Question

I plan on retiring at 70 years of age, I want to retire with a net income of $105,000 a year, total. I anticipate that social security will fund $20,000 of this total, but the social security will be taxable at 25%. The other portion is a ROTH IRA and not taxable at retirement.

How much will I need to have earned to fund this retirement at age 70 if I believe that I can retire for 30 years, to age 100, (no money left at 100, so it will be an annuity type investment, not perpetuity). I plan on earning 3.9% on my nest egg, or retirement savings for those 30 years. (lump sum). Round to the nearest dollar.

Answer 1

Retirement income expected	$         105,000
Social security receipts	$           20,000
Tax	25%
Social security receipt after tax	20000*(1-25%)
Social security receipt after tax	$           15,000
Balance retirement income required from corpus	105000-15000
Balance retirement income required from corpus	$           90,000
Retirement time in years	30
Interest rate	3.90%
Corpus value	?
PV of annuity
P = PMT x (((1-(1 + r) ^- n)) / r)
Where:
P = the present value of an annuity stream	To be computed
PMT = the dollar amount of each annuity payment	$           90,000
r = the effective interest rate (also known as the discount rate)	3.90%
n = the number of periods in which payments will be made	30
Corpus required=	PMT x (((1-(1 + r) ^- n)) / r)
Corpus required=	90000*(((1-(1 + 3.90%) ^- 30)) / 3.90%)
Corpus required=	$ 1,575,354.47