1. Write an equation that finds the expected future value of payments of $5000 at the beginning of each year beginning now and for the next 4 years. Assume that the overall rate of (that is the rate for all five years) return normally distributed with a mean of 6% per annum and a standard deviation of 0.5% . Find the expected future value at the end of 5 years of the account.

2.Repeat problem 1 but now assume that each annual rate of return is normally distributed with a mean of 6% per annum and a standard deviation of 0.5% . Also assume that the rate paid each year is independent of the rate pain in any other year. For example, a possible sequence of rates is 5.75%, 6.00%, 5.90%, 6.25% and 5%.

3.Repeat the scenario in problem 1 but now assume that the annual rates of payment are fixed at 6% but the annual payment amounts are independent and normally distributed with mean of $5000 and standard deviation 0f $50.