Compound Interest Calculator

Compound interest is the process of earning interest on both your original deposit and on previously earned interest. Interest on interest. This creates exponential rather than linear growth, which is why money grows so much faster the longer it stays invested.

This is different from simple interest, which only pays interest on the original deposit. Almost no real-world account uses simple interest; savings accounts, CDs, bonds, and investment portfolios all compound.

The Core Formula (No Contributions)

A = P × (1 + r/n)^(n×t)

Where:

• A = final amount
• P = principal (your initial deposit)
• r = annual interest rate as a decimal (7% = 0.07)
• n = number of compounding periods per year (1 = annual, 12 = monthly, 365 = daily)
• t = time in years
• Interest earned = A − P

For continuous compounding (the theoretical maximum), the formula is:

A = P × e^(r×t)

In practice, the difference between daily and continuous compounding is tiny, well under 1% over a typical investment lifetime.

With Regular Contributions

Most people don’t just deposit once and walk away. They contribute a fixed amount every month, to a 401(k), an IRA, or a brokerage account. The future value of those contributions is calculated using the future value of an annuity formula:

FV = P(1+i)^N + PMT × [((1+i)^N − 1) / i]

Where:

• P = initial deposit
• PMT = the monthly contribution
• i = monthly interest rate
• N = total number of months
• If contributions are made at the beginning of each month, multiply the PMT term by (1 + i). End-of-month contributions don’t get that bonus month of interest.

This calculator handles the math for you. Just enter the monthly contribution.

Compounding Frequency Effect

Effect of compounding frequency on $10,000 at 6% for 10 years (no contributions):

Notice how the gains shrink at each step. Annual to quarterly adds $232. Quarterly to monthly adds $54. Monthly to daily adds $26, and going all the way to continuous compounding, the theoretical ceiling, adds one more dollar. The frequency matters far less than people think. Rate and time are what move the number.

Worked Example (with Contributions)

You deposit $5,000 initially, contribute $300/month, at 7% annual interest, compounded monthly, for 25 years.

• Monthly rate: 7% ÷ 12 = 0.58333%
• Total months: 300
• Future value of initial $5,000: $5,000 × (1.0058333)^300 = $28,627
• Future value of $300/month contributions: $300 × [((1.0058333)^300 − 1) / 0.0058333] = $243,022
• Total final balance: $271,649
• Total contributed: $5,000 + ($300 × 300) = $95,000
• Interest earned: $176,649, almost twice what you put in

Carry the monthly rate to more decimal places than feels necessary. Rounding 0.58333% to 0.5833% looks harmless and moves the 25-year answer by about $900.

The Rule of 72

A quick mental shortcut to estimate how long it takes to double your money:

Years to double ≈ 72 ÷ annual interest rate

At 6%: 72 ÷ 6 = 12 years At 9%: 72 ÷ 9 = 8 years At 12%: 72 ÷ 12 = 6 years

It’s an approximation, but it’s accurate to within a few months for any rate between 4% and 15%.

Time vs. Contribution Size

The most important variable is time. Two scenarios for comparison:

• Saver A contributes $200/month from age 25 to 35 (10 years), then stops. At 7%, by age 65 they have ~$284,000.
• Saver B contributes $200/month from age 35 to 65 (30 years). At 7%, by age 65 they have ~$245,000.

Saver A contributed $24,000 total. Saver B contributed $72,000. Saver A still ends up with more, because their money had longer to compound. Starting 10 years earlier often matters more than contributing twice as much.

Beginning vs. End of Month

End-of-month contributions are the standard assumption (and what most automatic transfers do). Beginning-of-month contributions earn one extra month of interest each, which over 30 years adds roughly 0.5% to your final balance. On $610,000 that is about $3,600, small in percentage terms and not nothing in dollars.