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Compound Interest

Calculate savings growth over time with regular contributions.

Investment Inputs

Enter your initial deposit, rate, and monthly contribution.

Future Value
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Enter values to calculate.

Total contributions and interest are shown in the breakdown below.

Projection
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About this topic

The Power of Compounding Earning interest on your interest.

Compound interest is the process where interest is added to the principal, and future interest is calculated on that new, larger balance. Over time, this creates exponential growth.

Key formulas & rules

  • •Interest earns interest
  • •Grows exponentially
  • •Time is the most critical factor
  • •Higher frequency = faster growth
  • •Albert Einstein called it the 8th wonder
  • •Rule of 72 estimates doubling time

Examples

Input Output Note
$1000 at 5% for 10y $1,628.89 Annual
$1000 at 5% for 20y $2,653.30 Doubled
$1000 at 5% for 30y $4,321.94 Quadrupled
Rule of 72 72/5 = 14.4y Double time

Real-world uses

Retirement accounts Savings accounts Investment portfolios
Compounding Frequency How often interest is calculated and added.

Interest can be compounded annually, semi-annually, quarterly, monthly, or daily. The more frequently it compounds, the higher the effective annual yield.

Key formulas & rules

  • •Annually (1/yr)
  • •Semi-Annually (2/yr)
  • •Quarterly (4/yr)
  • •Monthly (12/yr)
  • •Daily (365/yr)
  • •Continuous (infinite)

Examples

Input Output Note
10% Annually 10.00% APY Baseline
10% Monthly 10.47% APY Higher yield
10% Daily 10.51% APY Slightly higher
10% Continuous 10.52% APY Theoretical max

Real-world uses

APY rates Loan interest Credit cards
Regular Contributions Adding money to the account over time.

Adding regular monthly contributions significantly accelerates growth. This is how 401(k)s and automatic savings plans work.

Key formulas & rules

  • •Monthly deposits increase principal
  • •Deposits also earn compound interest
  • •Time in market matters for contributions
  • •Dollar-cost averaging
  • •Employer matching accelerates growth
  • •Contributions are the main driver early on

Examples

Input Output Note
$100/mo for 10y at 5% $15,528 Contributions
Total contributed $12,000 Principal
Interest earned $3,528 Growth
$500/mo for 30y at 7% $609,984 Retirement

Real-world uses

401(k) plans Roth IRA Automatic savings

Modes & formulas

1

Compound Interest with Contributions

• Enter the initial principal, annual rate, time, monthly contribution, and compounding frequency. • The calculator computes the future value of the principal using A = P(1 + r/n)^(nt). • It also computes the future value of a series of monthly contributions and adds them together.
A = P(1 + r/n)^(nt) + PMT × [((1 + i)^m − 1) / i]

P is the principal, r is the annual rate (as a decimal), n is the compounding frequency, t is time in years, PMT is the monthly contribution, and i is the equivalent monthly rate.

How to use it

Enter the principal, annual rate, time horizon, monthly contribution, and compounding frequency. The calculator displays the future value, total contributions, and total interest earned.

Frequently asked questions

What is the difference between simple and compound interest?
Simple interest is calculated only on the principal. Compound interest is calculated on the principal plus all previously accumulated interest.
What is the rule of 72?
A quick estimate: divide 72 by the annual interest rate to find the number of years it takes for an investment to double.
What is compound interest?
Interest calculated on both the initial principal and the accumulated interest from previous periods.
What is compounding frequency?
How often interest is calculated and added to your balance (annually, monthly, daily).
Why does more frequent compounding yield more money?
Because interest starts earning its own interest sooner.
What is APY?
Annual Percentage Yield. It is the actual rate of return you will earn in one year, accounting for the effect of compounding.

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Read the full Compound Interest guide — examples & 18 FAQs