How much must be set aside each month at 12% annual growth compounded monthly for 30 years in order to be able to retire on $4,500 per month for 15 years at 3% annual growth compounded monthly?

Answer 1

x(1.01^360 - 1)/.01 = 4500(1- 1.0025^-180)/.0025
x(3494.964133) = 651624.6215
x = 186.4467..
x = $186.45

check:
amount of 186.45 deposited monthly for 360 months at .01
= 186.45(1.01^360 - 1).01
= 651636.06

if I use 186.4476.. I get 651624.6214 , the fact that your deposit gets rounded off to the nearest penny explains the $11.40 discrepancy.