Charlotte is negotiating a prenuptial agreement with Bunny. Under the agreement, Charlotte will be receiving 10% of $500K every three years (with the first payment occurring three years after the wedding). Bunny claims that under the agreement, and provided that the marriage lasts for 30 years, Charlotte's prenuptial agreement is worth $500K. (a) Charlotte has some doubts, and talks it over with Uma, who has studied some finance during her law school education. Uma claims that under the agreement, Charlotte is worth significantly less than $500K. Why is Miranda right, and what is her argument? (b) Uma advises Charlotte to negotiate an agreement under which she is worth $700K. What should each of the 10 (equal) payments be, provided that Charlotte's annual discount rate is 4%? 3. You want to have $1,000,000 when you retire at the age of 65. The monthly APR is 7%. (a) Right now you are 35. How much do you need to invest? (b) To decrease the burden you decided to invest at the age of 25, what is the amount then? (c) Assume that you decide to invest a fixed annual amount into your retirement plan and to increase the contribution by 3% every year for 40 years, starting at 25 and ending at 64. What is your initial contribution?