While both debt and equity investments can deliver good returns, they have differences with which you should be aware. Debt investments, such as bonds and mortgages, specify fixed payments, including interest, to the investor. Equity investments, such as stock, are securities that come with a "claim" on the earnings and/or assets of the corporation. Common stock, as traded on the New York or other stock exchanges, is the most popular equity investment. Debt and equity investments come with different historical returns and risk levels.
Caps can also be added to convertible debt. A cap sets a limit for how much the startup can raise before your shares stop getting diluted. It doesn’t value the convertible note, but it sets an upper limit. So in the example above, if the pre-money cap was $5,000,000, you would still get a discount of 20% up to that amount. If the startup raised at a valuation over $5,000,000, then the discount would increase to offset the additional dilution that was occurring. When you add a cap, the math gets a little trickier, as it can change with different funding scenarios.
For example, in January 2009 the CBO reported that for fiscal year 2008 (FY2008) the "on-budget deficit" was $638 billion, offset by an "off-budget surplus" (mainly due to Social Security revenue in excess of payouts) of $183 billion, for a "total deficit" of $455 billion. This latter figure was the one commonly reported in the media. However, an additional $313 billion was required for "the Treasury actions aimed at stabilizing the financial markets," an unusually high amount due to the Subprime mortgage crisis . This meant that the "debt held by the public" increased by $768 billion ($455B + $313B = $768B). The "off-budget surplus" was borrowed and spent (as is typically the case), increasing the "intra-governmental debt" by $183 billion. So the total increase in the "National debt" in FY2008 was $768B +$183B = $951 billion.  The Treasury Department reported an increase in the National Debt of $1,017B for FY2008.  The $66 billion difference is likely due to "supplemental appropriations" for the War on Terror, some of which were outside the budget process entirely until President Obama began including most of them in his FY2010 budget.