Solve the following:

Part a.Debra wins $200,000 in a lottery. She takes only $20,000 in cash and invests the balance at a rate of interest of 10% pa, with interest compounded on a monthly basis, on the understanding that she will receive 160 equal monthly payments with the first one to be made in 2 years. Find the size of the payments.

Part b.An investment firm (Firm A) pays 10% interest per annum, compounded on a quarterly basis. To remain competitive, the investment manager of another firm (Firm B) is willing to match the interest rate offered by Firm A, but interest will be compounded on a monthly basis. What nominal rate of interest must Firm B offer to its clients ?

Write all the formulas and explain your answer.