Compound Interest Calculator

How Compound Interest Is Calculated

Compound interest means each period's growth is added back to the balance, so future growth is earned on both your original principal and prior interest. This calculator also includes monthly contributions because most long-term investing plans grow through regular deposits, not only a one-time starting amount.

Future principal = P x (1 + r / n)^(n x t)
Future monthly deposits = PMT x (((1 + r / 12)^(12 x t) - 1) / (r / 12))

In the formula, P is starting principal, r is the annual return as a decimal, n is compounding periods per year, t is years, and PMT is the monthly contribution made at the end of each month.

Worked Example

With $10,000 invested, a 7% annual return, monthly compounding, and $250 added every month for 20 years, the ending value is much larger than the $70,000 personally contributed. That gap is the compound growth created by time and reinvested returns.

Compound Interest Formula

The standard compound interest formula is:

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

Where: A = final amount, P = principal (starting amount), r = annual interest rate as a decimal, n = number of compounding periods per year, t = time in years.

Worked example: $1,000 at 7% annual interest, compounded monthly for 10 years:

A = $1,000 × (1 + 0.07/12)^(12×10) = $1,000 × (1.005833)^120 = $2,009.66

The $1,000 principal more than doubled in 10 years at 7% — purely from compound growth with no additional contributions.

Compound Interest Growth Table: $1,000 at Various Rates

The table below shows how $1,000 grows at different annual interest rates over 10 to 40 years, compounded annually, with no additional contributions.

Years	3%	5%	7%	10%	12%
10	$1,344	$1,629	$1,967	$2,594	$3,106
20	$1,806	$2,653	$3,870	$6,727	$9,646
30	$2,427	$4,322	$7,612	$17,449	$29,960
40	$3,262	$7,040	$14,974	$45,259	$93,051

Notice how the gap between rates widens dramatically over time. At 7%, $1,000 grows to nearly $15,000 over 40 years; at 12%, it reaches over $93,000 — six times more, despite the rate being less than double. This illustrates why even small differences in return matter enormously over long time horizons.

The Rule of 72: How Long to Double Your Money

The Rule of 72 is a simple mental shortcut: divide 72 by the annual interest rate to estimate how many years it takes to double your money.

At 3%: 72 ÷ 3 = 24 years to double
At 6%: 72 ÷ 6 = 12 years to double
At 8%: 72 ÷ 8 = 9 years to double
At 10%: 72 ÷ 10 = 7.2 years to double

This is an approximation. The exact formula for doubling time is t = ln(2) / ln(1 + r). The Rule of 72 is most accurate at moderate rates (6%–10%) and slightly overestimates at very low or very high rates. It works just as well in reverse — if an investment doubles in 9 years, the implied annual rate is roughly 72 ÷ 9 = 8%.

Compounding Frequency

Annual, quarterly, monthly, and daily compounding change how often interest is credited. Frequency matters, but time horizon, return assumption, and contribution amount usually have a larger practical effect. Use frequency to match the account or product you are modeling.

Planning assumption: monthly contributions are treated as end-of-month deposits. The calculator does not subtract taxes, fees, inflation, or investment volatility.

Limitations and Financial Context

This is an educational planning calculator, not financial advice. Actual investment returns vary, and taxes, fees, withdrawal timing, inflation, and market losses can materially change real outcomes. For major retirement, college savings, or debt decisions, compare conservative and optimistic scenarios and consider professional advice.

Frequently Asked Questions

What is compound interest?

Compound interest is growth earned on both the original amount and prior interest. Over long periods, reinvesting returns can make the balance grow faster than simple interest.

Does monthly contribution timing matter?

Yes. This calculator assumes deposits are made at the end of each month. Deposits made at the beginning of each month would have slightly more time to grow.

Should I use nominal or real returns?

Use nominal returns for account-balance projections and real, inflation-adjusted returns when comparing future purchasing power.

Why does compounding frequency have a small effect?

When the annual return is the same, moving from monthly to daily compounding is usually less important than adding more time, increasing contributions, or changing the return assumption.

How often does compound interest compound?

Compound interest can compound annually, semi-annually, quarterly, monthly, daily, or even continuously. The compounding frequency determines how often earned interest is added back to the principal. More frequent compounding produces slightly more growth — for example, daily compounding at 7% yields marginally more than annual compounding at 7% — but the difference is small compared to the effect of time or rate.

What is the difference between compound and simple interest?

Simple interest is calculated only on the original principal: Interest = P × r × t. Compound interest is calculated on the principal plus all previously earned interest, so the balance grows exponentially over time. For example, $1,000 at 7% simple interest for 10 years earns $700 in interest ($1,700 total). The same amount at 7% compounded annually earns about $967 in interest ($1,967 total) — nearly 38% more.

What is the Rule of 72?

The Rule of 72 estimates how many years it takes to double your money at a given annual interest rate. Divide 72 by the rate: at 8%, your money doubles in about 72 ÷ 8 = 9 years. At 6%, it takes roughly 12 years. At 12%, about 6 years. It is an approximation; the exact formula is ln(2) / ln(1 + r), but the Rule of 72 is accurate enough for quick mental math at rates between 4% and 15%.

How much does $10,000 grow in 20 years at 7%?

Using the compound interest formula with monthly compounding: A = $10,000 × (1 + 0.07/12)^(12×20) = $10,000 × (1.005833)^240 ≈ $40,203. So $10,000 invested at 7% compounded monthly for 20 years grows to approximately $40,203 — about four times the original amount — with no additional contributions.

What is continuous compounding?

Continuous compounding is the theoretical limit of compounding more and more frequently. The formula is A = Pe^(rt), where e is Euler's number (approximately 2.71828). In practice, daily compounding is very close to continuous compounding. For example, $1,000 at 7% for 10 years: daily compounding gives $2,013.62, while continuous compounding gives $2,013.75 — a negligible difference.

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Common Tip Percentages

Service	Typical Tip Range	Notes
Restaurant (sit-down)	15–20%	20%+ for exceptional service
Food delivery	10–20%	Consider extra for long distances
Taxi / rideshare	10–20%	More for assistance with luggage
Hotel housekeeping	$2–5/night	Leave daily, not just at checkout
Barber / hair salon	15–20%	On pre-discount total
Pizza delivery	10–15% or $3–5 minimum	Higher in bad weather

General Household Budget Ratios (50/30/20 Rule)

Category	% of Net Income	Examples
Needs	50%	Rent, groceries, utilities, insurance
Wants	30%	Dining out, entertainment, hobbies
Savings / Debt	20%	Emergency fund, retirement, extra payments

Common Measurement Conversions for Everyday Use

Quantity	US / Imperial	Metric Equivalent
1 cup	8 fl oz	237 mL
1 pint	16 fl oz	473 mL
1 quart	32 fl oz	946 mL
1 gallon	128 fl oz	3.785 L
1 lb	16 oz	453.6 g
1 ft	12 in	30.48 cm

Compound Growth Checks

Your Compound Interest Results

Balanced Projection