# Compound interest

When it comes to calculating interest, there are two basic choices: simple and compound. Simple interest simply means a fixed percentage of principal each year and is rarely used in practice.

On the other hand, compound interest is applied to both loans and deposit accounts. Compound interest basically means “interest on interest” and this is the reason why many investors are so successful.

Comparison of simple and compound interest
Let’s say you invest \$ 10,000 at 8% simple interest. This means that after the first year, \$ 800 is added to your account. In the second year, \$ 800 more interest is paid, and the same with the third year, the fourth year, and so on.

If your investment returned 8% compound interest on an annual basis, it wouldn’t make a difference at first. After the first year, you will receive the same interest payment of \$ 800 as with a simple interest calculation. However, this is where it starts to get very different.

The second year, your 8% interest is calculated on your all new balance of \$ 10,800, not just the original \$ 10,000. This produces an interest payment of \$ 864 for the second year, which is then added to the principal when calculating your interest for the third year.

You might be surprised how quickly this can add up. At a simple interest rate of 8%, your \$ 10,000 investment would be worth \$ 34,000 after 30 years. However, using compound interest, the value would skyrocket to over \$ 100,000. Take a look at the comparison of simple and compound interest over a 50-year period:

The compound frequency makes the difference
In the previous example, we used annual compounding, which means interest is calculated once a year. In practice, compound interest is often calculated more frequently. Common dialing intervals are quarterly, monthly, and daily, but there are many other possible intervals that can be used.

The frequency of compounding makes a difference – in particular, more frequent compounding results in faster growth. For example, here is the growth of \$ 10,000 at an interest rate of 8% compounded at several different frequencies:

Time

Annual composition

Quarterly

Monthly

1 year

\$ 10,800

\$ 10,824

\$ 10,830

5 years

\$ 14,693

\$ 14,859

\$ 14,898

10 years

\$ 21,589

\$ 22,080

\$ 22,196

The compound interest formula and an example
To calculate interest compounded over time, there is a mathematical formula you can use: Where “A” is the final amount, “P” is the principal, “r” is the interest rate, expressed as a decimal, “n” is the number of compounding periods per year and “t” is the period of time in which years.

For example, let’s say you invest \$ 20,000 at 5% interest, compounded quarterly, for 20 years. In this case, “n” would be four, since quarterly dialing occurs four times a year. From this information, we can calculate the final value of the investment after 20 years like this: The \$ 15,978 Social Security bonus that most retirees completely ignore