At $24,$ you finish college and are fortunate enough to have a job waiting for you. Your first job has a starting

salary of $$75,000$ per year. This salary is expected to increase by $$5,000$ each year. You decide to start saving

for retirement right away. Each year you invest $5\%$ of the year$$s salary in an account that earns $10\%$ interest,

compounded yearly. For simplicity, assume the deposit is made at the END of each year $($so if age $24$ is t $=0,$

then the first deposit will be at age $25).$ If you continue to save in this manner, how much will be in your

retirement account immediately after you make the deposit at age $45?$

$2.$ When you are $32,$ you win $$20,000$ in the lottery. You decide to spend half of your winnings immediately and

place the other half in your retirement savings account. At $45($after making the retirement account deposit$),$

you decide to quit your job and take a two$-$year trip around the world. To help finance this trip, you withdraw

$15\%$ of the current balance in your retirement savings account. What is the balance of your account

immediately after the withdrawal?

$3.$ At $48,$ you settle back down at a new job. Your starting salary is $$180,000$ per year, and this salary is expected

to increase at a rate of $6\%$ each year. You begin saving for retirement again by placing $5\%$ of your salary each

year into the original retirement savings account that is earning $10\%$ interest, compounded yearly. Note, the

first deposit will happen at age $49.$ At $65$ you make your last deposit into the savings account and decide to

retire. What is the balance of your retirement account immediately after the last deposit?

$4.$ You want to begin making uniform annual withdrawals from your retirement account $($first withdrawal will be

in one year at age $66).$ Thinking of your $10$ grandchildren, you decide that you would like to have enough

money left in your retirement account to leave each of them $$125,000.$ If you estimate that you will make your

last withdrawal at age $85,$ what uniform annual withdrawal can you make from the retirement account such that

there is enough money left at the end to give each grandchild $$125,000?$