It has been proposed to Ruby that she invest $300 at the end of each month (star

Question

It has been proposed to Ruby that she invest $300 at the end of each month (starting at the end of the upcoming month) for 40 years in a high risk fund (no initial deposit) that earns 11% APR with monthly compounding, and then switch the funds in her retirement years to a more conservative fund that earns a guaranteed 4% APR with monthly compounding. Assuming that the high risk fund indeed pays at the stated rate, how much could she withdraw (equal amounts) at the start of each year during a 25 retirement period. It has been proposed to Ruby that she invest $300 at the end of each month (starting at the end of the upcoming month) for 40 years in a high risk fund (no initial deposit) that earns 11% APR with monthly compounding, and then switch the funds in her retirement years to a more conservative fund that earns a guaranteed 4% APR with monthly compounding. Assuming that the high risk fund indeed pays at the stated rate, how much could she withdraw (equal amounts) at the start of each year during a 25 retirement period.

Explanation / Answer

APR = 11%

So EAR = (1+11%/12)^12-1 = 11.57%

We have monthly Payment PMT =300

Rate = 11.57%/12 monthly

period = 40 yrs. SO nper =40*12=480 month

So FV after 40 Yrs = FV(rate,nper,pmt,pv)

= FV(11.57%/12,480,300,0) = $3,082,438.85

Now this corpus will be used over 25 yrs

So nper = 25*12 = 300

EAR = (1+4%/12)^12-1 = 4.07%

SO Rate = 4.07%/12

PV = $3,082,438.85

FV=0

So Monthly withdrawl = PMT(rate,nper,pv,fv)

= PMT(4.07%/12,300,-3082438.85,0)

= $16,389.60

So she can withdraw 16389.60 monthy for 25 yrs.

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