If you are 30 years old now and wish to retire at 65 and be able to withdraw $50,000 from your retirement account for 30 years, how much money must you deposit each and every month in your retirement account assuming that you could get 6% compounded monthly on your savings account?
Also, your annual withdrwals are indexed for the cost of living by 2% annually after the first $50,000 for the following 30 years. Any help would be appreciated. Thank you.
Will use this online financial calculator to figure this out.
https://arachnoid.com/finance/ First, the $50,000 payment already has 2% cost of living included in it. So, to find out the net payment, we simply divide:
$50,000 / 1.02 =$49,019.61 - This is the net first payment.
Now, will use the above calculator to find out the PV of the 30 payments. But, before we do that, we must adjust the net interest rate as follows:
1.06/1.02 =1.03921568627... - 1 x 100 =3.921568627% - This is the net interest rate.
Now we shall use the above calculator as follows:
Enter the above net interest rate under “ir”
Enter the above first net payment under “pmt” as negative(-), because it is money paid out.
Enter 30 years under “np”. Then simply press “pv” and we get:
=$855,779.60 - This is the PV of all 30 payments including the cost of living of 2%.
The above PV becomes FV for the 30-year person, which must be saved in the 35 years or 420 months. Again, will use the above calculator to give us the answer that we want, namely, the monthly payments required to save $855,779.60 in the future.
So, we enter $855,779.60 under “fv”
We enter 6%/12 =0.5 under “ir”
We enter 35 years x 12 =420 months under “np”
Finally, we simply press “pmt” and we get:
=$600.67 - This is the monthly deposit that must be made each month for 420 months.