What would be a better deal: depositing money at simple interest of 5% for 20 years, or 10% for 10 years (double the interest, half the time?)

Next, we consider compound interest. This is a more realistic scenario; you make a single deposit, but at the end of every year, the earned interest is added to the principle. Over the years, you earn interest on interest. The formula for compound interest is

FV = PV(1+i)t

Example: What's the future value of $100 invested at 5% interest, compounded annually, at the end of the first year (n=1)?

FV = 100.00(1+0.05)1=100.00(1.05)=$105.00

That's simple enough; we could probably have done that in our heads. But how much would $100 be worth, if left on deposit at 5% simple interest, for 20 years?

FV = 100.00(1+0.05)20=100.00(2.65)=$265.00

Where did the 2.65 come from? Almost all calculators will calculate the value of a number raised to a power. If you don't know how to do it on your calculator, get out the instruction book. Or find a scientific calculator online -- there are plenty of them.