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Judy,
Yes there is a lot to learn about. The 403b, 401k, and 457 plans are very similar. The DBPs are more employer specific. Filling these plans with extra cash is usually a great idea. You mentioned that this is part time. Does your part time status limit the way that the service time is calculated? Meaning, if you are working 20 hours a week for a year, you get .5 years credit for 1 year of part time service. If so, it will be hard to earn a meaningful amount of service credit to receive benefits. You mentioned that the wages are low. Most plans require a 5 or 10 year service credits for a vesting period to even qualify. DBPs are typically based on multiplying years of service credit by the average of your high three salaries, or similar calculation and offering a percent or two of the average high salary for each year of service credit. 10 years service credit, $9k, $10k, and $11k as your high 3 salary years, and 1.5%/year gives 10years x $10k x 1.5%/year = $1500/yr pension. If your high average is low due to low wages, this may be of little value.
You need to look at the return of buying years of service, there isn't a useful rule of thumb. Look at saving/investing the $139/mo for as long as it takes to buy back the service credit and the return you'd get in your investment choice. Then calculate your standard and improved DBP payouts and compare the difference to you saving the $139 on an outside investment. If you want help with crunching numbers, post your details and someone will probably do it for you. You might also look at the chance of getting steady raises to increase your highest salary years. If you can do this, it changes the calculations significantly. Also look at the possibility that buying years would also help you qualify for other benefits like paid for health insurance, life insurance, access to university gym equipment, ...
My advice is to see if you can get some quality time with a benefits person or ask around where you work. There is probably someone who really knows the benefits. Or, bring some more specific questions to this forum.
Good Luck,
Chris
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)but also to take advantage of the benefits for retirement. Believe me, it wasn't the money but I have another job that will pay the bills while I sock all I can into my retirement accts with the state. (I'm an RN, and you would laugh at my hourly wage with the U). I'm about 10yrs from FIRE. My problem is I have this alphabet soup of choices to make. The DBP is mandatory. But where can I find good information on 457s? I'm somewhat familiar with 401(k) as all I've had before was 403(b). Would it be better to roll my previous 403(b) into the state plan? They do have a Vangaurd plan. 
Hybrid Mode
