This is a classic retirement problem. A time line will help in solving it. Your

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Question

This is a classic retirement problem. A time line will help in solving it. Your friend is celebrating her 30th birthday today and wants to start saving for her anticipated retirement at age 65. She wants to be able to withdraw $121,000 from her savings account on each birthday for 20 years following her retirement; the first withdrawal will be on her 66th birthday. Your friend intends to invest her money in the local credit union, which offers 6.6 percent interest per year. She wants to make equal annual payments on each birthday into the account established at the credit union for her retirement fund. (SHOW WORK)

If she starts making these deposits on her 31st birthday and continues to make deposits until she is 65 (the last deposit will be on her 65th birthday), what amount must she deposit annually to be able to make the desired withdrawals at retirement? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

Suppose your friend has just inherited a large sum of money. Rather than making equal annual payments, she has decided to make one lump sum payment on her 30th birthday to cover her retirement needs. What amount does she have to deposit? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

Suppose your friend’s employer will contribute $3,100 to the account every year as part of the company’s profit-sharing plan. In addition, your friend expects a $171,000 distribution from a family trust fund on her 55th birthday, which she will also put into the retirement account. What amount must she deposit annually now to be able to make the desired withdrawals at retirement? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

Explanation / Answer

1 Using PV of ordinary annuity formula, we find the Pv of withdrawals for 20 yrs. @ 6.6% p.a. PV @retirement age (65)=121000*(1-(1+0.066)^-20)/0.066) 1322713.90 This amount must be the Future Value of deposits she should make for 35 years(her 31-65 yrs of age) Now,Using FV of ordinary annuity formula, we find 1322713.90= PMT*((1+0.066)^35-1)/0.066) = 10436.4 PMT=The amount she must deposit annually to be able to make the desired withdrawals at retirement = $ 10436.4 2 Using PV of ordinary annuity formula, we find the Pv of withdrawals for 20 yrs. @ 6.6% p.a. PV @retirement age (65)=121000*(1-(1+0.066)^-20)/0.066) 1322713.90 This amount must be the Future Value of one single deposit she should make for 35 years(on her 30th yr of age) Now using the Fv of single sum formula 1322713.9=PV*(1+0.066)^35 PV = 141241.97 Amount she have to deposit = 141242 one lump sum payment on her 30th birthday to cover her retirement needs 3 Using PV of ordinary annuity formula, we find the Pv of withdrawals for 20 yrs. @ 6.6% p.a. PV @retirement age (65)=121000*(1-(1+0.066)^-20)/0.066) 1322713.90 Future Value of employer's annual contribution for 35 years Using FV of ordinary annuity formula 3100*((1+0.066)^35-1)/0.066 = 392895.83 Future Value of family trust money for 10 years Using FV of Single sum formula 171000*(1+0.066)^10 = 324017.27 Sum of the above 2 = 392895.83+324017.27= 716913.09 Balance amt. to be deposited now= 1322713.90 Less 716913.09 605800.80 This amount must be the Future Value of deposits she should make annually for 35 years(65 yrs of age) Now,Using FV of ordinary annuity formula, we find 605800.8= PMT*((1+0.066)^35-1)/0.066) = 4779.85 PMT=The amount she must deposit annually to be able to make the desired withdrawals at retirement = $ 4779.85

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This is a classic retirement problem. A time line will help in solving it. Your

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