Sofia is 40 years old. She has 3 children, Meg age 2, Jo age 4 and Amy age 5. However, she is already planning for retirement. She plans on retiring in 15 years when she will be 55 years old. Sofia believes she will live until she is 100. In order to live comfortably, she thinks she will need to withdraw $10,000 every month during retirement. These monthly withdrawals will be made at the beginning of each month during retirement. Being a lover of animals, Sofia has pledged to donate $500 a week to World Wide Fund for Nature during her retirement. The payments will be made at the end of each week. The last payment will be made when she dies. In addition, she would like to establish a scholarship at Ryerson. The first payment from scholarship would be $80,000. The first scholarship payment would be made 4 years after she retires. Thereafter scholarship payments will be made every year. In order to keep pace with inflation, Sofia would like the amount of scholarship payments to increase by 3% each year. She wants the payments to continue after her death, therefore the payments will go on forever. During retirement, Sofia expects to earn 4% per year compounded semi-annually. Sofia also wishes to give each of children $200,000 when they reach the age of 30. She currently has $500,000 in a locked-in investment t hat earns 5% interest per year compounded monthly. Sofia currently contributes $4,000 every month to an investment account. These contributions are made at the end of each month and will continue until she retires at 55. Sofia expects to earn 6% per year compounded annually on her monthly contributions to her retirement account. a)How much money does she need when she retires at the age of 55? Be certain to include all her financial goals. b)How much money will she have when she retires? c)How much is she short? [Hint: that would be the difference between the amounts in parts (a) and (b)]d)In order to finance any shortfall, Sofia will make weekly contributions into a new retirement account. This new retirement account will earn 8% per year compounded semi-annually. The contributions will be made at the end of each week until she retires at 55. How much must she contribute each week to the new retirement account?