Simon recently received a credit card with a $15\%$ nominal interest rate. With the card, he purchased an Apple iPhone $11$ for $$650.$ The minimum payment on the card is only $$20$ per month.

a$.$ If Simon makes the minimum monthly payment and makes no other charges, how many months will it be before he pays off the card? Do not round intermediate calculations. Round your answer to the nearest whole number.

month$($s$)$

b$.$ If Simon makes monthly payments of $$65,$ how many months will it be before he pays off the debt? Do not round intermediate calculations. Round your answer to the nearest whole number.

month$($s$)$

c$.$ How much more in total payments will Simon make under the $$20-$a$-$month plan than under the $$65-$a$-$month plan? Do not round intermediate calculations. Round your answer to the nearest cent.

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