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Your Roth IRA account grows over time thanks to two funding sources: contributions and earnings. While your contributions to your individual retirement account, or IRA, are the most obvious source of growth, the potential for your savings to earn interest and the power of interest compounding are equally crucial factors.

What Is a Roth IRA?
IRAs are popular savings vehicles among those who understand the importance of planning ahead for retirement. Rather than relying on the retirement savings accumulated through payroll deferrals made to an employer-sponsored savings plan such as a 401(k), IRAs allow even the self-employed to contribute during working years to ensure financial stability later in life.
The defining characteristic of a Roth IRA is the source of contributions. Like 401(k) plans, contributions to traditional IRAs are made with pretax dollars, meaning you must pay income tax when you withdraw the funds later. Contributions to Roth IRA’s, conversely, are made with after-tax dollars, so any contributions you make are yours to withdraw tax-free at your discretion.

Roth IRA Growth
The beauty of an IRA, whether Roth or traditional, is your account can grow even in years you are not able to contribute. In addition, the amount of growth your account generates can actually increase each year through the magic of compound interest. Basically, this means that every year your contributions earn interest, your balance is increased. The following year, you earn interest on this increased balance, meaning the total amount of interest earned increases each year even if you are no longer contributing to your account. While simple interest is the interest earned on your contributions, compound interest is the interest earned on prior years’ interest.

Example:
Assume you contribute $3,000 to your Roth IRA for 20 years, for a total contribution of $60,000. In addition to your contributions, your account earns $5,000 in interest, giving you a total balance of $65,000. To ramp up your savings, you decide to invest in a mutual fund that yields 8% interest annually.
Even if you stop contributing to your account after the 20th year, you earn 8% on the full $65,000 in the 21st year. You earn $4,800 in simple interest and $400 in compound interest, increasing your account balance to $65,000 * 1.08, or $70,200.
The second year after your last contribution, you continue to earn 8% on the sum of your contributions and previous earnings, yielding another $70,200 * 0.08, or $5,616, in total interest. Your balance is now $75,816. You gained nearly $11,000 in just two years without making any additional contributions.
In the third year, you earn $6,065, increasing your balance to $81,881. If you fast forward another five years, your account earns another $38,429 in interest, and your total balance is $120,310. Without contributing anything further to your account, your Roth IRA has nearly doubled in the past eight years through the power of compound interest.

source: www.investopedia.com