2. Ann, who turns 35 today, purchases an annuity with the following terms: - A level contribution of $P is payable at the beginning of each month, until she reaches the age of 50 (excluding the contribution at exact age 50). - At and after age 50 , a level contribution of $0.75P is payable at the beginning of each month, until she reaches the age of 65 . (There is no contribution at exact age 65). - On Ann's 65th birthday, she will receive a benefit of $10,000. Thereafter, she will receive a monthly benefit that grows at a rate of 0.3% per month (i.e., the benefit is $10,030 one month after her 65 th birthday, $10,060.09 two months after her 65 th birthday, and so on). Benefits terminate after 20 years of payment. Assume that contributions and/or benefits will continue to be made if Ann dies before the policy expires (i.e., no mortality risk on the stream of payments). At an effective interest rate of 4% per annum, calculate the value of P so that the contributions will be enough to pay the benefits after accounting for the time value of money