You are saving for retirement. You wish to retire exactly 40 years from now. You

Question

You are saving for retirement. You wish to retire exactly 40 years from now. You want to pay yourself a nominal monthly retirement CF of $10,000 per month, each month, during your retirement. You don’t want the amount to increase with time (i.e. it will stay constant at $10,000 per month), and you want the CFs to start 1 month after you retire and last for 35 years. You can earn 8.4% APR, compounded quarterly, on your investments.

How much would you need to have saved in your retirement account by the time you retire (exactly 40 years from now) in order to fulfill your retirement goals?  

Explanation / Answer

We need to convert APR with quarterly compounding to APR with monthly compounding
APR with monthly compounding=(((1+8.4%/4)^4)^(1/12)-1)*12=8.3418765%

Amount needed in the retirement account 40 years from now:

Using financial calculator:
N=35*12=420
PMT=10000
I/Y=8.3418765%/12=0.6952%
CPT PV
=$1,360,054.61

Using excel:
=PV(8.3418765%/12,35*12,10000)
=$1,360,054.61

Using mathematical formula:
=10000/(8.3418765%/12)*(1-1/(1+8.3418765%/12)^(35*12))
=$1,360,054.61

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