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Your best friend Steve just celebrated his 30th birthday andwants to start saving for his anticipated retirement. Steve plansto retire in 30 years and believes that he will have 25 good yearsof retirement (he has looked at the life expectancy tables and isplaying the odds here) and believes that if he can withdraw$120,000 at the end of each year, he can enjoy his retirement. Inthis problem, assume that the full 25 years of retirement paymentsare made, and the account has a zero balance at the end. Assumethat a reasonable rate of interest for Steve for all scenariospresented below is 7% per year. This is an annual rate, review eachindividual question for more specifics on compounding periods peryear. Because Steve is planning ahead, the first withdrawal willnot take place until one year after he retires. he wants to makeequal annual deposits into his account for his retirement fund. A.If he starts making these deposits in one year and makes his lastdeposit on the day he retires, what amount must he deposit annuallyto be able to make the desired withdrawals at retirement? A1)First: Amount Steve needs to have saved as of his retirement (3pts): A2) The amount Steve must save each year (beginning at theend of the first year) to fund his retirement is (3 pts): A3) IfSteve decides to make monthly deposits for 35 years to reach hissame retirement goal, how much must Steve start depositing onemonth from today (3 pts)? B. If Steve decides he isn’t earningenough money yet and wants to wait several years before startinghis investment deposits. Assume that instead of startingimmediately (that is, the end of year 1), Steve waits for 7 years(first deposit at the end of year 7) leaving 7 fewer years to growhis retirement nest egg, what amount must he deposit annually to beable to make the desired withdrawals at retirement (4 pts)? C.Suppose your friend has just inherited a large sum of money. Ratherthan making equal annual payments, he has decided to make one lumpsum deposit today to cover his retirement needs. What amount doeshe have to deposit today? (3 pts) D. We are now back to Stevestaring his retirement investments at the end of the first year (30years to retirement). Suppose Steve's employer will contribute$2,500 to the account each year as part of the company's profitsharing plan. In addition, assume that Steve has a trust fund thatwill pay out $35,000 to him when he is 50 (20 years from now). Whatamount must he deposit annually under these assumptions to be ableto make the desired withdrawals at retirement? Hint: This is youranswer in part D4, D1-3 help you build to the final answer. To findthe amount of the annual deposit now, it is easier to break downthe components of the problem. Doing so for each of the followingto find your friend's annual deposit, we get: D1) Value ofemployer's contribution at retirement (1 pt): D2) Value of trustfund at retirement (1 pt): D3) Remaining amount that Steve needs atretirement (1 pt): D4) (Final answer) Amount to save each yearunder these assumptions (1 pt):
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