Med Diagnostics Inc. borrowed \($200\),000 from a lender for a new blood analyzer module to improve accuracy and consistency of its tests. The rate was 6 percent, 2 percent above the prime rate. The loan was to be paid back in equal monthly amounts over 7 years.

a. How much is the monthly payment?

b. Two years (24 months) of payments have been made. What is the principal remaining after 2 years?

c. The prime rate has now risen, and the bank can make loans to other customers, if it has the available capital, for 8.5 percent payable in equal monthly payments. The bank contacts Med Diagnostics and offers to let them pay off the loan immediately for the amount owed at the end of year 2, less \($X\). What is the range of \($X\) that would be beneficial to both the bank and Med Diagnostics?