Question

Paige invested $11,000 in a fund earning 6% compounded monthly. She withdraws $700 from the fund at the end of every quarter with the first withdrawal being made 5 years from now. How long will it take for the fund to be depleted?

Answer 1

Future Value of $11000 after 4 years and 3 quarters i.e. 57 months = Present Value*[(1+Interest Rate)^Number of months] = 11000*[(1+0.005)^57] = $14617

Effective Quarterly Interest Rate = [(1+Monthly Nominal Rate)^3]-1 = [(1+0.005)^3]-1 = 0.015075

PV of Annuity = P*[1-{(1+i)^-n}]/i

Where, PV = 14617, P = Annuity = 700, i = Interest Rate = 0.015075

Therefore,

14617 = 700*[1-{(1+0.015075)^-n}]/0.015075

14617*0.015075/700 = [1-{(1.015075)^-n}]

0.31479 = 1-{(1.015075)^-n}

{(1.015075)^-n} = 1-0.31479 = 0.68521

1.015075^n = 1/0.68521 = 1.4594

By Trial & Error,

1.015075^25 = 1.453628

1.015075^25.27 = 1.4595

Therefore, n = 25.27

Therefore, it will take 25 Quarters approximately.