Determine an interest rate less than 15%, a period of investment greater than two years, and a regular payment that will result in the total amount of interest you earn being equal to the total amount of money you put in. (For example, under what conditions will you have a future value of $1,000,000, having earned $500,000 interest?)

This problem can be solved using the compound interest formula: A=P(1+r/n)^(n*t). Here, A = the amount yielded, P = the principal (i.e. initial) invested amount), r = the interest rate (as a decimal), n = the number of times per year, and t = the time invested. A great way to solve a problem like this is graphically. That is, you can enter a quantity as the "P" value, let your interest rate be 16% (as a decimal, .16), and then simply set your equation up so that it is equal to the amount desired (here, double the principle).
Let's take your instructor's example of $500 invested, and let's let the interest rate be .14 (14%). Our variable will be the time. Now, it's worth remarking that we can always solve for as many variables as we have equations. Therefore, we could alternatively let the interest rate be the variable and fix the time at something like 3 years (to satisfy the conditions of this problem, which stipulate that the time has to be greater than 2 years). But for now, let's write the equation as if we are investing $500 at an annual interest rate of 14% (therefore the number of times per year, "n" equals 1). Our equation will look something like this:
A=500(1.14)^x, where "x" is the number of years.
Then, we fix the amount ("A") at $1000, and we have:
1000=500(1.14)^x
2=1.14^x
log1.14 (2)=x
x=5.29
So, if we invest $500 at 14% interest, it will take 5.29 years to double our money.
Another option to solve this equation is to graph it by subtracting "1000" from both sides and looking for the x-intercept, as follows:
y=500(1.14)^x-1000