Otto has the following strategy to save for his retirement. On January 1, 2022, he deposits $ 80,000 into a savings account. From then on, he will add an additional fixed amount x into his savings account on every following January 1 up to and including January 1, 2052. Assume that the annual interest rate is constant at 4% and is compounded yearly. a) What is the amount x if Otto wants to purchase a perpetual annuity, which pays $50,000 every January 1, starting on January 1, 2058? b) What is the amount x if Otto wants to purchase an fixed-time annuity which pays $50,000 every January 1, starting on January 1, 2058 with the last payment being received on January 1, 2087?