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I think finance and microeconomics are worth learning if you're a programmer, because it's important to understand how a company makes money. I've heard lots of cockamamy ideas from programmers who didn't know anything about business. It's even more useful if you're thinking about becoming a manager or entrepreneur at some point.
As a discipline, finance is mostly about evaluating projects or choices in today's terms. You have to have at least two options if you're going to use financial analysis. It's essentially comparative. It doesn't make any sense to say an option is good in itself. You have to say what it's better than, and you have to be able to do it using some kind of common scale.
The two metrics finance focuses on are risk and return. When you're talking about things whose prices are set by a market, risk and return tend to be correlated (at least, according to academics). Risky things may payoff big. Chances are, however, they'll cost you. That doesn't mean you shouldn't do them, only that you have to compare them to other possibilities.
Risk and return are not limited to assets or financial instruments. We think in their terms all the time. I'm a decent drummer, and I briefly considered trying to make drumming into a career. But I realized that the chances of becoming a professional drummer were pretty small. When I compared the risk and return of being a drummer to being a programmer, the choice was obvious. If I didn't like anything else or wasn't good at anything else, it would be a different story.
Financial analysts, of course, are typically interested in money. In the case of money, you almost immediately have to start talking about interest. And the weird thing about interest is that you gain interest on interest. This is called compounding. Everyone thinks they understand compounding from high school, but it never ceases to blow my mind.
Even if you're not interested in money, there is always a cost associated with doing something, since it involves not doing something else. This is called opportunity cost. When you think about whether or not you want to see a movie, for example, you could consider all the other things you could be doing. Businesses must make decisions that take opportunity cost into account. There's even a cost associated with having cash, since that money could be invested in something else.
In short, finance provides a lens for evaluating pretty much anything. It's not always the right lens, because it is highly simplistic, but it can give you a start when trying to get your head around very different options. For many choices, risk, return, and opportunity cost don't provide much help, such as choosing between hanging out with friends or staying in and reading poetry. Even if it's not the right tool in all cases, I think the overall goal of comparing things along a common axis is a useful way to begin thinking about many problems.
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