got #183, but that seems like a really big number, maybe I did something wrong

Answer 16

Whoops I mean 3183

Answer 17

Okay. For me, I NEVER want to see then answer choices until I think I have solved the problem.

Please tell me what you get for the monthly payment on the Miscellaneous Goods credit cards. We can then add the new value to the $231.81 already obtained, and we will have the result.

Answer 18

$3183.15

Answer 19

That's silly, and you know it. Try the formula again, VERY CAREFULLY, and produce a better result. I am not going to do this one for you. Do it like I did, above. Show EVERY intermediate result. No skipping steps. If you wander off, I can tell you exactly where.

Answer 20

$692.11

Answer 21

What is that?

Estimate first.

From the other card, the balance decreases by about half and the interest increases by about 1/3. So a good rough estimate would be 232.81*(4/3)/2 = 155 or so. Keep trying, VERY CAREFULLY, until you get something even close to that. No guessing and SHOW YOUR INTERMEDIATE RESULTS.

Answer 22

I'm confused, what are you asking me to do

Answer 23

b = Balance = 2960
i = Periodic Interest = 0.2810/12 = 0.02341666666666666666666666666667
n = Payments per Year = 12
m = Monthly Payment Amount -- The thing we seek
t = Loan Years = 3

Let's see what you get for this card.

Answer 24

I told you, I got 692.11

Answer 25

Well, then try it again and show me your intermediate results. Did you do it a piece at a time, like I did for the other card? Did you use a financial calculator. You are getting the wrong answer and there is no way for me to know how. You have to throw me some clues!

Answer 26

2960*0.023416(1+0.023416)^12*3/(1+0.023416)^12*3-1

Answer 27

Okay, you can write it. Now, let's see you calculate it.

What do you get for (1+0.023416)^12*3

Answer 28

2.300802215

Answer 29

Perfect. What do you get for:

(1+0.023416)^12*3/[(1+0.023416)^12*3 - 1]

Answer 30

1.768756

Answer 31

Perfect again.

What do you get for

2960 * 0.023416 * 1.768756

Answer 32

126.49

Answer 33

Try that again. Something went wrong.

Answer 34

122.59

Answer 35

That's it. This is the monthly payment for the second credit card. Now, we are ready to answer the problem. What is the total payment required to totally pay off BOTH in three years?

Answer 36

$355.40

Answer 37

Lol, you could have just said yes when I told you I got $355.40 it would have saved a lot of my time.

Answer 38

Yea!!!

I'm not much interested in time. If I had a time problem, I wouldn't be here volunteering. I'm interested in you learning.

I am not going to say this sort of problem is easy. I am going to say the hardest part is paying attention to every little detail.

Good work