Assessment and Learning in Knowledge Spaces (ALEKS) Basic Math Placement Practice Test

What is the formula for calculating compounded interest?

1. A = P(1 + r)^t

2. A = P(1 - r)^t

3. A = Prt

4. A = P + rt

The correct answer is: A = P(1 + r)^t

The correct formula for calculating compounded interest is A = P(1 + r)^t. In this formula, A represents the amount of money accumulated after n years, including interest. P is the principal amount, which is the initial sum of money that is invested or borrowed. The r denotes the annual interest rate (expressed as a decimal), and t represents the time the money is invested or borrowed for, usually in years. The essence of compound interest lies in the way the interest is calculated on the initial principal and also on the accumulated interest from previous periods. By using (1 + r), the formula acknowledges that interest is applied not just to the initial principal but also to the interest that has been added to it over time. As a result, the amount grows exponentially rather than linearly, which is the characteristic of compound interest. Understanding this formula is crucial for making informed financial decisions regarding investments or loans, as it clearly outlines how both the principal and the rates contribute to the total amount over a specified time frame.