Solve the following problems involving annuity functions.

a) Claire is planning for her retirement and estimates that she will need retirement savings total of $1.8 million on her 55th birthday. She plans to fund this by making annual deposits on each birthday up to and including her 55th and estimates that she can earn 6% interest. Find her minimum annual deposit if she starts them on her 30th birthday.

b) Claire decides to invest $X from age 30-50, and $2X starting at age 51. How much should X be to meet her goal?

c) A loan for $16,000 is to be repaid with 6 annual payments of $2850 with the first payment made today. Find the effective rate of discount d charged on the loan to the nearest %