$1.$ Assume that you will have a salary of $$65,000$ after graduation. If you earn a $3\%$ raise,

what will be your salary the second year on the job? What will be your salary in the fifth

year? Assume you start working when you are $22$ years old and work until you are $65($i$.$e$.,$

work for $43$ years$).$ What will be your final salary?

$2.$ Now according to financial planners, the average retiree requires approximately $70\%$ of their

last year$$s working salary each year to live comfortably in retirement. Assume that you

want to earn a fixed amount of interest each year in retirement. Your goal is to spend only

the interest and still live comfortably; thus, you will be able to spend the same amount of

money each year forever. Assume you retire at age $66$ and can earn a $6\%$ return on your

retirement savings. How much must you have saved to live only off the interest?

$3.$ Suppose you live through age $90.$ How much money will you be able to bequeath $($i$.$e$.$

pass on in your will$)?$

$4.$ Suppose you live through age $90.$ How much money will you be able to bequeath $($i$.$e$.$

pass on in your will$)?$

$5.$ Suppose instead, you plan to spend all your savings in retirement $($i$.$e$.$ the day before you

turn $91,$ you expect to have run out of money$).$ You will have $25$ years in retirement. Use

the answer from question $3$ as your annual spending in retirement.

a$.$ How much will you have needed to save to live comfortably in retirement if you

can earn a $6\%$ return on your savings?

b$.$ What about if you can only earn a $5\%$ return on your savings?

$6.$ Suppose instead of ensuring you have enough money to last through your lifetime, you

decide to spend $$200,000$ per year in retirement. How long until you run out of money?

Use your answer from question $5($a$)$ as the amount you saved for retirement.

$7.$ Assume you plan to leave nothing when you pass away, and you can earn a $6\%$ return on

your investment.

a$.$ If you start saving for retirement at age $25,$ how much will you need to save each

year to meet your savings goal?

b$.$ If you start saving for retirement at age $35,$ how much will you need to save each

year to meet your savings goal?