A perpetuity with annual payment is payable beginning of $10$ th year from now. The first payment is $10.$ Each annual payment thereafter is increased by $10$ until a payment of $50$ is reached. Subsequent payments remain level at $50.$

This perpetuity is purchased by means of $10$ annual premiums, with the first premium of $P$ due immediately. Each premium after the first is $105\%$ of the preceding one. The annual effective rates are $6\%$ during the first $9$ years and $3\%$ thereafter.

Calculate $P.$