Your client Adam is about to retire. You have calculated his statistical life expectancy of 22 years however in order to allow a buffer you and the clients agree that they would like their funds to provide for them for 27 years. They require approximately $55,000 p.a. during retirement - in real terms after tax and to be taken at the end of each year. Other than investment returns on the capital, your client doesn't expect any other income (incl. no Social Security). Assume a nominal rate of return of 6.5% p.a. and inflation of 2.5% p.a. (you can ignore tax as the investment will be held in a superannuation pension fund) and that they are happy to use up the returns and all of the initial lump sum over the 27 years. Calculate the lump sum that would need to be invested today to be able to fund the future cash needs of $55,000 p.a. and show your workings.