Compound Interest Calculator – Compute CI with Compounding

Calculate compound interest for daily, monthly, quarterly, or annual compounding with our free online calculator. See total interest earned and growth over time with a breakdown.

Principal (P)

Annual Interest Rate (%)

Time Period

Compounding Frequency

Examples:

Understanding Compound Interest

Compound interest is interest on interest – your money earns interest, then that interest earns its own interest, and so on. It's like a snowball rolling downhill, gathering more snow as it goes. The longer it rolls, the bigger it gets, and the faster it grows.

This is different from simple interest, where you only earn interest on your original principal. With compound interest, you earn interest on the principal plus all previously earned interest. Over time, this creates exponential growth – the curve gets steeper and steeper.

Albert Einstein supposedly called compound interest "the eighth wonder of the world." Whether or not he said it, the sentiment is right. Understanding compound interest is essential for building wealth through savings and investments, and equally important for avoiding the trap of compound interest on debt.

The Compound Interest Formula

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

Final amount (principal + interest)

Principal (initial investment)

Annual interest rate (as decimal)

Compounding frequency per year

Time in years

Compound Interest

A - P (interest earned)

Compounding Frequencies

Annualn = 1

Semi-annualn = 2

Quarterlyn = 4

Monthlyn = 12

Dailyn = 365

Effective Annual Rate

The effective rate tells you what simple annual rate would give you the same return as your compounded rate.

EAR = (1 + r/n)^n - 1

For 6% compounded monthly: EAR = (1 + 0.06/12)^12 - 1 = 6.17%. You actually earn 6.17%, not 6%.

Worked Examples

Example 1: Savings Account

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

P = $10,000

r = 0.06 (6%)

n = 12 (monthly)

t = 5 years

A = 10000(1 + 0.06/12)^(12×5)
A = 10000(1.005)^60
A = 10000 × 1.34885
A = $13,488.50

Interest earned: $3,488.50

Effective rate: 6.17%

Example 2: Retirement Investment

$50,000 at 7% annual interest, compounded quarterly, for 20 years

P = $50,000

r = 0.07 (7%)

n = 4 (quarterly)

t = 20 years

A = 50000(1 + 0.07/4)^(4×20)
A = 50000(1.0175)^80
A = 50000 × 4.0064
A = $200,320

Interest earned: $150,320

The investment quadruples in 20 years!

Example 3: Daily Compounding

$1,000 at 5% annual interest, compounded daily, for 1 year

P = $1,000

r = 0.05 (5%)

n = 365 (daily)

t = 1 year

A = 1000(1 + 0.05/365)^(365×1)
A = 1000(1.000137)^365
A = 1000 × 1.0513
A = $1,051.27

Interest earned: $51.27

Effective rate: 5.13% (vs 5% simple)

Example 4: Long-Term Growth

$100,000 at 8% annual interest, compounded quarterly, for 30 years

P = $100,000

r = 0.08 (8%)

n = 4 (quarterly)

t = 30 years

A = 100000(1 + 0.08/4)^(4×30)
A = 100000(1.02)^120
A = 100000 × 10.765
A = $1,076,500

Interest earned: $976,500

Nearly 11x growth over 30 years – the power of compounding!

Quick Fact

Jacob Bernoulli (1654-1705) discovered the mathematical constant e (approximately 2.718) while studying compound interest. He asked: what happens if you compound interest continuously – not daily or hourly, but at every instant? The answer involves e. The formula for continuous compounding is A = Pe^(rt). Bernoulli's work on this problem laid the foundation for calculus and the study of exponential growth, which describes everything from population growth to radioactive decay.

Frequently Asked Questions

What's the difference between compound and simple interest?

Simple interest is calculated only on the original principal. Compound interest is calculated on the principal plus all accumulated interest. On $1,000 at 5% for 10 years: simple interest earns $500, but compound interest (monthly) earns $647. The gap widens dramatically over time.

How much does compounding frequency matter?

More frequent compounding means more interest, but the difference diminishes. On $10,000 at 6% for 10 years: annual compounding gives $17,908, monthly gives $18,194, and daily gives $18,220. The jump from annual to monthly adds $286, but monthly to daily adds only $26.

What is the Rule of 72?

The Rule of 72 estimates how long it takes to double your money: divide 72 by the interest rate. At 6%, your money doubles in about 72/6 = 12 years. At 9%, it doubles in 8 years. It's a quick mental shortcut that's surprisingly accurate for typical interest rates.

Can compound interest work against me?

Absolutely. Credit card debt compounds, usually daily. A $5,000 balance at 18% APR with minimum payments can take over 20 years to pay off and cost $7,000+ in interest. This is why paying off high-interest debt should be a top priority – you're losing the benefit of compounding on your own investments.

What is continuous compounding?

Continuous compounding calculates and adds interest at every possible instant – infinitely frequent compounding. The formula uses e (Euler's number): A = Pe^(rt). It gives the theoretical maximum return. In practice, daily compounding is very close to continuous for most purposes.

How does inflation affect compound interest?

Inflation erodes purchasing power. If you earn 6% interest but inflation is 3%, your real return is only about 3%. Always consider the real rate of return (nominal rate minus inflation) when evaluating investments. A "safe" 2% return with 3% inflation means you're actually losing purchasing power.

When should I start investing for retirement?

As early as possible. Time is the most powerful factor in compound interest. Investing $200/month from age 25 to 65 at 7% gives you $525,000. Waiting until 35 gives you only $244,000 – less than half, despite investing the same amount for 30 years. The first 10 years matter enormously.

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