Mr.A deposits $5000 today in a fund earning interest at j₂ = 6%.He wishes to withdraw $490 every 6 months for as long as possible.He will make his first withdrawal exactly 2 years from today.When will he make the final smaller concluding (drop)withdrawal? A)End of 6.5 years B)End of 7 years C)End of 8.5 years D)End of 9 years

Question

Quizplus · Accepted Answer

First, we need to calculate the amount Mr. A will have in the fund after 2 years of compounding interest at 6%:

FV = PV x (1 + r)^n
PV = $5000
r = 0.06
n = 2

FV = $5000 x (1 + 0.06)^2
FV = $5,635.20

Now, we need to calculate the amount of each semi-annual withdrawal:

r = 0.06
n = 20 (since there are 20 semi-annual periods in 10 years)
PMT = $490

PV = PMT x ((1 - (1 + r)^-n) / r) 
PV = $490 x ((1 - (1 + 0.06)^-20) / 0.06)
PV = $6,614.50

So Mr. A will be able to withdraw $6,614.50 every 6 months for 10 years. The final withdrawal will be made at the end of the 20th semi-annual period, which is 9 years from now:

Final Withdrawal Date = 2 years + (20 x 6 months) = 2 years + 10 years = 12 years
Final Withdrawal Date = 9 years from now

MrA Deposits $5000 Today in a Fund Earning Interest at J2

MrA Deposits $5000 Today in a Fund Earning Interest at J₂