that was mentioned in class reported that Bill Ackman, who runs Pershing Square Capital Management, recently proposed the following: "...the government could establish and fund investment accounts for every child born in America. The funds could be invested in zero-cost equity index funds, be prohibited from withdrawal until retirement, and could compound tax free for 65 years. At historical rates of equity returns of 8% per annum, a $6,750 ot birth retirement account...would provide retirement assets of more than $1 million at age 65." 1. Exactly how much would a $6,750 investment yield after 65 years at an annual rate of return of 8%? 2. How much needs to be invested (a single one-time investment) in order to yield exactly $1 million after 65 years, assuming an annual rate of return of 8%? 3. Suppose that instead of making a single investment at birth, the government chooses to make contributions at the end of each year toward each child's retirement savings, starting 1 year after birth (65 contributions in total). Assuming an annual rate of return of 8%, how much will the government have to contribute each year per child in order to ensure that each child has $1 million after 65 years? http://www.courselero.com/file/74965293/Take-Home-Assessment-I-Ipdf 1 4. Suppose that the government contributes $6,750 per child at birth and that in addition, your family contributes $500 to your retirement savings at the end of each year after birth. What annual rate of return is required in order for you to have $5 million after 65 years? 5. Suppose that the government only contributes $2,000 per child at birth. Assuming an annual rate of return of 8%. How much additional savings would be required at the end of each year after birth (constant annual contribution) in order for you to have $1 million after 65 years? 6. The computations above do not account for inflation. Suppose the long-run expected annual rate of inflation is 2%. What annual rate of return would be required in order to achieve an 8% rate of growth in purchasing power annually