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# What is compound interest and how does it work?

Compound interest is a financial term that describes the growth of an investment over time. Unlike simple interest, which is calculated on the initial investment only, compound interest is calculated on both the principal amount and the accumulated interest from previous periods. As a result, compound interest can generate significant returns over time, even for small investments.

To understand how compound interest works, let’s take a look at an example. Suppose you invest \$1,000 in a savings account that pays an annual interest rate of 5%. At the end of the first year, your account will have earned \$50 in interest, bringing your total balance to \$1,050. In the second year, your account will earn interest on the new balance of \$1,050, which means you’ll earn \$52.50 in interest. Your total balance at the end of the second year will be \$1,102.50.

In the third year, your account will earn interest on the new balance of \$1,102.50, and so on. As you can see, the interest earned on the previous year’s interest can quickly add up, resulting in significant returns over time.

The formula for calculating compound interest is as follows:

A = P(1 + r/n)^(nt)

Where:

A = the final amount
P = the principal amount
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years

Let’s break down this formula using our previous example. If we plug in the values, we get:

A = 1000(1 + 0.05/1)^(1*3)
A = 1000(1.05)^3
A = \$1,157.63

This means that after three years, your initial investment of \$1,000 would have grown to \$1,157.63, thanks to the power of compound interest.

One thing to note is that the frequency of compounding can have a significant impact on the overall return on your investment. For example, if the interest in our previous example was compounded quarterly instead of annually, the final balance would be \$1,158.92. If the interest was compounded monthly, the final balance would be \$1,160.40. This is because the more frequently the interest is compounded, the more opportunities your money has to grow.

In addition to savings accounts, compound interest can also be found in other types of investments, such as bonds, mutual funds, and retirement accounts. It’s important to note that investments come with varying levels of risk, and it’s important to do your research before making any investment decisions.

In conclusion, compound interest is a powerful tool for growing your money over time. By reinvesting the interest earned on your initial investment, you can achieve significant returns, even on small investments. When making investment decisions, it’s important to consider the frequency of compounding and to choose investments that align with your financial goals and risk tolerance.