Compound Interest Calculator - Growth, Contributions & Rule of 72

One formula, four variables - and time does most of the work

Compound interest means earning interest on interest. Instead of calculating returns on the original principal alone, each compounding period adds earned interest back to the balance - so the next period's interest is calculated on a larger amount. The effect is small in year one, noticeable by year five and transformative over decades. This calculator handles the full formula including optional monthly contributions and six compounding frequencies from annual to daily.

The formula behind the numbers

    A = P x (1 + r/n)^(n x t)

      A = final amount

      P = initial principal

      r = annual interest rate (decimal, e.g. 0.07 for 7%)

      n = compounding periods per year (12 for monthly)

      t = number of years

When you add regular contributions, a second formula (the future value of an annuity) kicks in:

    FV_contributions = PMT x ((1 + r/n)^(n x t) - 1) / (r/n)
  

The calculator adds both parts together: growth of the lump sum plus growth of recurring deposits.

How to use this calculator - step by step

Initial principal - enter the starting amount. This can be 0 if you only plan to make monthly contributions.
Annual interest rate - enter the yearly rate as a percentage. Savings accounts typically offer 3-5%, broad index funds have historically returned 7-10%.
Time period - how many years you plan to invest. Even a 5-year difference makes a large impact.
Compounding frequency - how often interest is added to the balance. Monthly is the most common. Daily produces slightly more, but the difference is small at moderate rates.
Monthly contribution - optional recurring deposit. Even small amounts add up dramatically over long periods.
Read the results - you get the final value, total interest, multiplier, percentage gain and a Rule of 72 estimate.

Simple interest vs compound interest

Both start with the same principal and rate. The difference grows with time.

Scenario ($10,000 at 7%)	Simple interest	Compound interest	Extra from compounding
After 5 years	$13,500	$14,026	+$526
After 10 years	$17,000	$19,672	+$2,672
After 20 years	$24,000	$38,697	+$14,697
After 30 years	$31,000	$76,123	+$45,123

Compounding frequency comparison

$10,000 at 7% for 20 years. Different compounding frequencies, same nominal rate.

Frequency	Periods/year	Final value	Effective annual rate
Annually	1	$38,697	7.000%
Quarterly	4	$39,795	7.186%
Monthly	12	$40,088	7.229%
Daily	365	$40,547	7.250%

Practical examples

Example 1: $5,000 at 5% for 10 years, compounded monthly, no contributions.
Result: $8,235 (interest: $3,235, multiplier: 1.65x)

Example 2: $0 initial, $500/month for 20 years at 7%, compounded monthly.
Result: $260,462 (deposited: $120,000, interest: $140,462)

Example 3: $25,000 at 8% for 30 years, compounded annually.
Result: $251,566 (multiplier: 10.06x)

Example 4: $10,000 + $200/month at 6% for 15 years, compounded monthly.
Result: $82,462 (deposited: $46,000, interest: $36,462)

Example 5: $100,000 at 4% for 5 years, compounded quarterly.
Result: $121,899 (interest: $21,899)

The Rule of 72
Divide 72 by your annual interest rate to estimate how many years it takes to double your money. At 6%: roughly 12 years. At 8%: roughly 9 years. At 10%: roughly 7.2 years. It is an approximation - this calculator gives you the exact number.

FAQ - Frequently asked questions

What is the difference between simple and compound interest?

Simple interest is calculated only on the original principal - the same dollar amount every year. Compound interest adds earned interest back to the principal, so each subsequent period earns interest on a larger balance. Over 10 years at 7%, $10,000 grows to $17,000 with simple interest but $19,672 with compound interest. The gap widens with time and higher rates.

Does compounding frequency matter much?

At moderate rates (3-7%), the difference between annual and monthly compounding is small - typically 0.1-0.3% in effective annual return. At higher rates or over longer periods, the gap grows. Going from monthly to daily adds even less. For most savings accounts and index funds, monthly compounding is the practical standard.

What rate of return should I use?

It depends on the investment vehicle. High-yield savings accounts: 3-5%. Government bonds: 4-6%. Broad stock market index (S&P 500 historical average): 7-10% before inflation. Real estate (long-term average): 5-8%. Use a lower rate for conservative estimates and a higher one for optimistic scenarios. The calculator lets you compare both.

How accurate is the Rule of 72?

The Rule of 72 is most accurate for rates between 4% and 12%. At 6%, it predicts 12 years to double - the actual answer (with annual compounding) is 11.90 years. At 2%, it predicts 36 years; the actual is 35.00. At 20%, it predicts 3.6 years; the actual is 3.80. Good enough for mental math, but use this calculator for precision.

Does this calculator account for taxes and inflation?

The calculator shows nominal (pre-tax, pre-inflation) returns. To estimate real returns, subtract the expected inflation rate from your interest rate before entering it. For example, if you expect 7% returns and 3% inflation, enter 4% for a real-return estimate. Tax treatment varies by country and account type - consult a tax advisor for your specific situation.

Why do small monthly contributions make such a big difference?

Because each contribution starts compounding from the moment it is added. $200/month at 7% for 30 years produces $227,930 in interest on top of $72,000 deposited - a 3.17x multiplier. The early contributions compound for decades, which is why starting even with small amounts matters more than waiting until you can invest a large lump sum.

Related tools

Deposit Calculator

Calculate fixed deposit interest, net return after tax and inflation impact - See calculator

Loan Payment Calculator

Compare fixed vs declining loan instalments and see total interest cost - See calculator

Currency Converter

Convert between 10 major currencies with daily mid-market rates - See calculator

Bitcoin & Crypto Calculator

Convert BTC, ETH and other cryptocurrencies to USD with live prices - See calculator