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Rachel is 45 years old. She plans on retiring in 15 years when she will be 60 years old. Rachel believes she will live until she is 95. In order to live comfortably, she needs a substantial retirement income. She wants to receive an annual income during retirement. The payments will be made at the end of each year during her retirement. There will be a total of 35 payments. The first payment will be $150,000. She wants the annual payments to increase by 3% per year during retirement Also, Rachel has pledged to donate $2,500 a month to her favorite charity during her retirement. The payments will be made at the end of each month. 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 $50,000. The first scholarship payment would be made 1 year after she retires. Thereafter scholarship payments will be made every year. To keep pace with inflation, Rachel 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. Rachel has two children, Ashley age 20 and Elizabeth age 15. Rachel plans on giving each child $500,000 when the child turns 40 years old. During retirement, Rachel expects to earn 4% per year compounded annually. She currently has $150,000 in a locked-in investment that carns 6% interest per year compounded semi-annually. Rachel currently contributes $300 every week to an investment account. These contributions are made at the end of each week and will continue until she retires at 60. Rachel expects to earn 8% per year compounded annually on her weekly contributions to her retirement account a) How much money does she need when she retires at the age of 60? 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, Rachel will make monthly contributions into a new retirement account. This new retirement account will earn 7% per year compounded annually. The contributions will be made at the beginning of each month until she retires at 60. How much must she contribute each month to the new retirement account