Compound Interest Calculator

What Is Compound Interest?

Compound interest is interest calculated on both the initial principal and the accumulated interest from previous periods. Unlike simple interest — calculated only on the principal — compound interest causes your money to grow exponentially. Albert Einstein reportedly called this phenomenon "the eighth wonder of the world."

The NIST and the National Institute of Standards recognize compound interest calculations as foundational to financial mathematics. The key difference between compound and simple interest is that with compound interest, you earn interest on your interest. Over long time periods, this compounding effect can dramatically increase the value of your investments, savings, and retirement accounts.

How to Use the Compound Interest Calculator

Enter four values to calculate your investment growth:

• Principal Amount: The initial amount of money you are investing or depositing.
• Annual Interest Rate: The yearly interest rate, expressed as a percentage.
• Time Period: The number of years the money will be invested or saved.
• Compounding Frequency: How often interest is calculated and added to your account — daily, monthly, quarterly, semi-annually, or annually. More frequent compounding leads to slightly higher returns.

The Compound Interest Formula

The compound interest formula is:

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

Where:

• A = Final amount (principal + interest)
• P = Principal (initial investment)
• r = Annual interest rate (as a decimal)
• n = Number of times interest compounds per year
• t = Time in years

The interest earned is simply A − P.

Compound Interest Example

Suppose you invest $10,000 at a 7% annual interest rate, compounded monthly, for 20 years:

• P = $10,000
• r = 0.07
• n = 12
• t = 20

A = $10,000 × (1 + 0.07/12)^(12×20) = $10,000 × (1.005833)^240 ≈ $40,093

Your $10,000 investment grows to over $40,000 — a gain of $30,093 purely from compound interest, with no additional contributions.

The Power of Compounding Frequency

The frequency of compounding has a real impact on your final balance, though the differences are modest:

• Annual compounding: Interest added once per year
• Quarterly compounding: Interest added 4 times per year
• Monthly compounding: Interest added 12 times per year
• Daily compounding: Interest added 365 times per year

With higher compounding frequency, interest is added to your balance more often, which slightly increases your effective annual yield. For most savings accounts and investments, monthly or daily compounding is standard.

The Rule of 72

The Rule of 72 is a quick mental math trick to estimate how long it takes to double your money with compound interest. Simply divide 72 by the annual interest rate:

Years to double = 72 ÷ Interest Rate

• At 6% interest: 72 ÷ 6 = 12 years to double
• At 8% interest: 72 ÷ 8 = 9 years to double
• At 12% interest: 72 ÷ 12 = 6 years to double

Why Starting Early Matters

The most important factor in compound interest is time. Consider two investors:

• Investor A invests $5,000 at age 25 at 7% annual rate and never adds more
• Investor B invests the same $5,000 at age 35

At age 65, Investor A has approximately $74,872. Investor B has only $38,061 — despite investing the same amount. The 10-year head start is worth over $36,000 in this example. This illustrates why starting to save and invest early is one of the most impactful financial decisions you can make.

Simple Interest vs. Compound Interest

Simple interest is calculated only on the original principal:

Simple Interest = P × r × t

Compound interest calculates interest on the growing balance. For a $10,000 investment at 7% for 10 years:

• Simple interest: $10,000 + ($10,000 × 7% × 10) = $17,000
• Compound interest (monthly): approximately $20,097

The difference grows substantially over longer time periods.

Common Applications of Compound Interest

• Savings accounts: Banks apply compound interest to your deposits, growing your savings over time
• Retirement accounts: 401(k) and IRA accounts benefit enormously from decades of compounding
• Investment portfolios: Stock market returns compound over time through reinvested dividends and price appreciation
• Loans and credit cards: Compound interest works against you on debt — unpaid balances grow rapidly

Related Financial Calculators

• Mortgage Calculator — Calculate home loan payments
• Savings Calculator — Plan your savings goals
• Percentage Calculator — Calculate percentage returns
• Interest Rate Calculator — Find effective interest rates