Tutorial

How to Calculate Compound Interest: Formula and Worked Examples

Published 15 March 2026 · 8 min read

Compound interest is one of the most powerful concepts in finance. Unlike simple interest, which is calculated only on the original principal, compound interest is calculated on the principal plus all previously accumulated interest. This means your money grows exponentially over time, making it the driving force behind savings accounts, investments, and loans.

In this guide, you will learn the compound interest formula, understand how compounding frequency affects growth, and work through three detailed examples that cover annual, monthly, and continuous compounding.

The Compound Interest Formula

The standard compound interest formula is:

A = P\left(1 + \frac{r}{n}\right)^{nt}

$A$ = the future value (principal + interest)
$P$ = the initial principal (starting amount)
$r$ = the annual interest rate (as a decimal)
$n$ = the number of times interest is compounded per year
$t$ = the number of years

Simple Interest vs Compound Interest

With simple interest, you earn a fixed amount each period based only on the original principal. With compound interest, each period's interest is added to the principal, so the next period earns interest on a larger amount.

Simple Interest

A = P(1 + rt)

Growth is linear. After 10 years at 5% on $1,000, you earn $500 in interest.

Compound Interest

A = P\left(1 + \frac{r}{n}\right)^{nt}

Growth is exponential. After 10 years at 5% compounded annually on $1,000, you earn $628.89 in interest.

The difference between $500 and $628.89 is entirely due to compounding. Over longer time periods and at higher rates, this gap widens dramatically.

How Compounding Frequency Matters

The value of $n$ in the formula determines how often interest is calculated and added to the principal. Common compounding frequencies include:

Frequency	n value	$1,000 at 5% for 10 years
Annually	1	$1,628.89
Quarterly	4	$1,643.62
Monthly	12	$1,647.01
Daily	365	$1,648.66
Continuously	$\infty$	$1,648.72

Notice that more frequent compounding produces slightly higher returns, but the gains diminish as frequency increases. The jump from annual to monthly compounding is much larger than the jump from monthly to daily.

Worked Examples

Example 1: Annual Compounding

You invest $5,000 in a savings account that pays 6% interest compounded annually. How much will you have after 8 years?

Given: $P = 5000$ , $r = 0.06$ , $n = 1$ , $t = 8$ .

A = 5000\left(1 + \frac{0.06}{1}\right)^{1 \times 8}

A = 5000(1.06)^{8}

A = 5000 \times 1.593848

A = 7{,}969.24

After 8 years, your investment grows to $7,969.24. You earned $2,969.24 in compound interest.

Example 2: Monthly Compounding

You deposit $10,000 into an account earning 4.5% interest compounded monthly. What is the balance after 5 years?

Given: $P = 10{,}000$ , $r = 0.045$ , $n = 12$ , $t = 5$ .

A = 10{,}000\left(1 + \frac{0.045}{12}\right)^{12 \times 5}

A = 10{,}000\left(1 + 0.00375\right)^{60}

A = 10{,}000 \times (1.00375)^{60}

A = 10{,}000 \times 1.25204

A = 12{,}520.40

After 5 years with monthly compounding, your $10,000 grows to $12,520.40.

Example 3: Continuous Compounding

For continuous compounding, we use a different formula based on Euler's number $e$ :

A = Pe^{rt}

You invest $3,000 at 7% interest compounded continuously for 12 years. What is the final amount?

Given: $P = 3{,}000$ , $r = 0.07$ , $t = 12$ .

A = 3{,}000 \times e^{0.07 \times 12}

A = 3{,}000 \times e^{0.84}

A = 3{,}000 \times 2.31637

A = 6{,}949.11

With continuous compounding, your $3,000 more than doubles to $6,949.11 after 12 years.

The Rule of 72

The Rule of 72 is a quick mental shortcut for estimating how long it takes for an investment to double. Simply divide 72 by the annual interest rate:

\text{Doubling time} \approx \frac{72}{r\%}

For example, at 6% interest, your investment doubles in approximately $72 \div 6 = 12$ years. At 9% interest, it doubles in about $72 \div 9 = 8$ years.

This rule works best for interest rates between 2% and 12%. It is most accurate around 8%, where it matches the exact doubling time almost perfectly.

Solving for Other Variables

You can rearrange the compound interest formula to solve for any variable. Two common rearrangements are:

Solving for time

t = \frac{\ln(A/P)}{n \cdot \ln(1 + r/n)}

Solving for rate

r = n\left[\left(\frac{A}{P}\right)^{1/(nt)} - 1\right]

Common Mistakes

Forgetting to convert the rate to a decimal

An interest rate of 5% must be entered as 0.05 in the formula, not 5. This is the most common error in compound interest calculations.

Using the wrong compounding frequency

Make sure $n$ matches the actual compounding schedule. If interest compounds monthly, use $n = 12$ , not $n = 1$ .

Confusing APR with APY

The Annual Percentage Rate (APR) is the stated rate before compounding. The Annual Percentage Yield (APY) accounts for compounding. APY is always equal to or greater than APR.

Rounding intermediate calculations

Keep as many decimal places as possible during intermediate steps. Only round the final answer to avoid accumulating rounding errors.

Try It Yourself

Want to run your own compound interest calculations? Our percentage calculator can help you work through percentage-based problems quickly and accurately.

Open Percentage Calculator

For power calculations that underpin compound interest, try our Exponent Calculator.

15 Mar 20269 min read