1. (70 points) A family member named Fred is about to celebrate his 62nd birthday. He has a choice to make concerning Social Security. He can start collecting now at 70% of the full retirement benefit or he can wait 5 years until age 67 and collect 100% of the full retirement benefit or wait three more years until age 70 at which he could collect 124% of the full retirement benefit. Assume the full retirement benefit is $2,000 a month. (This should make it clear that monthly compounding is involved, but perhaps I should add in bold parentheses that monthly compounding is necessary for correct calculations.) What are the payback periods, the IRRS, the NPVS, and Profitability Index of Fred's three options: A) NOT collecting now versus starting to collect at age 67; B) NOT collecting now or at age 67 versus waiting until age 70; C) NOT collecting now versus waiting until age 70? The IRRS, NPVS, and Pls are dependent on an opportunity cost of capital (the discount rate, k, used to calculate present values) and how long Fred can be expected to live. Produce 3 matrixes like the one below to present your findings. OCC 2% 4% 6% 8% 10% 72 NPV IRR PI NPV IRR PI NPV IRR PI NPV IRR PI NPV IRR PI Age at Conclusion of Payments (Death) 77 82 87 NPV IRR PI NPV IRR PI NPV IRR PI NPV IRR PI NPV IRR PI NPV IRR PI NPV IRR PI NPV IRR PI NPV IRR PI NPV IRR PI NPV IRR PI NPV IRR PI NPV IRR PI NPV IRR PI NPV IRR PI 92 NPV IRR PI NPV IRR PI NPV IRR PI NPV IRR PI NPV IRR PI Payback Period is years. Finally, write-up in 50 words or fewer what you would recommend for Fred. 97 NPV IRR PI NPV IRR PI NPV IRR PI NPV IRR PI NPV IRR PI