Future Value of Multiple Cash Flows

Question

Assume that you contribute $180 per month to a retirement plan for 15 years. Then you are able to increase the contribution to $380 per month for the next 25 years. Given a 9.0 percent interest rate, what is the value of your retirement plan after the 40 years? 

Answer 1

First 15 years deposit amount = $ 180 per month

Later 25 years deposit amount = $ 380 per month

Interest rate = 9% per annum.

Future value annuity factor 9% , 15 years = ((1+0.09/12)^(15*12)-1)/(0.09/12) = 378.40577

Future value annuity factor 9%, 40 Years = ((1+0.09/12)^(40*12)-1)/(0.09/12) =4681.32037

Future value annuity factor 9%, 25 years later = 4681.32037-378.40577 = 4302.9146

Future vale of 15 years deposit = 378.40577*180 = $ 68113.04

Future value for 25 Years = 68113.04* (1+0.09/12)^300 = 640835.71

Future value of 25 years deposit = 4302.9146*380 = $ 1635107.55

Total amount after 40 years = 640835.71+1635107.55 = $ 2275943.26