A persistent myth is that you don’t pay compound interest on installment loans, such as mortgages, car loans, and other personal loans.  I’ll show that this is nonsense. One example of this myth comes from an Investopedia article on car loans : “Auto loans include simple interest costs, not compound interest.”  The reasoning is that if your payments cover all the interest that accrues each payment period, then there is no opportunity to build interest on top of interest. However, money is fungible.  Why can’t we think of each payment as going against principal and leaving the interest owing?  Then there would be interest building on top of interest.  We could also think of payments applied proportionally.  For example, if a payment represents 5% of the remaining amount owed, we could think of the payment covering 5% of the remaining principal and 5% of accrued interest.  This proportional method is the most useful way to think about how payments apply,...

In a previous post , I showed how the average real return in the US stock market from 1926 to 2000 is 9.3%, but that this translated into a compounded real return of only 7.4%. The reason for this difference is the volatility of the returns. Let’s go for a better understanding of the cost of volatility without any advanced math. A Simple Example Suppose that you have $10,000 invested for two years. In the first year you lose 10%, and the next year you make 10%. It might seem at first that you have your $10,000 back, but that isn’t exactly right. After the first year you were down to $9000, and then in the second year you earned 10% on that $9000 to get a total of $9900. In the end you lost 1% of your money. However, the annual returns were -10% and +10% for an average return of 0%. The lost 1% over the two years is not due to a negative expected return; it is due to the volatility of the returns. The average return is 0%, but the compounded return is about -0.5% per year. Anoth...

I intend to review the book Worry-Free Investing by Zvi Bodie and Michael Clowes, but for now I want to discuss one part of the book that reports historical U.S. stock market returns that are higher than I was expecting. In Chapter 6, the authors discuss U.S. stock returns from 1926 to 2000. They actually give real returns, which means the returns after inflation is subtracted out. Based on the historical data, they calculate the average yearly real return on stocks to be 9.3%. But, others say that the long-term real return on US stocks is 7%. This may not look like a big difference, but if you play around with one of the many free retirement calculators available online, you’ll find that an extra percent or two of return on your investments each year makes a big difference over the long term. So, which one is the correct historical average return? It turns out that they are both right because they are talking about different things. The 9.3% figure comes from taking the returns...

So what if the Management Expense Ratio that I pay on my mutual funds is 1% or 2% or 3%? If I’m planning to at least triple my money before I retire, why should such tiny percentages concern me? The short answer is that the MER is collected on the same money year after year, which makes it really add up. The government may take one-third of your income every year, but at least they don’t tax the same money as income again. Imagine if instead of taking one-third of your income the government added up the value of everything you have and demanded one-third of that every year. “Let’s see ... your house plus the rest of your stuff is worth about $450,000. That makes your taxes $150,000 this year. Pay up.” The MER is more like property taxes; you are taxed on what you have instead of what you make in a year. However, property tax rates are much lower than income tax rates. In my area, property taxes amount to between 1% and 2% of the value of a property each year. And at least the city ...