Question

If I hired you to work for me when you graduate paid you roughly $40,000 a year and together you ended up with $5,000 a year in your 401K for 5 years before you found out I was underpaying you and you left. Your 401K had that money and earned 7% a year for 35 years and your fees totaled about 1/2% and you never put any more money into it. How much would you have upon retirement?

Answer 1

FV of annuity
The formula for the future value of an ordinary annuity, as opposed to an annuity due, is as follows:
P = PMT x ((((1 + r) ^ n) - 1) / r)
Where:
P = the future value of an annuity stream	To be computed
PMT = the dollar amount of each annuity payment	5000
r = the effective interest rate (also known as the discount rate)	6.50%	7%-0.5%
n = the number of periods in which payments will be made	5
Corpus value after 5 years=	PMT x ((((1 + r) ^ n) - 1) / r)
Corpus value after 5 years=	5000* ((((1 + 6.5%) ^ 5) - 1) / 6.5%)
Corpus value after 5 years=	$ 28,468.20
Now this corpus remains invested for next 30 years so crpus after next 35 years=	28468.20*(1+6.5%)^30
Now this corpus remains invested for next 30 years so crpus after next 35 years=	$188,299.10