You might try reading up on microfinance, it seems like it's in the same reference class as your idea. Givewell writes about it here (and other places).
If I want to invest in companies being started in Africa, I'm going to have to do one of two things: make investments myself or give my money to someone else to invest it for me. If I make investments myself, I'll either do it remotely (which seems like a bad way to get to know investment opportunities, do due diligence, etc.) or travel to Africa and effectively work as an angel investor myself. Giving the money to someone else to invest seems like it might run in to the same sort of problems that giving the money to someone else to do good deeds with would, but it could be mitigated by my money manager's incentive to get a good return for me in order to attract additional clients. So this idea seems more or less equivalent to: find a venture capital firm operating overseas and invest your money with them. My impression is that venture capital firms typically have institutions rather than individuals as their clients; I'm not sure if there's a good reason for this.
Investing in the stock markets of developing countries is another idea. My friend who's an expert on economics has told me that it's common for a country's economy to grow well while its stock market performs poorly, I guess due to a high amount of turnover among the companies listed? I'm not sure how this would effect the EA implications of investing in a developing country's stock market.
I'd like to hear from people about a process they use to decide how much to give to charity. Personally, I have very high income, and while we donate significant money in absolute terms, in relative terms the amount is <1% of our post-tax income. It seems to me that it's too little, but I have no moral intuition as to what the right amount is.
I have a good intuition on how to allocate the money, so that's not a problem.
Background: I have a wife and two kids, one with significant health issues (i.e. medical bills - possibly for life), most money we spend goes to private school tuition x 2, the above mentioned medical bills, mortgage, and miscellaneous life expenses. And we max out retirement savings.
If you have some sort of quantitative system where you figure out how much to spend on charity, please share. If you just use vague feelings, and you think there can be no reasonable quantitative system, please tell me that as well.
Update: as suggested in the comments, I'll make it more explicit: please also share how you determine how much to give.