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I would pretty much concur with rjm1's recommendations, but with some reservations.

I was curious what is the best why to invest money into a emergency fund

Emergency money is money you may need in a cash emergency. As such, it should be reasonably liquid and reasonably safe. This rules out the stock markets (no individual stocks, no stock funds, not even an S&P500 index fund) because the stock market is pretty volatile with still lots of downside potential, so the money might not exist at the very time you need it the most.

My preference for an emergency fund, at least for the equivalent of 3 months of living expenses, is to have it in a money market fund at a major fund family or at a major brokerage. (Both the Vanguard Prime Money Market Fund (VMMXX) and the TIAA-CREF Money Market Fund (TIAXX) are frequently recommended, though there are others, too.) Or have the money in a money market account at a credit union or bank. (I keep the equivalent of 3 months of living expenses, as well as my annual property tax fund and savings for near-term major purchases in my credit union's money market account.)

I have reservations about locking up too much of one's emergency fund in a CD because some CDs cannot be liqiuidated before maturity and those that can have "substantial penalty for early withdrawal". If one has the equivalent of 6 months of living expenses, it may make sense to lock up 3 months of it in CDs or I-Bonds. (And in fact that is what I have done: for a few years I had the other 3 months of living expenses in CDs at my credit union that I can redeem with penalty, and now I have those same 3 months in I-Bonds, my thinking being that the smaller cash emergencies can be handled from my credit union's money market account, but the twice-in-the-last-25-years larger cash emergencies are rare enough that the better yield in a slightly less liquid but still quite safe place is probably worth it over the long run.)

what would be the best way to go about an IRA?

I am going to guess that your marginal income tax bracket right now is fairly low. If you have up to $2,000 earned income (such as salary as reported on your W-2) you can put up to that amount of salary or $2,000, whichever is less, into a Roth IRA. (Next year the limit goes to $3,000.) Vanguard has quite a bit of "investor education" material on their web site, good stuff whether or not one decides to invest through them, and one of the items covered is the Roth IRA. If you qualify for a Roth IRA, it can be great!

Roth IRA = (the late) Senator Roth (the one who sponsored this variant of the IRA), Individual Retirement Account (or Arrangement, the IRS literature use both "Account" and "Arrangement" in their literature). Like the name signifies, a Roth IRA is really intended for retirement. As such, I am reluctant to suggest using a Roth IRA as a place for one's emergency fund. The beauty of the Roth IRA is that if one follows the rules, the withdrawals in retirement will be tax free (at least under current tax laws), this being the only tax free income (besides municipal bond dividends) that the federal government allows.

As pointed out by rjm1, the Roth IRA allows you to remove the regular contributions at any time for any purpose, no tax, no penalty. The earnings, on the other hand, have to stay within the Roth IRA or they will be taxed at your income tax rates plus 10%. So, if need be, the contributions can come out if you need them. What wasn't mentioned is that if you take the money out and don't replace that money within 60 days, you cannot replace that money.

Since money taken out of a Roth IRA cannot be replaced if it takes over 60 days to put it back, I am reluctant to suggest having one's emergency money in a Roth IRA. My recommendation would be, if you can, build up an emergency fund separate from the Roth IRA. But if you cannot build up the equivalent of 3 months of living expenses plus the Roth IRA contribution, then go ahead and fund the Roth IRA but have the money inside the Roth IRA in a money market fund or money market account because you will never again be able to fund your Year 2001 Roth IRA after April 15, 2002. Later, once you have a fully-funded emergency fund outside of your Roth IRA, you can change the investment inside your Roth IRA to something more suitable for long-term investments, such as a stock index fund.

Generally, it is good to match investments with the time horizon at which one will be using that investment, regardless of whether it is in a regular (taxable) account or some flavor of retirement account:

For one's emergency fund or short term savings: money market funds or money market accounts are quite typical. If one knows when one will need one's money, treasuries or CDs that mature before one needs the money makes sense. An ultra-short bond fund is sometimes suggested.

For savings about 5 years out, the same types of instruments and short-term bond funds, treasuries, I-Bonds (Series I Savings Bonds) are worth considering.

For long-term investments, at least for 5 years but especially for over 10 years out, stocks or stock funds (especially no-load, low-expense stock funds based on broad indicies) are typically recommended for the majority of one's portfolio because, over the long run, stocks tend to have the best returns.

That may make more sense on why I recommend that if you are putting money in the Roth IRA but consider the Roth IRA contributions as part of your emergency fund, you put them in a money market fund or a money market account, but if you have a totally separate emergency fund in a regular (taxable) account so the Roth IRA is strictly retirement, consider changing the investments within the Roth IRA to stocks or a stock fund. Yes, I have reservations about using a Roth IRA as part of one's emergency fund, but I think it may be an acceptable concession to one having limited money to dedicate to both a Roth IRA and a separate emergency fund.

is now a bad time to invest in lets say the vanguard 500 fund because the market is low? I feel that it could be a great time because prices are a bit lower

The Vanguard 500 Fund (VFINX) is a good choice for a mutual fund one wants to invest in for the long run, either in the Roth IRA or in a regular account. Yes, I agree that now seems a reasonable time with the prices lower than just a year ago. But the S&P500 index still have lots of downside potential, which means funds that invest to follow the returns of the S&P500 index (such as the Vanguard 500 Fund) also have downside potential, so this should not be used for any short-term money nor money that makes up part of your emergency fund.

If you are new to investing, the normal market volatility may take a little getting used to. I ended up dollar cost averaging into the market (moving a part of my money to stock funds each month) and got used to market volatility in small doses. DCA is not an income maximizing strategy, but it does reduce the risk of putting all of one's money in at the top (or at the bottom, for that matter), as well as got me used to having my money change each month.
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