Calculating a simply complicated return?
Since you have the balance at equal periods and the cash flows at the period ends, the best return calculation in this case is the true time-weighted return. See http://en.wikipedia.org/wiki/Time-weighted_return#Formulae  So, notwithstanding some ambiguity about your figures, here is a calculation using the first three periods from your second table. Giving a total return over the three periods of -23.88% If the periods are months, multiply by four to annualise.
Toward the philosophical side of your question, it seems to me that what is most important is knowing how well your fund is performing versus it's benchmark. This is an actionable piece of information that can help you get out of an under-performing fund, although if you're already using Vanguard it's likely a low cost and broadly diversified fund. Ultimately, what you want to avoid over the long term is under-performing the market due to high fees, market timing, poor fund selection etc., and selecting a fund that closely tracks the market seems to be the best way to achieve this, assuming that you intend to be a passive investor. I don't see a clear benefit to calculating a personal rate of return. If the fund is performing well versus its benchmark, you are likely to stay with it, and if it is performing poorly, you  are likely to pull out. At the end of the day, the complicated accounting won't actually change the amount you've got in your account, so I'd recommend picking a good fund, checking up on it once in a great while, and putting your time to better purpose. This means that if your capital under my management ends up turning a profit, I will keep half of those profits, but if I lose you money, I will cover half those losses. The bold part is where you lose me. This absolutely exists with the exception of the loss insurance.  It just requires a lot more than the general retail consumer investor has to contribute.  Nobody wants to take on the responsibility of your money then split 50% of the gross proceeds of your $10,000 (or whatever nominal amount of money you're dealing with) investment and return it all to you after a year.  And NO money manager will insure that the market won't decline. Hedge funds, PE Firms, VC Firms, Investment Partnerships, etc all basically run the way you're describing (again without your loss insurance).  Everyone's money is pooled and investments are made.  Everyone shares the spoils and everyone shares the losses.  And to top it off, the people making investment decisions have their money invested in the fund.  All of them have to pay rent and accountants and other costs associated with running the fund and that will eat in to the proceeds to some degree; because returns are calculated on net proceeds. With enough money you can buy yourself in to a hedge fund, for the rest of us there are ETFs and other extremely fee-reasonable investment options.  And if you don't think the performance and preservation of assets under management is not an incentive to treat the money with care you're kidding yourself (your first bullet point). I'll add that aside from skewing the manager's risk tolerance toward guaranteed returns I doubt you would fair favorably over the long term compared to simply paying even an egregious 1% expense ratio on an ETF.  If you look at the S&P performance for 10 or 20 or however many years, I'd venture that a couple good years of giving up half of your gains would have you screaming for your money back.  The bad years would put the money manager out of business and the good years would squander your gains. Log-returns are very commonly used in financial maths, especially quantitative finance.  The important property is that they're symmetrical around 0 with respect to addition. This property makes it possible to talk about an average return. For instance, if a stock goes down 20% over a period of time, it has to gain 25% to be back where you started.  For the log-return on the other hand the numbers are 0.223 down over a period of time, and 0.223 up to get you back to square 1. In this sense, you can simply take an arithmetic average and it makes sense.  You can freely add up or subtract values on the log-return scale, like log-interest rates or log-inflation rates.  Whereas the arithmetic mean of (non-log) returns is simply meaningless: A stock with returns -3% and +3% would have 0% on average, when in fact the stock has declined in price? The correct approach on direct price-returns would be to take a different mean (e.g. geometric) to get a decent average.  And yet it will be hard to incorporate other information, like subtracting the risk-free rate or the inflation rate to get rate-adjusted average returns. In short: Log-returns are easier to handle computationally, esp. in bulk, but non-log-returns are easier to comprehend/imagine as a number of their own. RD Interest Calculator - Use the advanced Recurring Deposit Calculator from HDFC Bank to calculate the maturity amount earned on your investment. Simply key in your initial amount, at a desired rate of interest for a specific term for which you wish to invest. Find out how much do you earn through a Recurring Deposit! "Calculating beta is finding the correlation between the dependent variable, MSCI world benchmark, and the independent variable, your companies. If you know how to run liner regression models, run each company as the independent variable with the dependent MSCI. You can use Excel to gather this result (Y = MSCI price change at closing hour while X = company stock price closing prince). Running the regression will give you the Beta (and alpha when doing portfolios); which (from linear algebra) is the ""m"" in y = mx + b" You are comparing a risk-free cost with a risky return. If you can tolerate that level of risk (the ups and downs of the investment) for the chance that you'll come out ahead in the long-run, then sure, you could do that.   So the parameters to your equation would be: If you assume that the risky returns are normally distributed, then you can use normal probability tables to determine what risk level you can tolerate. To put some real numbers to it, take the average S&P 500 return of 10% and standard deviation of 18%.  Using standard normal functions, we can calculate the probability that you earn more than various interest rates: so even with a low 3% interest rate, there's roughly a 1 in 3 chance that you'll actually be worse off (the gains on your investments will be less than the interest you pay).  In any case there's a 3 in 10 chance that your investments will lose money. "You asked for simple, and I promise you this is... it just looks a bit math-heavy to start with because we have to handle a couple of different scenarios. Bear with me :) I find the best way to deal with these kinds of questions is to put together a ""Total cost"" for each option, for a sensible amount of time, and see what the difference is. We'll include the current cost for both options, plus the subsequent costs for 12 months: I find that more useful than a straight ""which is more expensive right now"" because it includes the potential costs of the next upgrade, and any changes to the plan. Let's throw some numbers together for the next 12 months (if your current plan is longer than 12 months, read the note at the bottom first) First, write down the cost of these things **The above assume that you have two options if you take the repair option (and only one option if you use the buy-out option). The two options we're assuming here are that you can either:  If you'd choose the same new plan regardless of whether you take the $100 or $150 option, there's no need to include both options: to simplify things you can just use the same numbers for both b/c and Pu/Py and the calculation below will still work. When you've found and written down the above, just do the sums below to find your two total costs over 12 months. Nothing fancy, just plug the numbers above into the equation. eg if Pe (eBay value of the phone) is $80, replace Pe with 80. Don't forget to do the parts in brackets first! That's your total cost for both options for the next year. Note: I'm assuming that your plan ends within the next 12 months. If not, just replace 12 in the above calculations with another term! You can also do this if you want to find out the price difference over a longer period (noting that if you upgrade to the same plan regardless of choice, you'll get the same answer for any period longer than your current contract)" Look into commodities futures & options. Unfortunately, they are not trivial instruments.