Compound Interest

The formula

One formula. All the math.

Compound interest has exactly one formula. Everything else — monthly deposits, inflation, effective APY — is a layer on top. Here it is, with a worked example you can poke at.

The core formula

A = P (1 + r/n)nt
A
The future value — what the balance becomes.
P
The principal — your starting amount.
r
The annual interest rate, as a decimal (8% → 0.08).
n
Compound periods per year (12 = monthly, 365 = daily).
t
The number of years the money stays invested.

With regular deposits

A = P (1 + r/n)nt + PMT · [ ((1 + r/n)nt − 1) / (r/n) ]

The second term is the future value of an annuity — a regular deposit ofPMT every period. End-of-period deposits use the formula as-is; start-of-period deposits multiply the annuity term by(1 + r/n) because each deposit earns one extra period of interest.

Worked example

$10,000 at 8%, monthly, for 20 years.

  1. 01

    Convert the rate.

    r = 0.08, n = 12. So r/n = 0.08 / 12 = 0.006667.

  2. 02

    Count the periods.

    n · t = 12 · 20 = 240 compounding periods.

  3. 03

    Raise 1 + r/n to the power nt.

    (1.006667)240 ≈ 4.9268. That's your growth factor — the balance will multiply by nearly five.

  4. 04

    Multiply by the principal.

    $10,000 × 4.9268 ≈ $49,268. That's the future value with no monthly deposits.

  5. 05

    Add a $200 monthly deposit.

    PMT · [(4.9268 − 1) / 0.006667] ≈ 200 × 589 ≈ $117,800. Combined with the principal growth, you end at roughly$167,000— of which only $58,000 is money you contributed.

The lesson

Of the final $167,000, $58,000 is yours and $109,000 is interest. That split — interest beating contributions — is the magic. It only shows up if you start early and don't touch it.

Try it live

Edit the inputs below — the formula runs instantly.

Live·

Inputs

$
%
Time horizon
Regular contributions: (optional)
$
%
Inflation & tax⌄
%

Shown as a "real" value in today's money.

%

Applied once at the end of the horizon.

Future value
—
—
After
—
Contributed
—
Principal + deposits
Interest earned
—
—
Effective APY
—
—

Growth over time

Principal, contributions, and interest — stacked year by year.

PrincipalContributionsInterest

Year-by-year breakdown

Opening balance, deposits, interest, closing balance.

Show table
YearOpeningNet flowsInterestClosing

Start compounding, keep compounding.

Open the calculator, change one number, and watch the long tail.

Open the calculatorRead the formula