2. (20 points) Today is December 31 of 2023 , and you are considering to buy an annuity. Its current market price is $1,000. It pays quarterly for 20 years, on January 1 , April 1 , July 1 , and October 1 of each year. Its first payment is going to come on January 1 of 2024 and the last one on October 1 of 2043 . Annual percentage rate is 8%. (a) (5 points) What is annual payment of this annuity? (b) (7 points) What will be the fair price of the annuity on January 1 of 2025 (right after the payment)? (c) (8 points) What will be the fair price of the annuity on December 1 of 2024