John and Jane Smith are a middle class couple that spends $$4,000\mathrm{.}00$ a month. John and Jane also have two children they wish to leave an inheritance to$.$ If John and Jane want to retire at the age of $67($and they are now $27)$:

A$.$ How much money will they be spending per month assuming $3\%$ inflation? How much is that per year? Assume that social security is still in existence and will meet four tenths $($or $40\%)$ of their spending needs.

B$.$ Assume that John and Jane primarily save for retirement through their $401($k$)$ plans at work. Please also assume that they can get an ending after$-$tax return of $3\mathrm{.}75\%$ on their retirement nest egg. You would get this rate if you assumed a $5\%$ return on retirement assets that are invested in low$-$risk securities $(5\%$ x $(1-\mathrm{.}25$ tax rate $=\mathrm{.}75)=3\mathrm{.}75\%).$ Hint: If you divide their annual retirement spending by $3\mathrm{.}75\%$ you will get the amount of the nest egg they need for retirement.

C$.$ Also assume that during their working years from age $27$ to $67$ they earn a $7\%$ return on their $401($k$)$ investments. How much money will they need to set aside in their $401($k$)$ plans per month and per year in order to have an adequate retirement nest egg that compensates for the other $60\%$ of their living expenses that social security does not cover.

D$.$ Please also assume that John and Jane Smith want to preserve their retirement nest egg in order to pass an inheritance to their adult children. This is the most risk adverse strategy John and Jane can adopt. By using this strategy, they will be more likely to leave something to their heirs, but incase of an unexpected medical or legal issue that affects John or Jane personally, John and Jane will be able to draw money out of their retirement nest egg in order to take care of themselves in case of an unexpected tragedy.

PLEASE NOTE: John and Jane could come up with a retirement plan where they use up their retirement nest egg during their retirement years. If they went this route their monthly savings amount needed would decrease, but they would not have as much money to leave to their children or other heirs. Also, if a tragedy occurred during their retirement years John and Jane might end up in a situation where they can not meet all of their financial obligations and they are too old to re$-$enter the work force.

PLEASE NOTE: Although their mortgage may go away and some other expenses may go away when they retire, it is safe to say that their out of pocket medical costs will greatly increase. Thus, please make the assumption that the monthly and annual amounts of money they will spend in retirement years are equivalent to the amounts they are spending during their working years.