$($Annuity payments$)$ Calvin Johnson has a $$$$4$ comma $500$ debt balance on his Visa card that charges $15\mathrm{.}8$ percent APR compounded monthly. In$2009,$ Calvin's minimum monthly payment is $3$ percent of his debt$$ balance, which is $$$$135.$ How many months$($round up$)$ will it take Calvin Johnson to pay off his credit card if he pays the current minimum payment of $ $135$ at the end of each$$ month? In$2010,$ as the result of a federal$$ mandate, the minimum monthly payment on credit cards rose to $4$ percent. If Calvin made monthly payments of $$$$180$ at the end of each$$ month, how long would it take to pay off his credit$$ card?

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Part $1$

a$.$If Calvin made monthly payments of $$$$135$ at the end of each$$ month, how long would it take to pay off his credit$$ card?

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enter your response here months$($Round up to the nearest$$ unit.$)$

Part $2$

b$.$If Calvin made monthly payments of $$$$180$ at the end of each$$ month, how long would it take to pay off his credit$$ card?

$$

enter your response here months$($Round up to the nearest$$ unit.$)$