Seems far off now at 20 years of age, but let\'s say you plan to retire at age 6
ID: 2773772 • Letter: S
Question
Seems far off now at 20 years of age, but let's say you plan to retire at age 60. You conclude that you need $2,750,000 to retire at 60 years of age and will live off of this until age 90.
How much do you need to put away each paycheck during your working years into your 401K to fully fund your retirement? Assume an 8% average annual market rate of return. Further assume that you are paid twice per month. Do not worry about tax implications, inflation or investment opportunities during retirement.
(For partial credit, state N, I, PV and FV used in calculation)
Explanation / Answer
Solution:
Let x be the amount required to be saved out of every paycheck. Now, the paycheck is given twice a month. Lets assume that the paycheck is given after 15 days. So amount x or PV is also kept after every 15 days and invested at a rate (i) = 0.3% (8%/(12*2))
Future value of this investment (FV) = $2,750,000
Number of periods (n) = 40 * 12 * 2 = 960 (Since compounding takes place twice a month)
Now, FV = PV * [((1+i)n - 1)/i]
2,750,000 = x * [((1+0.3%)960 - 1)/0.3%]
2,750,000 = x * [(24.40 - 1)/0.3%]
2,750,000 = x * [23.40/0.3%]
or x = 2,750,000 *0.3%/23.40
= 9166.667/23.40
= 391.698
or the amount which needs to be put away from every paycheck is $391.7