I. Your friend has a credit card debt of $$10,000$ on a card that charges $9\mathrm{.}5\%$ interest compounded monthly.

The credit card offers a promotion of no payment needs be made for the next $12$ months, but interest will

accrue.

a$.$ Your friend wants you to determine what she will owe at the end of the next twelve months if she

makes no payments until then.

b$.$ If your friend could take out a one year loan today from a bank at an annual rate

of $9\mathrm{.}75\%$ which she would use to pay the credit card balance off now, determine how much less or more

she would owe the bank at the end of the year than she would have owed the credit card company in part a$.$