# Determine credit card interest?

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• January 18th 2009, 06:36 AM
Lightheaded
Determine credit card interest?
How to determine credit card interest? I’m not sure how to use the example provided in my math book. It just does not seem to work for me.

Book example:

Previous Balance: $150.00 Minimum payment:$10.00
Interest per-annum: 18.6% (compounded daily)

$
140 * (1 + \frac {0.186}{365}) (365 * \frac {1}{12})
$

= 142.19

----------------

First off, if I enter that in my calculator I receive a syntax error; with or without the (365 x 1/12)

Second, if I use my own formula I receive a different answer:

1. 0.186 ÷ 12 = 0.0155 (Monthly Rate)
2. 0.0155 x 140 = 2.17 (different then the 2.19 shown in the example)

Please clarify!
• January 18th 2009, 09:41 AM
Grandad
Credit card interest
Hello Lightheaded
Quote:

Originally Posted by Lightheaded
How to determine credit card interest? I’m not sure how to use the example provided in my math book. It just does not seem to work for me.

Book example:

Previous Balance: $150.00 Minimum payment:$10.00
Interest per-annum: 18.6% (compounded daily)

$
140 * (1 + \frac {0.186}{365}) (365 * \frac {1}{12})
$

= 142.19

----------------

First off, if I enter that in my calculator I receive a syntax error; with or without the (365 x 1/12)

Second, if I use my own formula I receive a different answer:

1. 0.186 ÷ 12 = 0.0155 (Monthly Rate)
2. 0.0155 x 140 = 2.17 (different then the 2.19 shown in the example)

Please clarify!

The formula that the book gives (or, at least, should give) is:

$140\times\left(1 + \frac {0.186}{365}\right)^{ \frac {365}{12}}$

which does give the answer 142.19.

Let me explain (1) why this formula is correct; (2) why your method is incorrect.

(1) Assuming there are 365 days in a year, the daily percent interest rate is $18.6 \div 365= \frac{0.186}{365}$ as a decimal. So to find the total amount owing after one day, we multiply the original amount owing by $1 + \frac{0.186}{365}$. So if the original amount is \$140, then after one day the amount owing is $140 \times \left(1 + \frac {0.186}{365}\right)$.

Each day that passes, the amount owing is $1 + \frac{0.186}{365}$ times what it was the day before. So after 2 days the amount owing is:

$140 \times \left(1 + \frac {0.186}{365}\right) \times \left(1 + \frac {0.186}{365}\right) = 140 \times \left(1 + \frac {0.186}{365}\right)^2$

After $n$ days the amount owing will be $140 \times \left(1 + \frac {0.186}{365}\right)^n$

So in one calendar month (= $\frac{365}{12}$ days), the amount owing is:

$140 \times \left(1 + \frac {0.186}{365}\right)^{\frac{365}{12}}=142.19$

(2) The interest is compounded daily. So you need to calculate the amount owing at the end of each day, as I have shown you above. That means that in day 2, you'll pay a little bit more interest than you did in day 1: the interest on the interest you paid in day 1. And so on for day 3, 4 ... This extra bit each day adds up to a couple of pence by the end of the month.

Do you understand this now?

Grandad
• January 18th 2009, 11:11 AM
Lightheaded
re: Credit card interest
Hi Grandad - Thank you for your reply.

Your formula is correct, or rather better shown (smile). I was unsure on how to format the numbers with code, but slowly learning, by looking at your examples.

Your explanation is great, very clear and easy to follow – thank you!

Unfortunately, I’m having trouble entering the data into the calculator, and getting results.

140 x (1+0.186/365)^2 or any similar format I get a Syntax Error message

If I use the calculator in Microsoft Math, I receive the following:

Input: 140 (1+0.186/365)^2
Output: 233381425543/1665312500
Decimal: 140.142721286846

So I’m sure I understand the formula you presented, but I cannot for the life of me, enter the formula into the calculator and get a result I understand.

I’m using a Texas Instrument TI-34 II

Any additional help would be appreciated.

Cheers,
• January 18th 2009, 12:34 PM
Grandad
Calculator
Hello Lightheaded-

While I'm working on the computer I use the Windows Calculator - in Scientific view. To get the answer to a formula like that, I use the button labelled x^y. (I expect you have a similar one on your TI calculator as well.)

So y is the index, which = 365/12. Work this out and store the result in memory. x is the value you get for $\left(1+ \frac{0.186}{365}\right)$. When you've got this value, press the x^y button, and then memory recall, and =, and you have your result. Multiply by 140 to find the final answer.

OK?

Grandad
• January 18th 2009, 02:13 PM
Lightheaded
Thank you very much, you've been very helpful. I appreciate your time.

Cheers. Until I have another question. (smiles)
• January 19th 2009, 05:59 AM
Lightheaded
Grandad: I finally figured out why I was having difficulties with the formula input on the calculator. Rather than use the division key I was using the forward slash “/”, as I would for a fraction. This was causing the syntax error. I was under the impression that the slash would act the same as division.

Again, thanks for your help and guidance!

Cheers,