Question

bob Katz has saved $22,000 annually for the last 30 years in an account earning 8%. if bob estimates that he will live for 25 years during his retirement, how much would he withdraw annually at 6% interest

Answer 1

Amount in fund at the time of retirement is:

FV of annuity	=	P * [ (1+r)^n -1 ]/ r
Periodic payment	P=	$              22,000.00
rate of interest per period	r=
Rate of interest per year		8.0000%
Payment frequency		Once in 12 months
Number of payments in a year		1.00
rate of interest per period		0.08*12/12	8.0000%
Number of periods
Number of years		30
Number of payments in a year		1
Total number of periods	n=	30
FV of annuity	=	22000* [ (1+0.08)^30 -1]/0.08
FV of annuity	=	2,492,230.64

Amount in retirement fund is $2,492,230.64

Yearly payment	=	[P × R × (1+R)^N ] / [(1+R)^N -1]
Using the formula:
Loan amount	P	$                                                       2,492,231
Rate of interest per period:
Annual rate of interest		6.000%
Frequency of payment	=	Once in 12 month period
Numer of payments in a year	=	12/12 =	1
Rate of interest per period	R	0.06 /1 =	6.0000%
Total number of payments:
Frequency of payment	=	Once in 12 month period
Number of years of loan repayment	=	25
Total number of payments	N	25 × 1 =	25
Period payment using the formula	=	[ 2492230.64 × 0.06 × (1+0.06)^25] / [(1+0.06 ^25 -1]
Yearly payment	=	$                                                    194,959.02

Annual withdrawal for 25 years will be $194,959.02

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