3. Marie Nutley wanted to have $300,000 at the end of twelve years. She purchased an investment that promised a 12% annual return. She made equal annual payments for the first four years and earned the promised annual return. Then, the return fell to 8% for the final eight years. This caused her to increase her (equal) annual payments in years five through twelve to get to her goal. a. What equal payments did she make for the first four years? b. What equal payments did she make in the final eight years to achieve her goal? 4. Suppose that Marie (in the previous problem) knew at the time she made the investment that her rate of return would change after the fourth year as above. What (twelve) equal annual payments should she have planned to make in order to achieve her goal?