Remedial Maths for IRA Calculation
January 9, 2017 1:31 PM   Subscribe

How do you mathematically calculate the value of an IRA -- sub question, how often does interest on an IRA accrue?

I am, after far too long, finally getting some adult stuff around my retirement lined up this year. As part of prepping to talk to financial planners, I'd like to understand some of the math behind IRA calculations. Not because I plan on doing this myself, but just because I'd like to have a baseline understanding of what's going on.

As I understand it, an IRA is a collection of investments (bonds, stocks, etc) with a value. I can invest money in the IRA, and if the value of the investments go up, I see a profit.

My vague memories of high school math and some internet searching tell me I want to use the Compound Interest Formula
    A = P(1 + r/n)^nt
Or the
formula in Excel/Numbers.

What I'm a little fuzzy on is the n in this calculation. How often do IRAs compound, and, more importantly, **why**? Will this vary base on the fundamental investments inside the IRA? Or is it just that I'm allowed to reinvest my IRA profits directly back into the fund on an -- annual? monthly? -- basis? Will this vary from IRA to IRA? Is compounding something I need to opt into? Does this reinvesting count against my $5,500 ($6,500 if I'm above 49 years old) per year contribution cap?

I know there's online calculators a-plenty for this, but I'd like to understand the reasons for the math because I'm broken inside. Also, if my questions makes absolutely no sense but you know all the wrong assumptions I'm making, I welcome any IRAsplaining that's bubbling in your heads. Thanks all!
posted by alan to Work & Money (7 answers total) 1 user marked this as a favorite
If your investments are primarily stocks, then "earnings" that add to the principal will be minimal; your gains are realized directly as increases in the stock price.

If there are bonds involved, interest payments (and any stock dividend payments) will depend on the security, but I think they're typically paid quarterly. They are paid as cash, not as additional shares (though with a "DRIP"-dividend reinvestment plan, or some mutual funds, they can be).

Finally, of course, the return is not constant; it's variable due to the day-to-day vagaries of the market.

So it's not a continuously-compounding, exponential growth. But it can be approximated that way, as a simplifying assumption.
posted by Huffy Puffy at 1:46 PM on January 9, 2017 [1 favorite]

Also: the contribution limit is on money that you put into the IRA. Growth of/earnings from within the IRA investments don't count.
posted by Huffy Puffy at 1:48 PM on January 9, 2017

I think you may be a little confused about how IRAs work?

You can put (most) consumer investments into an IRA: stocks, bonds, CDs, etc., although most people just go with mutual funds. The value of the IRA account is the total market value of those investments, because...that's what it is, those investments. There's no trick to it, no mechanism for calculating value overlying it all.

Therefore, there's no compounding unless the investment involved compounds (e.g., a CD), and then it will compound at whatever rate the underlying investment compounds. That has no effect on your contribution limit. If your IRA is, e.g., all in mutual funds, and the market goes down, you take those losses (at least on paper).
posted by praemunire at 1:48 PM on January 9, 2017 [4 favorites]

(In other words, IRAs are basically just investment accounts that are tax-deferred and thus have rules about when and what you can invest and withdraw.)
posted by praemunire at 1:50 PM on January 9, 2017

This doesn't make a lot of sense, but I have an idea of the assumptions you're making.

An IRA isn't exactly a collection of particular investments; it's simply an investment account. It has some special rules and features for tax purposes, but it's really just an ordinary financial account. When you put money into it, that money will sit in a default sweep investment, usually a money market fund, where it pays very little interest. Your money will stay in that account until you invest it somewhere else by buying stocks, bonds, mutual funds, exchange traded funds (ETFs), etc...

It is those investments that produce a return. That return comes in two forms. First, the investments you buy can appreciate in value. You can buy a share of Apple for $119 today and find it is worth more (or less) than that next year. Second, the investments can pay you back, such as dividends from stocks, dividends and capital distributions from mutual funds, and repayments from bonds. These funds are generally deposited in your account as cash, but you can choose to reinvest them automatically if you wish. With a reinvestment plan, the dividends you receive will be used to purchase more of the investment, and those new shares in the investment will also start to pay dividends as scheduled. In this way, the value of your investment will compound, but it still doesn't really follow a straight compound interest formula (the whole fund could lose money, for example). If you don't reinvest dividends automatically, they'll sit in your money market account until you choose to invest them in something else.

None of this touches your contribution limit. That limit defines the amount of new money you're allowed to add from outside sources into to the account every year. There's no limit on what happens with the money already in your account, though there are tax consequences associated with taking the money out.

So there's no real standard interest rate or compounding in an IRA. Your money can compound, but it's simply a matter of what you choose to do with your investments, which could gain in value, pay you back money, or lose you money. For the sake of figuring out how your investments are performing, you can calculate an annual return percentage for your account (this is often shown on your account statements).

You might consider a book like the Bogleheads' Guide To Investing as an introductory guide to learn more.
posted by zachlipton at 1:57 PM on January 9, 2017 [3 favorites]

As others say, the IRA is just a container for a variety of investments whose value may fluctuate wildly, instead of paying out interest on a regular schedule.

But, to answer your question: you still might want to do interest calculations of the kind you're talking about, for example if your IRA is mainly in stocks, and you've heard that stocks on average have increased about x% a year, and you want to know what that might mean for you. For the purposes of those calculations, you should assume people mean "compounded annually", though the difference doesn't really matter much in practice.

And of course that kind of calculation, while useful, is just a vague approximation, since, again, your IRA probably isn't (and shouldn't be) invested in stuff that pays out regular interest.
posted by floppyroofing at 3:13 PM on January 9, 2017 [2 favorites]

When IRAs first came out, I set them up for my wife and myself through our credit union. I funded mine through payroll deduction; hers we just threw money in at tax time to get the deduction. After a few years we stopped adding money because 401Ks were available and my company had a good matching $$$ plan. The IRAs just sat in the CU accumulating interest as CDs.

Around 2000 I finally noticed that the interest being paid was crappy, like 1 or 2 percent. I worked with a person at the CU and was able to move both CDs into an insurance company thing that paid 6 percent for the first nine years, which was pretty good for the time. After the nine years was up I looked into moving to something else but everything paid peanuts. Then I read the fine print and found the insurance company would pay 3 percent after the nine years was up. So I just left it there. Seeing as how my "high interest" savings account at my bank pays .30 percent I thing I am getting a good deal.
posted by leaper at 3:38 PM on January 9, 2017

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