Question

Mildred and Georgia are both 40 years old. When mildred was 25 years old she began depositing $1000 a year into a retirement account which averaged 5% APR. She made deposits for the first 10 years, at which point she was forced to stop making deposits. However, she left her money in the account where it continues to earn 5% interest.

Georgia didn't start thinking about saving for retirement until now. How much money must she invest per year until age 66 so she has the same amount as Mildred will have at age 66? assume Georgia's account also earns an average annual return of 5%

Answer 1

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AGE		25 yrs	34 Yrs		Present age 40 yrs		Retirement age 66 yrs
Mildred		Deposit $1000 /yr @ 5%	Till 10 yrs she deposits				Fund balance = x
Georgia					Wants to invest per yr an amount @ 5%		Fund balance = x

Future value of Annuity of $ 1000 deposited for 10 yrs @ 5% IS     

F = P * ([1 + I]^N - 1 )/I   where P = 1000 , I = 5% , N = 10yrs

F = $14,206.79 OR $14,207

Now this amount is untouched till age 66 yrs from 34 yrs earning int @ 5% i.e 32 yrs

So $14,207 received interest @ 5% till 32 yrs . Hence Its Future value = P (1+ i)ⁿ

= 14207 ( 1.05)³² = $ 74634 (approx)

Now Georgia wants the same amount as Mildred at the age of 66 yrs . She will start depositing at the age of 40 yrs till 66 yrs and earn interest @ 5% .

So , her annuity amount = x which will grow(FV ) to = $ 74634 after 17 yrs , assuming she deposits in this yr also .

F = P * ([1 + I]^N - 1 )/I

$ 74634     = P * [1 + 0.05]^17 - 1 )/0.05

So , P = $ 2888.27 or $ 2888 approx .

SO Georgia will invest every yr $ 2888