Look at these two competing credit card offers:

$\backslash$table$[[$Offer $A,$Offer B$],[\backslash$table$[[$$$120$ annual fee$],[0\%$ interest for the first year $(22\%$ interest$],[$thereafter$)],[$Extra travel miles$],[0\mathrm{.}5\%$ interest on CashAdvance$],[$Discount on travel insurance$],[$$$300$ free credit when signing up$],[21$ day grace period$],[$No minimum payment$]],\backslash$table$[[$No annual fee$],[18\mathrm{.}99\%$ interest rate$],[3\mathrm{.}8\%$ interest on CashAdvance$],[{21}_{d}ay{?}_{(})$ grace period$],[$Minimum payment of $$10$ or $2\%$ of balance$],[$$$50$ penalty charge for missing a payment$]]]]$

a$.$ Describe a situation where Offer A would be a better deal and a situation where Offer B would be a better deal.

b$.$ Suppose you charge $$1200$ to one of these cards. Assuming that interest is compounded monthly, under which card would you be better off if you don't pay anything $...$

i$.$ For $6$ months

ii$.$ For $1$ year

iii. For $3$ years

c$.$ Show your calculations and any assumptions you made for your answer to part $($b$).$