How to Calculate Compound Interest

Deposit $5,000 at 6% interest for 10 years. With simple interest, you'd end up with $8,000. With interest compounded monthly, you'd have $9,096.98.

That extra $1,097 comes from earning interest on your interest. It's the defining feature of compound interest, and the formula behind it is one of the most useful pieces of math for everyday finances.

Compounding More Often Helps Less Than You'd Think

Switching from yearly to monthly compounding makes a noticeable difference. But going from monthly to daily, or even to compounding every instant, adds surprisingly little. For $5,000 at 6% over 10 years:

Moving from daily to continuous compounding adds just 45 cents. There's a hard ceiling, and it involves the number e.

The Formula

A = P × (1 + r/n)^(n × t)

• A = final amount
• P = principal (starting amount)
• r = annual interest rate as a decimal (6% = 0.06)
• n = number of times interest compounds per year
• t = number of years

The interest earned is A − P.

Step-by-Step Example: Monthly Compounding

$5,000 at 6% for 10 years, compounded monthly:

Step 1: Identify the values. P = 5,000, r = 0.06, n = 12, t = 10

Step 2: Find the periodic rate. r/n = 0.06 / 12 = 0.005

Step 3: Find the number of periods. n × t = 12 × 10 = 120

Step 4: Calculate the growth factor. (1.005)¹²⁰ ≈ 1.8194

Step 5: Multiply. A = 5,000 × 1.8194 ≈ $9,096.98

Interest earned: $4,096.98. Verify it with the compound interest calculator, and compare with the simple interest calculator.

Continuous Compounding

As compounding becomes infinitely frequent, the formula approaches:

A = P × e^(r × t)

where e ≈ 2.71828. For our example:

A = 5,000 × e^(0.06 × 10) = 5,000 × e^0.6 ≈ $9,110.59

Compute e^x with the scientific calculator or use natural logs from the logarithm calculator.

Adding Regular Contributions

Most savers add money regularly. If you deposit PMT at the end of each period, the future value of those contributions is:

FV = PMT × ((1 + r/n)^(n × t) − 1) / (r/n)

Depositing $200 per month at 6% for 10 years:

FV = 200 × ((1.005)¹²⁰ − 1) / 0.005 ≈ $32,775.87

You contributed $24,000; compounding added about $8,776. Add this to the growth of any starting balance to get your total. See the financial formulas.

How Long to Double Your Money?

Solve (1 + r/n)^(nt) = 2 for t:

t = ln(2) / (n × ln(1 + r/n))

At 6% compounded monthly: t ≈ 11.6 years. For a quick estimate, use the Rule of 72: 72 ÷ 6 = 12 years. See Why Does the Rule of 72 Work?

Common Mistakes

1. Using the annual rate per period. At 6% compounded monthly, the rate per month is 0.5%, not 6%. Always divide r by n.

2. Forgetting to multiply the years. Ten years of monthly compounding is 120 periods, not 10.

3. Entering the rate as a whole number. Use 0.06, not 6. Otherwise the growth factor becomes absurdly large.

4. Ignoring fees and taxes. A 1% annual fee on a 6% return leaves roughly 5% compounding, and over 30 years that difference can cost nearly a quarter of the final balance.

An Insider Reference: How Compound Interest Led to e

In 1683, Swiss mathematician Jacob Bernoulli studied a compound interest question. Suppose you invest $1 at 100% annual interest. How much do you have after one year if interest compounds:

• Once: $2.00
• Twice (50% each half-year): 1.5² = $2.25
• 12 times: (1 + 1/12)¹² ≈ $2.613
• 365 times: (1 + 1/365)³⁶⁵ ≈ $2.7146

Bernoulli realized the amount approaches a limit as compounding becomes more frequent, a value between 2 and 3. That limit is the number now called e ≈ 2.71828, later named and studied extensively by Leonhard Euler.

You may have seen a quote attributing to Albert Einstein the claim that compound interest is "the eighth wonder of the world." There's no reliable evidence he ever said it. The math, however, is every bit as powerful as the quote suggests.

Two Concepts Worth Knowing

Annual Percentage Yield (APY)

APY shows the effective yearly return including compounding: APY = (1 + r/n)ⁿ − 1. A 6% rate compounded monthly has an APY of about 6.17%. Compare savings accounts by APY, not the nominal rate.

Exponential Growth

Compound interest is exponential growth: the balance multiplies by the same factor each period. That's why time matters so much. See The Mathematics of Compound Interest.

Quick Answer: How Do You Calculate Compound Interest?

Use A = P(1 + r/n)^(nt), where P is the principal, r is the annual rate as a decimal, n is the number of compounding periods per year and t is the number of years. For $5,000 at 6% compounded monthly for 10 years, A = 5,000 × (1.005)¹²⁰ ≈ $9,096.98. Subtract P to find the interest earned.

Try Them Yourself

• Compound Interest Calculator: run your own scenarios
• Simple Interest Calculator: see what compounding adds
• Financial Formulas: future value and annuity formulas
• Logarithm Calculator: solve for time to reach a goal
• Natural Logarithm Table: the constant e
• Retirement Calculator: compound interest over a career

Calculate what $100 a month would grow to at 7% over 30 years, then over 40 years. The extra decade will show you exactly why starting early matters.