Introductory rate on a credit card is 2.1% per year compounded monthly
for 6 months, then increases to 21% compounded monthly. If I transfer
a balance of 6000 to this card, and make NO monthly payments - how
much interest will be owed at the end of one year?

This was a nice question and it made me realise the sort of interest I
am paying on my credit card!

As you may know compound interest is interest that is paid based on
previous interest. Due to this your monthly interest per month break
down is as follows.

Month 0    $6000 Interest of 2.1% $126 
Month 1    $6126 Interest of 2.1% $128.65
Month 2    $6254.65 Interest of 2.1% $131.343566
Month 3    $6385.99 Interest of 2.1% $134.11
Month 4    $6520.10 Interest of 2.1% $136.92 
Month 5    $6657.02 Interest of 2.1% $139.8
Month 6    $6796.82 Interest of 21% $1427.33 
Month 7    $8224.15 Interest of 21% $1727.07
Month 8    $9951.22 Interest of 21% $2089.76
Month 9    $12040.98 Interest of 21% $2528.61
Month 10    $14569.59 Interest of 21% $3059.61
Month 11    $17629.20  Interest of 21% $3702.13
Month 12    $21331.33

Your final bill will be $21331.33.

You will owe a total of $15331.33 in interest.

I hope this answers your question, any comments let me know.

--Keystroke-ga

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Clarification of Answer by keystroke-ga on 27 Jul 2006 05:56 PDT

The comments below are EXACTLY the reason I have come back to clarify my answer.

You canause this website to check any future questions

http://math.about.com/library/blcompoundinterest.htm

I believed my initial answer to be incorrect, 

The amount you will owe after the first 6 months is

6062.67 
Interest of 62.67

In the calculator enter 6000 as the starting balance, enter 2.1 as the
rate and enter the period as 0.5 years (6 months).

To work out the remaining compound interest take the total of 6062.67
as your starting rate, change the interest rate to 21 and click
calculate again, this gives you a total of 6668.94.

Total interest of 668.94

The person who posted "Correct amount is $1531.78 in interest...I'd
get your $5 back" is wrong.

As you can see from the calculator, even if you had a full year of
interest, without an introductory rate, at 21%, your total final
interest is only $1260 giving you a total of $7260 payable at the end
of the year. Even baring this in mind $1531.78 is much too high.

I am sorry about my first mistake and hope that my clarification
restores your faith.

--Keystroke-ga

The answer is incorrect. The interest rates given in the question are
per year, NOT per month.

Correct amount is $1531.78 in interest...I'd get your $5 back

In order to pay close to 1531.78 dollars in interest on this loan, the
person would have to borrow 7294 dollars at 21% for the full year.

--Keystroke-ga

You should definately get your $5 back.  The answer of $668 you
received is wrong (though not nearly as wrong as the first answer you
were given), because you've specifically requested that interest be
compounded on a monthly basis, yet the $668 figure does not take this
into account.  With the interest being compounded monthly (which is
how the credit card company would in fact calculate the interest), the
actual figure is $728.  But what would I know, it's not like I'm
charging for this stuff...