Tulip Company contacted two banks to obtain a $$10,000$ bank loan. Bank A will give a $120-$day loan at an annual rate of $12\%,$ while Bank B will give a $90-$day loan at an annual rate of $15\%.$ Assume a $365-$day year.a$.$ Based on the amount of interest to be paid, which bank loan should Tulip choose?b$.$ Compare the $120-$day and $90-$day rates on the loans by finding the effective annual rate for each loan. Assume each loan is rolled over throughout the year under the same terms and circumstances.c$.$ Based on the effective annual rate for each loan, which bank loan should Tulip choose?