Assuming there would be rent paid or a mortgage, the budget would be tight.
I would accumulate some short term saving in a FDIC insured saving account.
That money would help to ease the paid should you end up being between jobs.
Don't put the saving into a free checking account, but look for an account returning a higher rate (see AmtrustDirect banks website.
Next, take advantage of any retirement programs offered by the employer. If they will match what you put into the program, that would be great. Also check for employer offered tax sheltered programs. Next, try to put $50 a month or so into either a Roth IRA or some type of conservative mutual fund. Some mutual funds can be started with as little as $50 when using an automated plan of investing.
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A person in that situation will barely have any income left to save, but saving anything is always a good idea if one can manage it. The taxable income will be so low that very little income tax may be due. Either a Roth IRA or a 401K, or both, is a good idea. A conventional IRA is not as good for two reasons: (1) no money may be taken out without penalty until age 59 1/2 except under very restricted conditions and (2) the money that is taken out later will probably be subject to a higher tax rate than she is paying now. With a Roth IRA, the amount invested can be withdrawn at any time for any reason without penalty, but the earnings and capital gains should remain invested. The money earned in a Roth IRA will be tax free after retirement -- a major advantage. A 401(k)should be enrolled in if the employer offers a plan to partially match the employee's investment. You are basically throwing away money if you don't accept the matching funds - even if they are in the company stock. Many companies offer matching 401(k)funds, up to a certain limit. There are usually well managed and conservative options for investing the money in 401(k)s.