Retirement Case

Mr$.$ Lee, aged $40,$ single, has steady job and income. Currently, Mr$.$ Lee's living

expenses is $$200,00020,000$ per yearmently. He plans to retire at age $65$ and wants

his financial planner to establish an appropriate retirement plan for him.

After reasonable analysis, he feels that he can reduce the expenditure to $70\%$ of the

current level at his retirement. His life expectancy after retirement is $20$ years.

Including the portion from his employer, his monthly MPF contribution is $$2,000.$

$($Assume the expected average inflation rate in the future will be $7\%$ per year and the current average return on investment is $13\%.)$

Mr$.$ Lee understands that the investment after retirement should be more conservative so he expects the investment target after retirement will be those assets with lower risk and return. Accordingly, the return at that time will reach $9\%$ per year.

Based on the above data, calculate the retirement fund required in order to maintain the $70\%$ of Mr$.$ Lee's current living standard level and how much additional saving is required per month?

$(1)$ $$200,00070\%=$$$140,000(2)$

$PV=12\mathrm{.}581\mathrm{.}772\mathrm{.}17$

$(3)$

$PmT=2,000,n=2512,i=13\%$

$FV=4\mathrm{.}494\mathrm{.}183\mathrm{.}04$

$(4)$

$F{v}_{\text{d}\text{i}\text{f}\text{f}\text{e}\text{r}\text{e}\text{n}\text{c}\text{e}}=12\mathrm{.}581\mathrm{.}772\mathrm{.}17-4\mathrm{.}494\mathrm{.}183\mathrm{.}04$

$=8,087\mathrm{.}589\mathrm{.}13$

$n=2512,i=13\frac{\%}{12},Pm7=3,599\mathrm{.}14$~~$3600$ permonth