Question

Rita owes $9,739 on a credit card with a 21.5% interest rate compounded monthly. What monthly payment should she make to pay off this debt in six years, assuming she does not charge any more purchases with the card?

Can anyone explain this? step-by-step?

Answer 1

i = .215 -- The annual interest rate.

What is the monthly interest rate?

Answer 2

I don't know :/

Answer 3

0.017?

Answer 4

0.215 / 12 = 0.017916...

Use WAY more decimal places. Three will just not do.

Answer 5

Okay! Got it! Now what? :)

Answer 6

Let's just think about it for a moment. If we paid off the whole thing in ONE month, how much would we pay?

Answer 7

Hmm.. I don't really know. I don't know how to even calculate that :(

Answer 8

Really, then, you cannot solve this problem. Why have you been given this problem? Is it a placement exam?

Answer 9

Yeah, it's a practice/pretest sort of thing and I want to know how to solve this kind of problem. So I can learn:)

Answer 10

Well, you will have to know how to pay interest and how to discount for interest.

The whole idea stems from a concept called the "Time Value of Money"? Heard of it?

Answer 11

Mm I think briefly.

Answer 12

The idea is simple enough.

Which of these two is more valuable to you?

$100 today
or
$100 one month from now
??

Answer 13

probably today? Lol

Answer 14

Good. Keep smiling. I'm going to mess with your head a little.

How about these two:

$100 today
or
$200 one month from now
??

Answer 15

Hmmm...I'm still gonna say 100 today.

Answer 16

It probably depends on how much you need the $100!!

Anyway, this is the idea. Money in the future is just not worth as much as the same money RIGHT NOW. You just demonstrated that sometimes MORE money in the future might not be as valuable as LESS money right now.

Unfortunately, everyone has a different opinion, right? I suppose you will believe that many folks would have picked the $200, even though they had to wait a month.

Answer 17

Right. Now how does this help solve my question?? ;)

Answer 18

You have been very patient. That's the philosophy. Since everyone has a different opinion, we had to invent some sort of mechanism to talk about the difference in Time Value of Money. This mechanism is "Interest".

If we say interest is at 3%, we could be saying that we feel EXACTLY the same $100 TODAY as we do $100 + 3%($100) = $100(1 + 3%) = $100(1.03) = $103 a year from now. Make sense?

Answer 19

Yes :)

Answer 20

Said another way, since we know that $100 today is the same as $103 in a year, since $100*(1.03) = $103, we might also say that $100 in a year is the same as $100/1.03 = $97.09 today.

It is important that you see that factor of 1.03 can be used both ways.

It can INCREASE current value to a future value: $100*(1.03) = $103.00 or
It can DECREASE future values to a current value: $100/1.03 = $97.09

Answer 21

Okay, I know that(: This all makes sense.

Answer 22

I only have 10 minutes to finish this question )):

Answer 23

I'm pretty sure the answer is $241.82 but I'm not sure how to do it step-by-step to make sure it is the right answer.

Answer 24

Whew! That was a big piece. Now, you are ready to answer my first question.

We have $9,739 on a credit card.
ANNUAL interest is 21.5% or 0.215
MONTHLY interest we said was 0.01791666...

My question was, if we pay it all of in one month, how much will we pay? In other words, we have a value TODAY of $9,739. What is the value of this sum in one month, given that monthly interest is 1.791666...%?

Answer 25

Would I times 9739 by 0.01791666?

Answer 26

Great try, but not quite. That is just the interest that will need to be paid. Add the original sum and you have it.

9739 + 9739*(0.01791666..) = 9739(1.0179166..) = 9913.49

Answer 27

Ahhh okay. So what next? :)

Answer 28

We need some words to go on. Another way to SAY that whole thing is this.

9739 TODAY is equivalent to 9913.49 in one month at 1.791666% interest. Here's the important language, "The have the same PRESENT VALUE"

Like this:

The present value of 9739 today is 9739. That's pretty obvious.

What is the present value of 9913.49 payable in one month? Well, that's 9913.49/1.017916666 = 9739

You need to see how this works and what that language means. How are we doing?

Answer 29

Good :)

Answer 30

We are about to take a massive leap.

What is the Present Value of $10,091.11 payable in TWO months?

Answer 31

I don't....I....9739.002? Or??? Not sure.

Answer 32

Running out of time :((

Answer 33

There is some rounding, since you can't use infinitely many decimal places.

Just numbers for a moment. Then I'll talk about them
10091.11 / 1.0179166666 = 9913.49
9913.49 / 1.0179166666 = 9739.00

What we just said was this:

The present value of 9739 today is 9739.
The present value of 9913.49 in one month is 9739.
The present value of 10091.11 in two months is 9739.

You should be at least a little astounded that they all came out with the SAME present value.

We have quite a bit to go. I can write the whole book and spend all night. If you're out of time, then you're out of time.

Answer 34

Well, I know the answer I just want to see how someone would solve it. It's a lot easier for me to have someone show the steps and solve it. I learn better that way. To see the process.

Answer 35

Oh, we're learning the process. Frankly, I think you are doing quite well.

If you can get anywhere near this next question, you are ready for the WHOLE answer!

We have established that if we want to pay off the 9739 NOW, it will cost 9739.
We have established that if we want to pay off the balance in one month, it will cost 9913.49.
We have established that if we want to pay off the balance in two months, it will cost 10091.11.

The REALLY BIG question is this. If we with to pay it off in TWO equal installments, one in one month and the other in two months, how much shall we pay for each installment?

If you get this, we are almost done.

Hint: Don't say anything that isn't about 1/2 the numbers we've been talking about. It's two payments and they are not very far into the future.

Answer 36

5435.741?

Answer 37

Well, let's see...

9739, today increases to 9739*(1.017916666) = 9913.49 <== This is at time One Month

If we then pay off 5435.74, that leaves 9913.49 - 5435.74 = 4477.75 <== This is still at time One Month

4477.75 at time one month increases to 4477.75*(1.017916666) = 4557.98 <== This is at time TWO months.

If we then pay off 5435.74, that leaves 4477.75 - 5435.74 = -957.99 <== This is still at time Two Months.

And we have WAY OVERpaid. Are you happy with that result?