## 22 September 2008

### Interest for the Masses

My recent encounter with the seedy underside of consumer financing has led me to conclude that I should have a better understanding of compound interest. Of course, everyone learns the basics in school -- i.e., that if your APR is x percent, and your principal is k, and the interest is compounded, say, monthly, then your principal will accumulate (x / 1200) * k in interest over one month. Roll this out into compounding, and after z months, you end up with (1 + x / 1200) ^ z * k.

Things get a little murkier if you make payments, however. Ever wonder where your credit card's minimum payment comes from? How about your auto loan payment? Most financial companies have a simple financial calculator where they input the relevant parameters of the loan, e.g. interest rate, principal balance, number of payments, and (often implicitly) the future value, then compute the minimum payment required to achieve the value. This is some pretty basic math, based largely on Geometric Series, but it's often helpful to have a specialized calculator to experiment with different payment schemes.

Tons of financial calculators exist on the web. Hell, I'm sure there are even some free ones. However, the one I'm most familiar with (a component of the GnuCash financial package) gives incorrect results; when I put our auto-loan into the program, it concluded that I would pay an entire extra payment's worth of interest -- a difference of over $250. One very bored and cramped train ride later, I cooked up the basics of a financial calculator, following the GnuCash calculator model. I didn't even try to simplify the math, rather using binary search and enumeration to compute everything. I was able to use it to figure out roughly how much interest we will be paying off for various monthly repayment schemes for our car, which is pretty cool. Give me some time and I'll throw together a web page for the thing, and maybe write some more about it.

Fun Fact: I found that if you have two million dollars and you can invest it at a 7% APR (compounded monthly) -- which is probably possible, at this scale -- you can receive a fat paycheck of $11k per month. Which leaves me wondering how lotto winners ever go broke.

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