First of all, I'm new so forgive me if I'm posting this in the wrong area.
I am going to assume we all know the interest formulas A = P * e^rt and A = P(1 + (r/n))^nt. The first is continuously compounded interest and the second is compounded interest n times per year. Also, we know that the continuously compounded interest formula is derived from the limit as n->infinity of the latter formula.
So here's the problem my class is running into:
We found that (given a $1000 principle, 5% interest rate, and t = 1 year) that if you compound the interest minutely (that is, n = 31536000) you earn more interest than if you compound it continuously, which doesn't make sense because you should be making the most you possibly can when compounded continuously. We then made a table of values and graphed it for extreme values of n and found that it jumps all over the place. (Try it, graph y = 1000(1 + .05/x)^x and look at the right side when x is 1000000000.)
My question: Is this a calculator malfunction? Is it because of rounding errors? That's what I thought but I wanted to see your opinions on it.