A self employed individual, Jimmy Carpenter, is opening a retirement account at a bank. His goal is to accumulate P$2371976$ in the account by the time he retires from work in $20$ years. A local bank is willing to open a retirement account that pays $10\%$ interest compounded semiannually, throughout the $20$ years. He wishes to start with a deposit at the end of the end of $1$st semiannual and increase the deposit by $5\%$ per semiannual thereafter. What should be the size of his first semiannual deposit?

Note: Draw the cash flow diagram and use interest rate with five decimal places. Box your final answer and upload the picture of your solution.

Round your answer to $2$ decimal places.