If you invest $100 for two years at 10% interest, compounded annually, how much do you have at the end of two years?

To determine the total amount after two years with an initial investment of $100 at a 10% annual interest rate, compounded annually, it's important to understand the effect of compound interest.

The formula for compound interest is given by:

A = P(1 + r)^n

Where:

• A is the amount of money accumulated after n years, including interest.

• P is the principal amount (the initial sum of money).

• r is the annual interest rate (decimal).

• n is the number of years the money is invested or borrowed.

In this case, the principal amount is $100, the interest rate is 10% (or 0.10 as a decimal), and the investment period is 2 years.

Plugging the values into the formula:

A = 100(1 + 0.10)^2

A = 100(1.10)^2

A = 100(1.21)

A = 121

After two years, the total amount accumulated will be $121. This illustrates how compound interest allows the interest earned in the first year to itself earn interest in subsequent years, resulting in greater growth compared to simple interest calculations which would yield a lower amount.

Therefore, the correct