Please show all formulas used and work please.

1.) Your financial planner has advised you to initiate a retirement account while you are still young. Today is your 35th birthday and you are planning to retire at age 65. Actuarial tables show that individuals in your age group have a life expectancy of about 75. If you want a $50,000 annuity beginning on your 66th birthday which will grow at a rate of 4 percent per year for 10 years:

a. What amount must you deposit at the end of each year through age 65 at a rate of 8 percent compounded annually to fund your retirement account?

b. After you have paid your last installment on your 65th birthday, you learn that medical advances have shifted actuarial tables so that you are now expected to live to age 85. Determine the base-year annuity payment supportable under the 4 percent growth plan with a 9 percent interest rate.