Welcome to the video on compound interest! In this chapter, we'll explore the basics of compound interest and how it works.

Imagine you deposit $1000 into a savings account with a 5% annual interest rate. Simple interest would only pay you interest on that initial $1000. But with compound interest, things get more exciting!

Compound interest means you earn interest not just on your initial deposit, but also on the accumulated interest from previous periods. This snowball effect leads to exponential growth over time.

Now let's look at the formula that governs this magical growth.

This is the compound interest formula: A equals P times 1 plus r divided by n, all raised to the power of nt. Where A is the final amount, P is the principal, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.

Let's break it down. The more frequently interest is compounded (n), the faster your money grows. And the longer you let it grow (t), the more significant the effect becomes.

Let's see how compounding frequency and time impact your returns.

Here's a comparison: Daily compounding yields slightly more than annual compounding, but the difference becomes more dramatic over longer periods.

Over 30 years, the difference between annual and daily compounding becomes substantial. This highlights the power of letting your money grow over time.

Now let's discuss how you can use compound interest to your advantage.

Start saving early! The earlier you start, the more time your money has to grow exponentially.

Use online calculators to easily model different scenarios and see how changes in interest rates and time affect your returns.

Remember, compound interest isn't just for savings accounts; it applies to investments too!