Jim Nasium is age $50$ and plans to retire in $20$ years $($at age $70).$ He has retirement savings in a mutual fund account, which has a current balance of $$100,000($Jim does not plan to add any additional money to this account$).$ Also, Jim opened a $401$K retirement account with his new employer and will contribute $$10,000$ per year into his $401$K until retirement.

$$ If Jim$$s mutual fund account grows at an annual rate of $5\mathrm{.}0\%$ how much money will Jim have in his mutual fund account at age $70?$

$$ If Jim$$s $401$K account grows at an annual rate of $5\mathrm{.}0\%$ per year, how much money will Jim have in his $401$K account at age $70?$

$$ What is the total investment balance of Jim$$s retirement account at age $70?(5$ points$)$

$$ At retirement, Jim plans take the investment balance from his mutual fund account and the balance from his $401$K account and combine them into an IRA account. To minimize risk, his IRA account will invest in more conservative securities$.$ As a result, Jim anticipates his annual IRA returns to be about $4\mathrm{.}0\%$ during retirement. While in retirement, Jim plans to withdraw $$40,000$ per year from his IRA account over the next $20$ years. Is this possible? Explain why or why not?$(5$ points$)$