A perpetuity with annual payments is payable beginning $10$ years from now. The first payment is $50.$ Each annual payment thereafter is increased by $10$ until a payment of $150$ is reached. Subsequent payments remain level at $150.$ 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 interest rates are $5\%$ during the first $9$ years and $3\%$ thereafter. Calculate

P

$.$