You are 65. Social Security is giving you two choices: Option A, which is to start...

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You are 65. Social Security is giving you two choices: Option A, which is to start collection 10,000 dollars a year starting at age 65, or Option B, which is to start collection 20,000 dollars a year at age 70.5. You can assume that there is an investment that will pay 6 percent a year compounded continuously. You can also assume that the money that you are getting in either option will be a continuous constant income stream. Ultimately you will need to determine which option you should take. Your goal will be to maximum the present value of the income stream. You do not have an immediate financial emergencies to take of nor are there any pressing business interests that you want to invest in. Note that your choice may depend on when you die. If you die at age 69, it is clear that you should choose option A. For part a, determine the present value of each option if you live to be 75 and if you live to be 90. For part b, determine the age at which the present value of either Option A or Option B is the same. Your answers must be in the format You are 65. Social Security is giving you two choices: Option A, which is to start collection 10,000 dollars a year starting at age 65, or Option B, which is to start collection 20,000 dollars a year at age 70.5. You can assume that there is an investment that will pay 6 percent a year compounded continuously. You can also assume that the money that you are getting in either option will be a continuous constant income stream. Ultimately you will need to determine which option you should take. Your goal will be to maximum the present value of the income stream. You do not have an immediate financial emergencies to take of nor are there any pressing business interests that you want to invest in. Note that your choice may depend on when you die. If you die at age 69, it is clear that you should choose option A. For part a, determine the present value of each option if you live to be 75 and if you live to be 90. For part b, determine the age at which the present value of either Option A or Option B is the same. Your answers must be in the format