Simon recently received a credit card with a $15\%$ nominal interest rate. With the card, he purchased an Apple iPhone $7$ for $ $360\mathrm{.}34.$ The minimum payment on the card is only $ $10$ per month. month$($s$)$ b$.$ If Simon makes monthly payments of $ $35,$ 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$)$ $