The Main Idea  The principal is the amount of money that is borrowed or invested. For example, if you take out a student loan for [latex]$10,000[/latex], the principal is [latex]$10,000[/latex]. Simple interest is the interest that is calculated only on the principal amount, without taking into account any interest that has accumulated over time. Simple interest is typically calculated as a percentage of the principal amount and is added to the principal at regular intervals, such as monthly or annually. For example, if you have a savings account with a principal of [latex]$1,000[/latex] and a simple interest rate of [latex]5\%[/latex], you would earn [latex]$50[/latex] in interest over the course of a year, which would be added to the principal balance of the account. Simple interest is a straightforward way to calculate the interest earned or paid on a loan or investment.

The Main Idea  Simple one-time interest refers to the interest that is earned or paid on a principal amount over a single period of time. This means that interest is only calculated once, at the end of the specified period, and it is based on the initial principal amount. Simple one-time interest is typically used in situations where the length of the investment or loan period is short and the interest rate is fixed. It is a straightforward way to calculate interest and can be useful for comparing different investment or loan options.

The Main Idea  Compound interest refers to the interest that is earned on the initial principal amount as well as on the accumulated interest over time. In other words, the interest earned on an investment or the interest charged on a loan is added to the principal amount at regular intervals, and the new balance earns interest in the subsequent period. For example, if you invest [latex]$100[/latex] in a savings account with a compound interest rate of [latex]5\%[/latex] per year, at the end of the first year, you will earn [latex]$5[/latex] in interest, bringing your balance up to [latex]$105[/latex]. In the second year, you will earn interest on the new balance of [latex]$105[/latex], which means you will earn [latex]$5.25[/latex] in interest. This means that over time, your interest earnings will grow at an increasing rate because you are earning interest on both the initial principal amount and the previously earned interest. Compound interest can lead to significant growth in the value of an investment over time, especially when the interest rate is high and the investment period is long. However, it can also result in higher costs for loans that charge compound interest, as the interest charged on the loan grows over time.