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Emily Jacob is 45 years old and has saved nothing for retirement.Fortunately, she just inherited $ 75,000. Emily plans to put a large portion of that money into an investment account earninga(n) 11% return. She will let the money accumulate for 20 years, when she will be ready to retire. She would like to deposit enough money today so she could begin making withdrawals of $50,000 per year starting at age 66(21 years fromnow) and continuing for 24 additionalyears, when she will make her last withdrawal at age 90. Whatever remains from herinheritance, Emily will spend on a shopping spree. Emily will continue to earn 11% on money in her investment account during her retirementyears, and she wants the balance of her retirement accountto be$0 after her withdrawal on her ninetieth birthday.a. How much money must Emily set aside now to achieve thatgoal

Answer :

abiolataiwo2015

Answer:

A. $51,772.60

B. $65,296.16

C. $535,793.5

Explanation:

a. Calculation for The amount Emily must set aside now

First step is to calculate the present value of the amounts of 50,000 that was withdraw for 24 years at age 65

Present Value of 50,000 = 50,000*(1-(1+11%)^-24)/11%

Present Value of 50,000 = 417,406.83

Now let calculate the Amount to be set aside

Amount set aside = 417,406.83/(1+11%)^20

Amount set aside= $51,772.60

Therefore The amount Emily must set aside now is $51,772.60

b) Calculation for The amount Emily needs to set aside to achieve her goal

First step is to calculate the present value of the amounts of 50,000 that was withdraw for 24 years at age 65

Present Value of 50,000 = 50,000*(1-(1+8%)^-24)/8%

Present Value of 50,000 = 526,437.91

Now let calculate the Amount to be set aside

Amount set aside = 526,437.91/(1+11%)^20

Amount set aside = $65,296.16

Therefore The amount Emily needs to set aside to achieve her goal is $65,296.16

c) Calculation for The amount that will be left in the account for her heirs

First step is to calculate the Face Value of 75,000 at year 65

Face Value of 75,000 = 75,000*(1+11%)^20

Face Value of 75,000= 604,673.37

Second step is to calculate the present value of the amounts of 50,000 that was withdraw for 24 years at age 65

Present value of 50,000= 50,000*(1-(1+8%)^-24)/8%

Present value of 50,000 = 526,437.91

Third step is to calculate the Value at age 65

Value at age 65 = 604,673.37 - 526,437.91

Value at age 65= 78,235.45

Last step is to calculate the Amount left at age 90

Amount left = 78,235.45*(1+8%)^25

Amount left = $535,793.5

Therefore The amount that will be left in the account for her heirs is $535,793.5

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