Sam is currently 40 years old and is planning to retire at age 65. She has $100,000 invested in a superannuation fund that currently yields 5% per annum, on average. It is expected that the long term

inflation rate will be 3% per annum during Sams retirement.

Q1) A well-established strategy for funding a retirement is spending 4% of the retirement savings in the first year of retirement over a 30-year period and adjusting that amount annually to keep pace with the expected inflation rate. Applying this strategy to sams retirement and assume that she will continue to earn 5% annual return throughout her retirement, what is the actual proportion of the retirement savings at the beginning of the first year she can have access to according to the strategy? If Sam would like to start with a $100,000 for her retirement, how much does she need to save by the time she retires? Briefly explain your working steps and show your formulas and calculations.

hints:

-The 3% inflation needs to be used as a compounding factor to adjust for the spending requirement.

-this is a 2 stagw problem. stage 1: 25 years investment accumulation stage before the retirement at year 65; stage 2: 30 years spending stage from year 65.

- We need to solve the amount of retirement savinf account, X, at the year of 65. from spending stage point of view, this X is the PV for the entire spending stage. Every year, we withdraw a fixed amount then adjusts for 3% inflation. Continue doing this for 30 years, the saving is fully withdrawn. Here, it asks what the proportion if the yearly soending (a) is out of the total X. The actual proportion may not be 4% but will be close. we need go make sure that the PV of soending a*X adjusted for inflation matches X.

- The second part we need to work out the total balance of the retirement account on the retirement day if Sam changes the first year spending to $100,000. We can calculate this using the calculated ratio of first year soending to the total balance in the first step.