Consider the same problem of Alice wanting to borrow $1000 from the bank for 2 years at 10% interest per year. Rather than charging simple interest on the loan, the bank can use a more widely used form of interest calculation, compound interest.
Compound interest is interest that is added to the principal of a loan such that the added interest also earns interest. The addition of interest to the principal amount is referred to as compounding.
This means that for the first year, you can borrow $1000, and adding the interest for the first year, means that you owe the bank $1000*(1+0.10) = $1100 at the end of the year.
$\mathrm{S\_\_1}\=dollar;1000plus;0.10\cdot \left(1000\right)equals;dollar;1100$${}$${}$
Then for the second year, the principal owed is $1100, and subsequently you owe the bank interest on that amount at the end of the term.
$\mathrm{S\_\_2}\=dollar;1100plus;0.10\cdot \left(1100\right)equals;dollar;1210$${}$
Using compounded interest, the bank receives $10 more than with simple interest.
Compound interest can also be used to your advantage. Buying guaranteed investment certificates (GICs) or government bonds, can make the bank pay you interest. GICs pay compound interest, which as you will see, is much better than simple interest for investments.