Question

Joseph is 28 and would like to retire at 55. He has $25,000 to invest today and would like to have $1,000,000 in his retirement account when he retires. Joseph has found an investment that will pay him a return of 6% until retirement. How much will Joseph have to invest each month in order to reach his retirement?

Answer 1

Use the mortgage formula:
Future value = FV = 1000000
payment per period = P (to be found)
rate of interest (per period) = i (0.06/12=0.005 per month)
R = 1+i = integrated rate = 1.005
n = number of periods = (55-28)*12=324
then
FV=P(1+R+R²+R³+....+R^n-1)
=P(R^n-1)/(R-1)
1000000=P(1.005^324-1)/(.005)
=>
P=1000000*.005/(1.005^324-1)
=1239.85

Note: because of rounding, the FV of the above answer will be missing almost $3, while 1239.86 will yield an FV of $5.2 in excess.

Answer 2

What about the initial $25,000 that he starts with ?

i = .06/12 = .005

25000(1.005)^324 + R(1.005^324 - 1)/.005 = 1,000,000
R(806.5468...) = 874,181.64
R = $1083.86

Answer 3

Oops! Good catch! Thanks.
Elcia, please go with Reiny's answer.