Question

How much money should be deposited at age 50 in order to withdraw $30000 at the end of each year for 5 years if the first withdrawal is made at age 65. The account earns 8.25% compounded quarterly. Hint: Round effective rate to two decimal places. For the time where no withdrawals are being made, use 8.25% compounded quarterly.

Answer 1

In order to calculate the target FV for the said withdrawals we calculate the required FV as

FV required = Yrly withdrawals * ((1-(1+r)^-t) / r

Or the

FV = 30,000 x ( 1-(1+0.0825)^-5) / 0.0825)

FV= 118996.18

Now

In order to calculate the monthly deposits required at age of 50, we calculate

Total deposit time = 15 years

Target FV = = 118996.18

Fv annuity = PMT * ((1+r)^t -1 ) / r

Where r = rate

T= time

So we get

PMT of Monthly payment as

PMT = 118996.18 * 0.0825 /(1+0.0825)^15 -1

So

Monthly Payments = 4298.02

Thanks. Please Upvote if you like .

The Schedule of the deposit withdrawals as per is as follows

AGE	Begin Balance	Interest	Deposit / Withdrawl	Closing Balace
50	0	0	4298.022	4298.022
51	4298.022	354.5868	4298.022	8950.630815
52	8950.630815	738.427	4298.022	13987.07986
53	13987.07986	1153.934	4298.022	19439.03595
54	19439.03595	1603.72	4298.022	25340.77841
55	25340.77841	2090.614	4298.022	31729.41463
56	31729.41463	2617.677	4298.022	38645.11334
57	38645.11334	3188.222	4298.022	46131.35719
58	46131.35719	3805.837	4298.022	54235.21616
59	54235.21616	4474.405	4298.022	63007.64349
60	63007.64349	5198.131	4298.022	72503.79608
61	72503.79608	5981.563	4298.022	82783.38125
62	82783.38125	6829.629	4298.022	93911.03221
63	93911.03221	7747.66	4298.022	105956.7144
64	105956.7144	8741.429	4298.022	118996.1653
65	118996.18	9817.185	30000	98813.36485
66	98813.36485	8152.103	30000	76965.46745
67	76965.46745	6349.651	30000	53315.11851
68	53315.11851	4398.497	30000	27713.61579
69	27713.61579	2286.373	30000	0