Your financial planner at the bank offers you a new investment product that earns interest using the following scheme: Any amount deposited does not earn interest for the first month it is in the account. Afterwards, it earns interest at a rate of 0.5% at the end of every odd month (January, March, May, July, September, November), and 1% at the end of every even month (February, April, June, August, October, December). (Note: These rates are not APRs.) You'd like to make three equal deposits of P to the account on October 1, 2022, February 1, 2023, and April 1, 2023. Determine P so that you have exactly $2000 on July 1, 2023.