a. Suppose your client is 35 years old and has already saved $150,000 for retirement. How much does your client need to contribute to a fund each month for the next 25 years (first payment at the end of this month), to reach a retirement goal of 4,000,000, if the fund is expected to earn an effective annual rate of 12%?

b. Suppose your client is also very generous, and wishes to leave the entire $4,000,000 in savings to charity and her children upon her death. Also, to help assure its value, at retirement she plans to move all her savings into a less risky fund expected to earn an effective annual rate of 3%. Given her goal and the change in expected return, how much can she plan to withdraw from her account each month until her death?