Please solve manually using formulas/actuarial symbols. Show complete solutions.

1. A fund earning 8% annual effective rate of interest is being accumulated with payments of 500 at the beginning of each year for 20 years. Find the maximum number of withdrawals of 1000 that can be made at the end of every year under the condition that once a withdrawal is made, withdrawals must continue through the end of the 20-year period.

2. Max has an inheritance in a trust fund left by his recently deceased grandfather that will pay 50,000 at the end of each year indefinitely into the future. He just turned 60 years old and he believes that this perpetuity-immediate does not meet his retirement needs. He wishes to exchange the value of his inheritance in the trust fund for a 5-year deferred annuity-immediate that provides annual payments for 20 years. If the trustee agrees to his proposal, how much annual retirement income would he receive? The trust fund is earning an annual effective rate of interest of 5%.