ACTUARIAL SCIENCE. PLS USE ACTUARIAL NOTATION. SHOW ALL WORK PLEASE. TQ

You are given the following information: (i) A life insurance policy pays 50 at the end of the year of death. (ii) Premiums are payable at the beginning of each year. (iii) i=6% (iv) px=0.9 for any x. (v) The life insurance company loses money when the present value of the benefit payment is greater than the present value of premiums received. Using the percentile principle, calculate the smallest annual premium such that the probability of the life insurance company losing money is less than 20%