We want to retire in 50 years, and we shall need $50,000 income per annum during our retirement, which will last 20 years. We can save $35,000...

We want to retire in 50 years, and we shall need $50,000 income per annum during our retirement, which will last 20 years. We can save $35,000 annually during the ten years between10 to 20. Furthermore, we shall buy a yacht costing $300,000 in year 40. Additionally, we shall send our niece to college, which will cost $42,000 each year for 4 years starting in year 16 from now. Moreover, we know that our parents will need nursing care in 12 years for 18 years. The cost of the care is $60,000 now, and it will rise by the 2% inflation rate for the time before they are admitted. At that point, the cost will stabilize and be the same for the remaining period every year. First, we would like to know what the pension fund should be to finance our retirement. Second, how much are the total expenses we incur as of year 50. Third, how much is our savings of the first ten years, as of year 50? Fourth, what is the total expense of the nursing home? Fifth, what should be the annual savings we accumulate from years 45 to 50 to be able to fund all the aforementioned expenses and our retirement? We have a discount rate (or compound rate) of 10%.