Simon recently received a credit card with an $18\%$ nominal interest rate. With the card, he purchased an Apple iPhone $11$ for $$700.$ The minimum payment on the card is $$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?

b$.$ If Simon makes monthly payments of $$70,$ how many months will it be before he pays off the debt?

c$.$ How much more in total payments will Simon make under the $$20-$a$-$month plan than under the $$70-$a$-$month plan? Make sure you use three decimal places for N$.$