Alex has $42,000 that he wants to invest. He has the following possible investments: (1) Purchase a perpetuity immediate with annual payments for $42,000. The perpetuity will pay $100 at the end of the first year, $200 at the end of the second year, $300 at the end of the third year, etc. (2) Make a loan of $42,000 to Mary. Mary will repay the loan with level annual payments of $3,000 followed by a balloon payment. The annual effective interest rates for both investments are the same. (a) Find the annual effective interest rate for each investment. (b) Find the amount of the balloon payment.