Ms$.$ Reti Rement is currently $35$ years old and has an annual income of R$850000$ from her small business. She figures her income will grow by $6,5\%$ per year for the

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next $30$ years, by which time she plans to retire. She does not belong to a pension or provident fund.

$12\mathrm{.}1$ What will her final income at retirement be$?12\mathrm{.}2$ Once Reti has retired, she reckons she will only need $80\%$ of her final income to live comfortably. Although one cannot predict these things, Reti has looked up life insurance statistics and found that her life expectancy is $86$ years. What capital amount will Reti need to invest at retirement to provide for her remaining years if the growth rate on the capital is $8,0\%$ per annum? Assume inflation will be $4,5\%$ per year. How does this number compare to the rule of thumb provided in the lectures? Comment on the difference, if any. $12\mathrm{.}3$ If Reti only starts saving now, how much should she put away each month to ensure the required capital amount at retirement, assuming a growth rate of $9\%$ per annum? Do you think Reti will be able to afford the required monthly saving? $12\mathrm{.}4$ If Reti started saving when she was $25,$ how much should she then have put away per month until retirement? What is your conclusion from this?