Not only does the interest get charged from Day 1 on new purchases as long
as you have a revolving balance, but the credit card agreement often says
something to the effect that any partial payment is applied first to the
interest to date, and then transfer balances on which no interest is being
charged and so the bank is losing money on it, then to other transfer
balances and cash advances (and no refund of that 3% fee that was
collected up front on the cash advance) and finally
to the purchases starting from the most recent back to the oldest one.
Even the FAQ on my card site says in simple language
"We apply payments and credits at our discretion, including in a manner most favorable or convenient for us." (see mhoran_psprep's
answer).
The moral is indeed what Dheer has already told you: do not carry a
revolving balance on a credit card and if you have a revolving balance,
pay it off as soon as possible, Do not wait for the end of the
grace period; if possible, pay it off the day the statement is
issued, or if you can make only a partial payment, make it as soon
as possible. Make multiple partial payments each month if you have
cash flow problems, or improve your cash flow by forgoing one or more
of the many Grande Vente Mocharino Espresso Lattes you consume each
day. Credit card debt is close to the worst kind of debt that you
can have, and it is best to get out from under as soon as possible.
Remember, there is effectively no grace period as long as you have
a revolving balance on your credit card. You are paying interest
for every one of those days.