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Rayna has saved ​$76,900.00. If she decides to withdraw ​$3,304.00 at the beginning of every six...

Rayna has saved ​$76,900.00. If she decides to withdraw ​$3,304.00 at the beginning of every six months and interest is 4.97 % compounded monthly comma for how long can she make​ withdrawals? Express your answer in years and months​ (from 0 to 11​ months).

Solutions

Expert Solution

Rayna has saved amount today = $76,900

Periodic withdrwal at the beginning of every six months = $3304

Interest rate = 4.97% compounded monthly

Calculating 6 monthly interest from monthly compounding:-

where, r = Interest rate = 4.97%

m = no of times compounding = 12

= 2.5109%

Now, Calculating the no of withdrawals can be made using Present Value of Annuity due formula:-

Where, C= Periodic Withdrawal = $3304

r = Periodic Interest rate = 2.5109%

n= no of periods

Present Value = $76,900

Taking Log on Both sides,

Log(0.42990704867) = -n*Log(1.025109)

-0.3666254342 = -n*0.0107700464

n = 34.04 periods

So, the time she can make withdrawal = 34.04/2 = 17.02years (as semi-annual withdrawal dividending the no of periods by 2)

Hence, 17 years

jeff jeffy answered 2 years ago
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