Read the instructions for this question carefully. This is a "personalized" question that requires your own input.

First, provide three estimates based on your personal expectations:

In how many years $($call it $x)$ do you think you can retire? X$=$ years

How many years $($call it $Y)$ do you expect to live after retirement? $Y=$ years

How much money $($call it Z$)$ do you think you'll need to spend per year in retirement to live comfortably? For you, $Z=$$

Next, use your input of $x,Y$ and $Z$ to solve the questions below.

You are trying to decide how much to save for retirement. Assume you plan to save $$15,000$ per year with the first investment made one year from now. You think you can earn $4\%$ per year on your investments and you plan to retire in $x_{?}$ years, immediately after making your last $$15,000$ investment.

a$)$ How much will you have in your retirement account on the day you retire?

b$)$ If$,$ instead of saving $$15,000$ per year, you want to make one lump$-$sum investment today for your retirement that will result in the same retirement account balance you calculated in part a$),$ how much would that lump sum need to be$?$