Wednesday, June 8, 2011

The Simple Dollar(TSD) and confusion over the maths

The reason why The Simple Dollar's readers are confused is because IF at the end of year 1, the amount was $1,015 only, then it implies that he is using flat interest of 1.5% per annum and that interest is paid only at the end of the year.

Yet the later years utilises some type of semi-annual or quarterly compounding which you can see in my calculations below. There are only a handful of blogs out there that have thousands of subscribers and the The Simple Dollar has 13,000 subscribers. I wonder how many people actually read what they subscribe to? Or better yet, take action on what they've read? Could 13,000 people have simply glossed over TSD's numbers without even noticing something has gone astray?

Screenshot from The Simple Dollar: Trent has posted up some confusing numbers and maybe one of my dear readers can correct me if I'm wrong but I can't seem to generate the figures that he provided with using either simple interest, compound interest or simple interest with additional principal amounts of $1,000 invested.

He has some confused readers commenting about how they can't figure out how he calculated his numbers and I'm just as confused. To check what he may have done, I cranked out some numbers on the spreadsheet and you'll see why his calculations from the screenshot above has me baffled:

Scenario 1: $1,000 initially invested at the start of the year, all interest earned is reinvested at 1.5% per annum. In 15 years you would have a balance of $1,250.23

Scenario 2: $1,000 initially invested at the start of the first year, all interest earned is re-invested and compounded monthly at the rate of 1.5% per annum(ie: interest compounds monthly for 15 years). In 15 years you would have a balance of $1,252.15

Scenario 3: $1,000 initially invested at the start of every year for 15 years, all interest earned is reinvested at 1.5% per annum. At the end of 15 years you would have a balance of $15,240.23.

I don't know how Trent arrived at the figure of $16,932.37 without knowing how many times he compounded the interest in the year.

If he used $1000 invested at the start of every year, with 1.5% per annum interest compounded quarterly, the balance would be $16,942.64 and this is the closest that I can get without having to recalculate using interest being paid every half year. I can't be bothered to run another lot of calculation but judging by how close it is to his numbers then we can narrow it down to the rate of compounding and the way he is rounding his numbers up and down that may cause the numbers to be a few dollars off.

Why does it matter? As you can already see by the numbers provided above, it makes a HUGE difference depending on whether you keep re-investing or whether the interest is calculated and paid monthly, quarterly, semi-annually or annually. The best option is when your interest is paid monthly and is re-invested because then you get your interest income compounding every month. The interest that you earned in January is working hard for you every single month, every single year...until you spend it of course.

We are simply discussing the investment of $1,000 per annum. Imagine if you were saving $20,000 or $50,000 every year. You would be looking at differences of hundreds of thousands of dollars over the course of a few years and it could either be in your favour, or working against you. If you don't think you'll ever get to that stage, then you need find some bigger dreams for yourself.

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