Question

You just graduated from college and are starting your new job. You realized the importance to save for the future and have figured out that you will save $2,000 per month for the next 14 years; and then increase to $6,000 per month for the following 6 years. The amount accumulated at the end of these investments will be your retirement egg nest. You plan to start retirement and start withdrawing monthly amounts the following month (you will be in retirement for 30 years). If your required rate of return is 12% compounded monthly, how much are your monthly withdrawals?

Answer 1

We first need to calculate the amount of corpus that we will be having after saving for 14+6 years:

Thus we need to calculate Future value of annuity of $2,000 for 168 months @12% PA compounded monthly + Future value of annuity of $6,000 for 72 months @12% PA compounded monthly

Future value of annuity =P{[(1+r)^n]-1/r}

For $ 2,000:

where P=Annuity amount=2000

r=ROI=12%/12=1%=0.01

n=14*12=168

FV=2000*{[(1+0.01)^168]-1/0.01}

=2000*{[(1.01)^168]-1/0/0.01}

=2000*[5.32097-1/0.01]

=2000*4.32097/0.01

=2000*432.0969

=864193.96

For $ 2,000:

where P=Annuity amount=6000

r=ROI=12%/12=1%=0.01

n=6*12=72

FV=6000*{[(1+0.01)^72]-1/0.01}

=6000*{[(1.01)^72]-1/0/0.01}

=6000*[2.04709-1/0.01]

=6000*1.04709/0.01

=6000*104.70993

=628259.59

So we will be having corpus of $ 1,492,453.55 (864193.96+628259.59) after 20 years.

Now we need to calculate equate the present value of future annuities of monthly withdrwals with above value to find out the amount of monthly withdrawls.

Then using above formula again we get,

1492453.55=P{[(1+r)^n]-1/0.01}

P=to be found

r=0.01

n=30*12=360

then,

P=1492453.55/{[(1+0.01)^360]-1/0.01}

=1492453.55/{[35.9496]-1/0.01}

=1492453.55/{34.9496/0.01}

=1492453.55/{3494.9641}

=$427.027

Thus we can withdraw $427.03 every month for 30 years after retirement.

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