please solve this problem without using excel and show all steps

Karl borrows $200,000 on January 1, 2017 to be repaid in 30 annual installments at an effective annual rate of interest of 6%. The first payment is due on January 1, 2020. Instead of annual payments she decides to make monthly payments equal to one-twelfth the annual payment beginning on July 1, 2020. Determine how many months will be needed to pay off the loan. A. 423 B. 424 C. 425 D. 426 E. 427