The Association of Super Funds Australia $($ASFA$)$ suggests that to achieve a modest retirement lifestyle, a couple would require $$45,800$ a year $($based on today currency$)$ assuming that they own their home and are relatively healthy. However, David and Belinda aspire to have a comfortable retirement that allows them some luxuries such as overseas travel and fine dining. This is estimated to cost $$70,000$ a year $($based on today currency$).$ The current plan is for the couple to retire at the same time when David is $63$ and Belinda $60$ and they expect to have $25$ years in retirement.

i$.$ Assuming that inflation is $3\%$ per annum, how much do David and Belinda need a year for them to achieve a modest retirement lifestyle when they retire. How much do they need a year for a comfortable lifestyle?

ii$.$ If David and Belinda expect to have $25$ years in retirement, how much money do they need at the time of retiring to achieve a modest and comfortable lifestyle?