Question
In: Accounting
2) Today, you celebrated your 30th birthday. Also, you just landed a new job, thanks to...
2) Today, you celebrated your 30th birthday. Also, you just landed a new job, thanks to your excellent education at BW. The new firm provides you a 401-k plan, and you decide to deposit $400 every month for first 20 years. After that (since your kids are out in college and your living expenses are lower) you increase your contribution by $200/month, that results in a total contribution of $600/month. The firm matches it at 100% and deposits the money to the same account once a year. You retire on your 65th birthday and stop contributing to 401-k after your retirement. You will leave the account with the employer where it continues to earn interest. The account pays an interest of 6% per year compounded monthly. a) What is the account balance on your 65th birthday? b) What is the account balance on your 70th birthday? assuming you had a onetime withdrawal of $100,000 on your 67th birthday?
My answers were as follows: PLEASE LET ME KNOW IF THESE responses are correct if not can I receive some assistance.
Answer:
$400.00 * 12 months = $4800.00 1st year of contribution with employer matching the 100% = $9600.00
$9600.00 * 20 years = $192,000.00 is what you have after the 20 years of your contribution and the firms 100% match yearly.
Next 15 years of contributions $600.00 * 12 months = $7200.00 * 15years = $108,000.00 * 2 (firms $108,000.00 match) = $216,000.00
Retire at age 65 401-k has a total of
(192,000.00 + 216,000.00) = $408,000.00
You retire on your 65th birthday and stop contributing to 401-k after your retirement. You will leave the account with the employer where it continues to earn interest.
The account pays an interest of 6% per year compounded monthly.
What is the account balance on your 65th birthday? $408,000.00 What is the account balance on your 70th birthday? assuming you had a onetime withdrawal of $100,000 on your 67th birthday? Account Balance on 70th birthday is $376,489.99
Solutions
Expert Solution
| 401 k plan | ||||||||
| Year | Contribution/month | Yearly Contribution | Firms/ contribution | Total contribution | Interest | Withdrawal | Total balance | |
| 30 | 400.00 | 4,800.00 | 4800 | 9600 | 0 | 0 | 9600 | |
| 31 | 400.00 | 4,800.00 | 4800 | 9600 | 576 | 0 | 19776 | |
| 32 | 400.00 | 4,800.00 | 4800 | 9,600.00 | 1186.56 | 0 | 30,562.56 | |
| 33 | 400.00 | 4,800.00 | 4800 | 9600 | 1833.754 | 0 | 41996.31 | |
| 34 | 400.00 | 4,800.00 | 4800 | 9600 | 2519.779 | 0 | 54116.09 | |
| 35 | 400.00 | 4,800.00 | 4800 | 9600 | 3246.966 | 0 | 66963.06 | |
| 36 | 400.00 | 4,800.00 | 4800 | 9600 | 4017.783 | 0 | 80580.84 | |
| 37 | 400.00 | 4,800.00 | 4800 | 9600 | 4834.85 | 0 | 95015.69 | |
| 38 | 400.00 | 4,800.00 | 4800 | 9600 | 5700.942 | 0 | 110316.6 | |
| 39 | 400.00 | 4,800.00 | 4800 | 9600 | 6618.998 | 0 | 126535.6 | |
| 40 | 400.00 | 4,800.00 | 4800 | 9600 | 7592.138 | 0 | 143727.8 | |
| 41 | 400.00 | 4,800.00 | 4800 | 9600 | 8623.666 | 0 | 161951.4 | |
| 42 | 400.00 | 4,800.00 | 4800 | 9600 | 9717.086 | 0 | 181268.5 | |
| 43 | 400.00 | 4,800.00 | 4800 | 9600 | 10876.11 | 0 | 201744.6 | |
| 44 | 400.00 | 4,800.00 | 4800 | 9600 | 12104.68 | 0 | 223449.3 | |
| 45 | 400.00 | 4,800.00 | 4800 | 9600 | 13406.96 | 0 | 246456.3 | |
| 46 | 400.00 | 4,800.00 | 4800 | 9600 | 14787.38 | 0 | 270843.6 | |
| 47 | 400.00 | 4,800.00 | 4800 | 9600 | 16250.62 | 0 | 296694.3 | |
| 48 | 400.00 | 4,800.00 | 4800 | 9600 | 17801.66 | 0 | 324095.9 | |
| 49 | 400.00 | 4,800.00 | 4800 | 9600 | 19445.76 | 0 | 353141.7 | |
| 50 | 600.00 | 7,200.00 | 4800 | 12000 | 21188.5 | 0 | 386330.2 | |
| 51 | 600.00 | 7,200.00 | 4800 | 12000 | 23179.81 | 0 | 421510 | |
| 52 | 600.00 | 7,200.00 | 4800 | 12000 | 25290.6 | 0 | 458800.6 | |
| 53 | 600.00 | 7,200.00 | 4800 | 12000 | 27528.04 | 0 | 498328.6 | |
| 54 | 600.00 | 7,200.00 | 4800 | 12000 | 29899.72 | 0 | 540228.3 | |
| 55 | 600.00 | 7,200.00 | 4800 | 12000 | 32413.7 | 0 | 584642 | |
| 56 | 600.00 | 7,200.00 | 7200 | 14400 | 35078.52 | 0 | 634120.6 | |
| 57 | 600.00 | 7,200.00 | 7200 | 14400 | 38047.23 | 0 | 686567.8 | |
| 58 | 600.00 | 7,200.00 | 7200 | 14400 | 41194.07 | 0 | 742161.9 | |
| 59 | 600.00 | 7,200.00 | 7200 | 14400 | 44529.71 | 0 | 801091.6 | |
| 60 | 600.00 | 7,200.00 | 7200 | 14400 | 48065.49 | 0 | 863557.1 | |
| 61 | 600.00 | 7,200.00 | 7200 | 14400 | 51813.42 | 0 | 929770.5 | |
| 62 | 600.00 | 7,200.00 | 7200 | 14400 | 55786.23 | 0 | 999956.7 | |
| 63 | 600.00 | 7,200.00 | 7200 | 14400 | 59997.4 | 0 | 1074354 | |
| 64 | 600.00 | 7,200.00 | 7200 | 14400 | 64461.25 | 0 | 1153215 | |
| 65 | 600.00 | 7,200.00 | 7200 | 14400 | 69192.92 | 0 | 1236808 | At the age of 65 |
| 66 | 0.00 | 0.00 | 0 | 0 | 74208.5 | 0 | 1311017 | |
| 67 | 0.00 | 0.00 | 0 | 0 | 78661.01 | 100000 | 1289678 | At the age of 67 |
| 68 | 0.00 | 0.00 | 0 | 0 | 77380.67 | 0 | 1367058 | |
| 69 | 0.00 | 0.00 | 0 | 0 | 82023.51 | 0 |
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