$(30$ points$)$ Andy is $23$ years old, just graduated from college, accepted his fist job and has just started thinking of retirement plans. Andy has a job offer for $$80,000$ post graduation. His employer has a voluntary retirement savings plan incentive whereby employees are allowed to contribute up to $7\%$ of their gross annual salary $($up to the legal maximum of $$19,500$ per year$)$ and the company matches every dollar the employee contributes. Andy is planning a $3\%$ inflation each year.

Andy believes his income will increase by inflation each year until he retires at age $65.$ He is planning a retirement horizon of $25$ years after retirement. He plans to contribute the maximum for the employer match into his retirement account. He has a retirement account that earns $8\%$ average return annually pre$-$retirement and $5\%$ after retirement.

$1.$ If Andy does not change jobs,, and his income continues to increase with the rate of inflation as he predicted, what would his annual income be at retirement age, age $65?$

$2.$ Andy believes, after retirement, he can live on $90\%$ of his pre$-$retirement income. Then, what is his planned post$-$retirement annual income needs?

$3.$ If his retirement account earns $5\%$ return per year after retirement, how much money should Andy have saved in his retirement account upon retirement?

$4.$ If Andy can receive $$20,000$ per year after retirement from social security benefits, then how much is his shortfall?

$5.$ If Andy starts contributing to his employer$$s retirement plan as planned above, how much will he have saved at retirement? $($Use a spreadsheet to calculate the amount saved and matched each year. Then find the FV of the savings. When you reach the maximum, you can just use the FV formula or continue to use the spreadsheet you created.$)$

$6.$ Is his retirement plan solid? Will he have enough saved for retirement at age $65?$

$7.$ Andy has started considering saving alternatives. He thinks he may be too young to worry about retirement yet. So he wants to wait until he is $30$ to start saving for retirement. If he goes with this plan, how much savings will he have forgone by age $30?$ How much lower would his savings be at retirement? Will Andy still have enough money saved at retirement?