Pat Davis has $750,000 in a retirement fund. Pat plans to start taking out funds at the end of the coming year. He expects that as he ages, he will need less money each year. His plan is to take out 12 monthly payments of $10,000 in the first year. In the second year he would take out 5% less or 12 payments of $9,500. Each year thereafter the payments would be similarly reduced by 5% less than the previous year, etc. The fund earns interest at a rate of 4% EAR.
a How much will be in the fund at the end of five years.
b How long will the funds last for Pat with this scheme?