Interest is the cost of borrowing money, and is a percentage of the
borrowed amount, usually expressed an an annual percentage rate (APR).
Interest applies both to consumers when they borrow money from banks in
the form of car and home loans, and to banks when they borrow money
from consumers in the form of savings accounts.

There are two main types of interest: simple and compound. For simple
interest, the amount every year is based on the borrowed amount, which
is called the principal. Car and home loans use simple interest, which
was discussed in a previous section. For compound interest, the amount
every year is based on both the principal and accumulated interest.
Savings accounts use compound interest. When earning money from
interest, the annual percentage rate is called an annual percentage
yield (APY).

To calculate an account balance from a principal, APY, and number of
years, divide the APY by 100 to get a decimal, multiply that by the
principal to get the interest amount for the first year, and add that
to the account balance. Then multiply the account balance by the
interest rate to get the interest amount for the second year, and add
that to the account balance. Repeat this process for the total number
of years.

For example, you deposit $100 into a savings account with 10% interest,
and keep it there for 3 years. To calculate the account balance, do the
following:

percent = 10 decimal = 10 ÷ 100 = 0.1 years = 3 principal = $100.00

1st year interest = $100 × 0.1 = $10.00 1st year balance = $110.00

2nd year interest = $110 × 0.1 = $11.00 2nd year balance = $121.00

3rd year interest = $121 × 0.1 = $12.10 3rd year balance = $133.10

In the example above, interest is added to the account once per year. In
reality, interest can be added at more frequent intervals, such as
monthly or daily. This is called the compounding frequency, but that's
beyond the scope of this section. For the exercises below, assume that
interest is added to the account once per year.

account balance = principal × (1 + interest rate)

Using the original example above with a $100 deposit and 10% interest:

account balance = $100 × (1 + 0.1)

Now let's say you deposit $1,000 into a savings account with 5% interest, and keep it there for 10 years. Using an exponent, what is the account balance?