A loan of $100,000 is made today. The borrower will make equal repayments of $2950.82 per month with the first payment being exactly one month from today. The interest being charged on this loan is constant (but unknown).

For the following two scenarios, calculate the interest rate being charged on this loan, expressed as a nominal annual rate in percentage:

(a) The loan is fully repaid exactly after 38 monthly repayments, i.e., the loan outstanding immediately after 38 repayments is exactly 0.

(b) The term of the loan is unknown but it is known that the loan outstanding 2 years later equals to $50014.53.