Suppose that you have saved $$10,000$ for retirement and are currently $20$ years old. Moreover,

assume that you will earn the historical return of about $6\%$ on your portfolio of stocks. Consider

how the balance in your retirement account evolves as you age under different assumptions

below. $($Using a spreadsheet program like Excel will make the analysis easier.$)$

a$.$ Compute the balance in your retirement account when you will be $25,30,40,50,$ and $65$

years old if there are no deposits or withdrawals.

b$.$ Do the same calculations for rates of return of $4\%$ and $8\%.$ How sensitive is the calculation

to the rate of return?

c$.$ Plot your retirement account balance by year for these three scenarios on a standard

scale.