A deposit account pays $10\%$ per annum with continuous compounding. Consider the following statements. I. The equivalent semi$-$annually compounded annualized interest rate is $10\mathrm{.}2542\%.$ II$.$ The interest paid at the end of the first $3$ months on an initial investment of $$1,000,000$ in the deposit account is $$51,271($rounded to the nearest dollar$)$ Which of the following is correct? Question $9$Answer a$.$ Statement I is correct, Statement II is incorrect. b$.$ Both statements are correct. c$.$ Both statements are incorrect. d$.$ Statement I is incorrect, Statement II is correct.