You deposit $5,000 per year at the end of each of the next 25 years into an account that pays 8% compounded annually. How much could you withdraw at the end of each of the 20 years following your last deposit if all withdrawals are the same dollar amount? (The twenty‐fifth and last deposit is made at the beginning of the 20‐year period. The first withdrawal is made at the end of the first year in the 20‐year period.)

$3487.66 is the amount to be withdrawn at the end of ach of the 20 years

Explanation:

PV = $5000

FV = ?

r = 8%

n = 25

Looking for PMT =?

So first we calculate the future value of the deposits

FV = PV × (1+r)^t

     =5000 × (1+0.08)^25

      =$34242.38

The FV of the deposits becomes the PV of the annuity in which the withdrawals for the 20 year period will be made

PVA = pmt × {1- (1+r)^-n/r }

34242.38 = pmt {1-(1+0.08)^-20/0.08}

34242.38 = pmt × 9.8181

pmt  = 34242.38/9.8181

         =$3487.66

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