Slim made a single deposit of $5,000 in an account that pays 7.2% in 2012. What

Question

Slim made a single deposit of $5,000 in an account that pays 7.2% in 2012. What equal-sized annual withdrawals can Slim make from the account if the first withdrawal occurs in 2017 and the last occurs in 2022? Answer Gives: $1,393.87 Please show work The equation i have received is: Let PMT be the annual withdrawal from t = 2017 to t = 2022 Compute the PV of all above withdrawal at t = 2016 Formula: PV = PMT [N-year annuity factor] + FV [N-year discount factor] PV = (PMT/RATE)*[1 – 1/(1 + RATE)^N] + FV/(1 + RATE)^N As amount left over at the end of 2022 is zero, FV = 0. RATE = 7.2%, N = 6 PV = (PMT/0.072)*[1 – 1/(1 + 0.072)^6] Now compute PV at 2012 PV at 2012 = (PV at 2016) / 1.072^4 = (PMT/0.072)*[1 – 1/(1 + 0.072)^6]*(1/1.072^4) 5000 = PMT*3.587132 and PMT = $1393.87 Where, (1/0.072)*[1 – 1/(1 + 0.072)^6]*(1/1.072^4) = 3.587132

where does the ^6 and ^4 come from

Explanation / Answer

The future value of deposit in 2016, i.e. 4 years from now can be calculated using TVM function

FV = PV x (1 + r)^n = 5,000 x (1 + 7.2%)^4 = $6,603.12

Now, annual withdrawal can be calculated using payment for annuity formula

P = r x PV / (1 - (1 + r)^-n),

where PV - Value of account in 2016, r - interest rate = 7.2%, n - no. of withdrawals = 6

Annual withdrawal = 7.2% x 7,078.54 / (1 - (1 + 7.2%)^-6) = $1,393.87

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