Is compounding interest on investments a myth?
"The S&P 500 index from 1974 to present certainly looks exponential to me (1974 is the earliest data Google has).  If you read Jeremy Siegel's book there are 200 year stock graphs and the exponential nature of returns on stocks is even more evident.  This graph only shows the index value and does not include the dividends that the index has been paying all these years.  There is no doubt stocks have grown exponentially (aka have grown with compound interest) for the past several decades and compounded returns is definitely not a ""myth"".  The CAGR on the S&P 500 index from 1974 to present has been 7.54%: (1,783 / 97.27) ^ (1 / 40) - 1 Here is another way to think about compounded investment growth: when you use cash flow from investments (dividends, capital gains) to purchase more investments with a positive growth rate, the investment portfolio will grow exponentially.  If you own a $100 stock that pays 10% dividends per year and spend the dividends every year without reinvesting them, then the investment portfolio will still be worth $100 after 40 years.  If the dividends are reinvested, the investment portfolio will be worth $4,525 after 40 years from the many years of exponential growth: 100*(1 + 10%)^40" Compound growth isn't a myth, it just takes patience to experience.  A 10% annual return will double the investment not in 10 years, but just over 7.  Even though a mortgage claims to use simple interest, if your loan is 5% and there's 14 years to go, $100 extra principal will knock off $200 from the final payment. The same laws of compounding and Rule of 72 are at play. So my Question is this, in reality is investment in equities like the   stock market even remotely resemble the type of growth one would   expect if investing the same money in an account with compounding   interest? Generally no as there is a great deal of volatility when it comes to investing in stocks that isn't well represented by simply taking the compounded annual growth rate and assuming things always went up and never went down. This is adding in the swings that the market will take that at times may be a bit of a rude surprise to some people. Are all these prognosticators vastly underestimating how much savers   need to be socking away by overstating what is realistic in terms of   growth in investment markets? Possibly but not probably. Until we know definitively what the returns are from various asset classes, I'm not sure I'd want to claim that people need to save a ton more. I'll agree that the model misses how wide the swings are, not necessarily that the averages are too low or overstated. "This post may be old anyhow here's my 2 cents. Real world...no. Compounding is overstated. I have 3 mutual funds, basically index funds, you can go look them up. vwinx, spmix, spfix in 11 years i've made a little over 12,000 on 50,000 invested.  That averages 5%. That's $1,200 a year about. Not exactly getting rich on the compounding ""myth?"". You do the math. I would guess because overly optimistic compounding  gains are based on a straight line gains. Real world...that aint gonna happen."
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! "Most likely that's the amount of interest that accrued on the loan while you were in school.  If you had paid that amount before 6/21, you would have just paid off accrued interest and your loan balance would have stayed the same. Since you did not pay the interest, it will be added to your loan balance and you will just pay it off as part of the loan (plus compounded interest).   If you pay off your loan at 5% over 30 years (hopefully you won't, but that's what they're amortized for), that $350 will compound and become $1,563.  Essentially you're ""borrowing"" $350 at 5% interest for 30 years. Hopefully that motivates you to pay it off sooner that that..." "(Ignoring any ethical considerations of defaulting on a mortgage obligation) If your credit score fell, future costs of borrowing would be greater, if you could borrow money at all. The true financial cost of these penalties would depend on your own intentions and circumstances. The value of a credit score cannot be quantified in any absolute sense because of these circumstances which will vary from person to person. Suppose a decision would result in your score falling from 700 to 600. As a result, a future car loan would cost something like 2% more in interest per year. Let's also suppose you would not be able to find a bank to give you money to buy a new home.  The difficulties caused by this situation would depend on the person. Some people have no intention of taking out another mortgage or buying another car, and to them, a lowered credit score might make no difference. To others, it would be desirable to avoid these penalties. The value of credit score would be equal to how much you would be willing to pay in the present to avoid these future penalties.  If you intend to borrow money in the near future, and somehow know how much more interest you will pay as a result of your lower score, then you could approximate the value of the credit drop by summing all of the additional interest costs discounted into the present. Something a little like this: Year's Additional Cost in Interest / (1 + Your Personal Opportunity Cost of Funds) ^ (Years in the future this extra interest will be paid).  See time value of money explanation: Can you explain ""time value of money"" and ""compound interest"" and provide examples of each? It could also be the case that you miss out on valuable financial opportunities as a result which could be added to the present value of the credit score drop.  For example, if the drop made you totally unable to purchase an investment property that would net you $10,000 in cash flows /year (which would yield cash flows immediately). The value of that investment would have been $10,000 / (1 + Your Personal Opportunity Cost of Funds). Since you would not be able to make that investment (in this example) as a result of the decreased score, the present value of the investment would be an opportunity cost of the lower score. There are other hard-to-quantify costs of low credit to consider as well, ranging from housing to employment to bragging rights.  Hopefully this has helped :)" "Well, the first one is based on the ""Pert"" formula for continuously-compounded present value, while the second one is the periodically-compounded variant.  Typically, the continuously-compounded models represent the ideal; as the compounding period of time-valued money shrinks towards zero, and the discount rate (or interest rate if positive) stays constant over the time period examined, the periodic equation's results approach that of the continuously-compounded equation. Those two assumptions (a constant rate and continuous balance adjustment from interest) that allow simplification to the continuous form are usually incorrect in real-world finance; virtually all financial institutions accrue interest monthly, for a variety of reasons including simpler bookkeeping and less money paid or owed in interest. They also, unless prohibited by contract, accrue this interest based on a rate that can change daily or even more granularly based on what financial markets are doing. Most often, the calculation is periodic based on the ""average daily balance"" and an agreed rate that, if variable, is based on the ""average daily rate"" over the previous observed period. So, you should use the first form for fast calculation of a rough value based on estimated variables. You should use the second form when you have accurate periodic information on the variables involved. Stated alternately, use the first form to predict the future, use the second form in retrospect to the past." "Question 2 Some financial institutions can provide a way to invest small amounts with low or no cost fees over a period of time (like monthly, weekly, etc).  For instance, a few brokerages have a way to buy specific ETFs for no cost (outside of the total expense ratio). Question 3 When someone says that investing is like buying a lottery ticket, they are comparing an event that almost always has at least a 99.9% of no return (large winnings) to an event that has much better odds.  Even if I randomly pick a stock in the S&P 500 and solely invest in it, over the course of a given year, I do not face a 99.9% chance of losing everything. So comparing the stock market to a lottery, unless a specific lottery has much better odds (keep in mind that some of these jackpots have a 99.9999999% of no return) is not the same.  Unfortunately, nothing truly safe exists - risk may mutate, but it's always present; instead, the probability of something being safe and (or) generating a return may be true for a given period of time, while in another given period of time, may become untrue. One may argue that holding cash is safer than buying an index fund (or stock, ETF, mutual fund, etc), and financially that may be true over a given period of time (for instance, the USD beat the SPY for the year of 2008).  Benjamin Franklin, per a biography I'm reading, argued that the stock market was superior to gold (from the context, it sounds like the cash of his day) because of what the stock market represents: essentially you're betting on the economic output of workers.  It's like saying, in an example using oil, that I believe that even though oil becomes a rare resource in the long run, human workers will find an alternative to oil and will lead to better living standards for all of us. Do civilizations like the Mongolian, Roman, and Ottoman empires collapse?  Yes, and would holding the market in those days fail?  Yes.  But cash and gold might be useless too because we would still need someone to exchange goods with and we would need to have the correct resources to do so (if everyone in a city owns gold, gold has little value).  The only ""safe bet"" in those days would be farming skill, land, crops and (or) livestock because even without trading, one could still provide some basic necessities." "I don't follow the numbers in your example, but the fundamental question you're asking is, ""If I can borrow money for a low cost, and if I think I can invest it and receive returns greater than that cost, should I do it?"" It doesn't matter where that money comes from, a mortgage that's bigger than it needs to be, a credit card teaser rate, or a margin line from your stock broker. The answer is ""maybe"" - depending on the certainty you have about the returns you'd receive on your investments and your tolerance for risk. Only you can answer that question for yourself. If you make less than your mortgage rates on the investments, you'll wish you hadn't! As an aside, I don't know anything about Belgian tax law, but in US tax law, your deductions can be limited to the actual value of the home. Your law may be similar and thus increase the effective mortgage interest rate." There are many Shariah compliant investments, so that could direct your resulting searches. Shariah compliance is a very strict interpretation of Islam and for investing offers strict guidelines in what to invest in and excludes investments in companies that engage in certain businesses such as gambling, tobacco, pork and trading of gold and silver on a deferred basis (and more). Many multinational financial service companies such as the Standard & Poors (S&P) offer Shariah Compliant funds and indices, as such, it makes it easier to invest in a variety of different assets through them. You can also look at their fund's constituents and invest in those assets directly. Secondly, going back to your original question about a compound interest equivalent, you can look at the products offered by Shariah Compliant banks. Now, if it is really important for you to adhere to the strictest interpretations of your faith, you should know that most Islamic Banks have interest bearing assets within them and that they disguise that fact. The global financial system is based on interest bearing instruments such as bonds, and Islamic banks are large holders and issuers of those instruments, and all of their consumer products are also based on the interest rates of them. Even convoluted alternatives such as Islamic mortgages, where they are advertised as non-interest bearing equivalents, many times are also the interest bearing version. Unfortunately, these lies are enough for the banks to continue to get business from their target audiences, but outside of Islam this is a very standard and stable business practice. The point is that you should look very carefully at the alternatives you find. I'm not a financial guy, but I handle decent amounts of money. I don't care how much money you take in, money only makes so much money. Sure, $1 million throws off decent interest (at least it used to), but it doesn't generate enough money to ever sustain a Ponzi scheme. Don't be fooled by what $20 million generates everyday in an account. It's never enough to pay back investors a fair return on their money.