What are “trailing 12-month total returns”?
( t2 / t1 ) - 1 Where t2 is the value today, t1 is the value 12 months ago.  Be sure to include dividend payments, if there were any, to t2.  That will give you total return over 12 months. "Total Return is the percent change in value (including andy dividends) of an instrument.  The ""trailing 12-month"" means that your starting point is the value 12 months ago.  So the formula is: where V is the value of the instrument on the reference date, V0 is the value of the instrument 12 months prior to the reference date, and D is the amount of dividends paid between the two dates."
"What exactly do you need explained?  Short term returns show ""fat tails"" in their distribution.  Long term returns converge towards a gaussian distribution.  The authors think there's a connection between this and the ""long memory"" of volatility (i.e. that the autocorrelation of absolute volatilities also has a fat tail)." For the period 1950 to 2009, if you adjust the S&P 500 for inflation and account for dividends, the average annual return comes out to exactly 7.0%. Source. Currently inflation is around 2%.  So your 2% APY is a 0% real return where the stock market return is 7%.  I.e. on average, stocks have a return that is higher by 7.   If you mix in bonds, 70% stocks to 30% bonds, your real returns will drop to around 5.5%, but you are safer in individual years (bonds often have good years when stocks have bad years).   We're making a bit of a false dichotomy here.  We're talking about returns on stocks in retirement accounts versus returns on CDs in regular accounts.  You can buy stocks in regular accounts and it is legally possible to have a CD in a retirement account.  So you can get bankruptcy protection and tax advantages with a CD. While the S&P500 is not a total return index, there is an official total return S&P500 that includes reinvested dividends and which is typically used for benchmarking.  For a long time it was not available for free, but it can currently be found on yahoo finance using the ticker ^SP500TR. A quick Excel calculation tells me that, if you are earning a guaranteed post-tax return of 12% in a liquid investment, then it doesn't matter which one you pick. According to the following Excel formula: You would be able to invest ₹2,124 now at 12% interest, and you could withdraw ₹100 every month for 24 months.  Which means that the ₹100/month option and the ₹2100/biennium option are essentially the same. This, of course, is depending on that 12% guaranteed return.  Where I come from, this type of investment is unheard of.  If I was sure I'd still be using the same service two years from now, I would choose the biennial payment option. You asked in the comments how to change the formula to account for risk in the investment.  Risk is a hard thing to quantify.  However, if you are certain that you will be using this service in two years from now, you are essentially achieving 13% in a guaranteed return by pre-paying your fee.  In my experience, a 13% guaranteed return is worth taking.  Trying to achieve any more than that in an investment is simply a gamble. That having been said, at the amount we are talking about, each percent difference in return is only about ₹22.  The biggest risk here is the fact that you might want to change services before your term is up.  If these amounts are relatively small for you, then if there is any chance at all that you will want to drop the service before the 2 years is up, just pay the monthly fee. "I was afraid of this. If you are using 12 P/Y and 12 C/Y, then your interest rate should not be divided by 12. Also, you should use ""END"" as this means monthly payments are made at the end of the month - a usual default." Yes those are really yields. A large portion of the world has negative yielding bonds in fact. This process has been in motion for the past 10 years for very specific reasons. So congratulations on discovering the bond market. You could use  the Gordon growth model implied expected return: P = D/(r-g) --&gt; r = D/P (forward dividend yield) + g (expected dividend growth). But obviously there is no such thing as a good market return proxy. That's not 100% correct, as some leveraged vehicles choose to re-balance on a monthly basis making them less risky (but still risky).  If I'm not mistaken the former oil ETN 'DXO' was a monthly re-balance before it was shut down by the 'man' Monthly leveraged vehicles will still suffer slippage, not saying they won't.  But instead of re-balancing 250 times per year, they do it 12 times.   In my book less iterations equals less decay. Basically you'll bleed, just not as much.  I'd only swing trade something like this in a retirement account where I'd be prohibited from trading options. Seems like you can get higher leverage with less risk trading options, plus if you traded LEAPS, you could choose to re-balance only once per year. What you're missing is the continuous compounding computation doesn't work that way.  If you compound over n periods of time and a rate of return of r, the formula is e^(r*n), as you have to multiply the returns together with a mulitplicative base of 1.  Otherwise consider what 0 does to your formula.  If I get a zero return, I have a zero result which doesn't make sense.  However, in my formula I'd still get the 1 which is what I'm starting and thus the no effect is the intended result. Continuous compounding would give e^(-.20*12) = e^(-2.4) = .0907 which is a -91% return so for each $100 invested, the person ends up with $9.07 left at the end.  It may help to picture that the function e^(-x) does asymptotically approach zero as x tends to infinity, but that is as bad as it can get, so one doesn't cross into the negative unless one wants to do returns in a Complex number system with imaginary numbers in here somehow. For those wanting the usual compounding, here would be that computation which is more brutal actually: For your case it would be (1-.20)^12=(0.8)^12=0.068719476736 which is to say that someone ends up with 6.87% in the end.  For each $100 had in the beginning they would end with $6.87 in the end. Consider someone starting with $100 and take 20% off time and time again you'd see this as it would go down to $80 after the first month and then down to $64 the second month as the amount gets lower the amount taken off gets lower too.  This can be continued for all 12 terms.  Note that the second case isn't another $20 loss but only $16 though it is the same percentage overall. Some retail stores may do discounts on discounts so this can happen in reality.  Take 50% off of something already marked down 50% and it isn't free, it is down 75% in total.  Just to give a real world example where while you think a half and a half is a whole, taking half and then half of a half is only three fourths, sorry to say.  You could do this with an apple or a pizza if you want a food example to consider. Alternatively, consider the classic up and down case where an investment goes up 10% and down 10%.  On the surface, these should cancel and negate each other, right?  No, in fact the total return is down 1% as the computation would be (1.1)(.9)=.99 which is slightly less than 1. Continuous compounding may be a bit exotic from a Mathematical concept but the idea of handling geometric means and how compounding returns comes together is something that is rather practical for people to consider. It's not compound interest. It is internal rate of return.  If you have access to Excel look up the XIRR built-in function. Thanks for your reply. I’m not familiar with the term “Held-For-Trading Security”. My securities are generally held as collateral against my shorts. To clarify, I am just trying to track the “money in” and “money out” entries in my account for the shorts I write. The transaction is relatively straight forward, except there is a ton of information attached! In simple terms, for the ticker CSR and short contract CSRUQ8, the relevant entries look something like this: There are no entries for expiries. I need to ensure that funds are available for future margin calls and assignments. The sale side using covered calls is as involved. It looks like their three months ending and six months ending June 30, 2012 income statements are the same?? Did they start April1, 2012?  Anyways, it looks bad though that was the first quarter. Hard to judge if that's the case "The author is using an approximation to what you have exactly, which is called a ""true"" time-weighted rate of return. You have expressed the total time-weighted return for the period in question.  In order to express this as an annual rate, you may annualize it by adding one, raising to the 1/y power, and subtracting one again, for a period of y years. The alternative to a time-weighted return is a money-weighted return, which is actually another name for the internal rate of return." Damn, helpful Harry above me.   So, in general, when compounding the value of an investment, if you're seeing an annualized interest rate of 4%, and the interest compounds monthly (or n number of times per year), you're going to multiply the Principal P by the growth rate (the interest rate), adjusted for the number of periods that your investment grows in a year. P_end = P * (1 + 0.04/n)^(n * t), where n = number of periods, and t = number of years. If the interest compounds annually, you earn P *(1.04), if it compounds monthly, you earn (1 + 0.04/12)^(12 * 1).   Apply this logic to discounting future cash flows to their net present value. When discounting future cash flows, you're essentially determing the opportunity cost of now being unable to put your investment elsewhere and earning that corresponding interest (discount) rate.   Thus, you would discount $1000 by (1 + 0.08/12)^1, and $2000, $3000 in a similar fashion. Then, as icing on the cake, sum up to get your cumulative net present value.  Please let me know if any portion of my explanation is unclear; I would be happy to elaborate! The Telegraph had an interesting article recently going back 30 years for Mutual's in the UK that had beaten the market and trackers for both IT and UT  http://www.telegraph.co.uk/finance/personalfinance/investing/11489789/The-funds-that-have-returned-more-than-12pc-per-year-for-THIRTY-years.html