# What is compound interest? | Opto

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## Definition of compound interest

Compound interest is the interest on a deposit or loan that takes into account both your original principal and the interest that amount has accrued in previous periods. Since you not only earn interest on the principal amount each period, but on the cumulative amount, you will get more for your money.

For example, take a savings account that has \$ 10,000 in it and earns 2% compound interest each year.

• After the first year, you will have \$ 10,200 in your account (\$ 10,000 principal + 2% of \$ 10,000)
• After year 2, you will have \$ 10,404 in your account (balance of \$ 10,200 + 2% of \$ 10,200)
• After year 3, you will have \$ 10,612.08 in your account (\$ 10,404 balance + 2% of \$ 10,404)

After three years, your initial capital of \$ 10,000 has increased by \$ 612.08

You can compare compound interest to simple interest using the same example, where 2% interest is charged each year only on the principal amount.

• After the first year, you will have \$ 10,200 in your account (\$ 10,000 in principal + 2% of \$ 10,000)
• After year 2, you will have \$ 10,400 in your account (balance of \$ 10,200 + 2% of \$ 10,000)
• After year 3, you will have \$ 10,600 in your account (balance of \$ 10,400 + 2% of \$ 10,000)

After three years, your initial capital of \$ 10,000 has increased by \$ 600.

## So what is composition then?

Composition is the process by which the profits of an asset, such as capital gains or reinvested dividends, lead to additional growth in profits over time. The investment will continue to produce capital gains and gains accumulated in previous periods.

For example, reinvesting your dividends in cash to buy more stocks will increase your returns from future dividend payments. Note that the composition works for both assets and liabilities.

To calculate the future value of an investment through the compound effect at a certain rate of return per period, you can use the following formula:

VF = PV x (1 + i) ^ n

• VF = Future value
• PV = Current value
• I = Rate of return / interest rate for the period
• m = number of periods per year

If you are investing \$ 100,000 and want to know the size of your investment assuming an annual return of 8% compounded over 10 years, here is the solution using the above formula:

VF = \$ 100,000 x (1 + 0.08) ^ 10

VF = \$ 215,892.50

Profit = \$ 115,892.50

To show the true power of compounding, you can use the same example as above but apply a simple 8% interest rate on the principal each year, with nothing that can be reinvested.

Profit = \$ 100,000 x 0.08 x 10 = \$ 80,000

As you can see, the difference in earnings between the two types of investments is significant. The spread is \$ 35,892.50 after ten years, or 44.87% more if funded rather than just receipt of interest.

Once you’ve got a well-rounded investment plan in place, you can harness the power of compound interest to dramatically accelerate your journey to your financial goals.

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