Compound Interest Calculator

Compound interest calculator — the eighth wonder of the world

Compound interest is often called "the eighth wonder of the world" — a line usually (and almost certainly wrongly) attributed to Albert Einstein. The quote is apocryphal, but the math is very real: small consistent contributions earning compound interest over decades become unrecognisably larger than the sum of the contributions. Our calculator models the full path — initial deposit, monthly contributions, compounding frequency, and time horizon — and gives you the final balance plus a breakdown of contributions vs interest earned.

The compound interest formula

For a single initial deposit with no further contributions:

A = P × (1 + r/n)^(n × t)

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

With ongoing monthly contributions, the formula becomes the future value of an annuity:

A = P × (1 + r/n)^(n × t)
    + PMT × [((1 + r/n)^(n × t) − 1) / (r/n)]

Where:
PMT = monthly contribution

The first term is the initial deposit growing exponentially. The second is the future value of every monthly contribution growing for whatever time it has left to compound. Our calculator does this monthly so the result is precise.

The numbers that surprise everyone

Compound interest is so unintuitive that almost no one guesses the right answer the first time. Here are three projections that change the way most people think about saving:

• $200/month for 40 years at 7% real return → $525,000. The contributions alone are only $96,000. Compound interest does the rest.
• Start at 22 vs start at 32: the 10-year head start is worth roughly 2× the final balance at retirement, even though the late starter contributes for 8 more years overall. Time matters more than amount.
• Doubling your contribution at age 50 cannot offset starting late. The math just runs out of compounding years.

How to use this calculator for retirement

Plug in your current 401k / IRA / pension balance as the initial deposit. Use 6–8% as the annual return (conservative real return on a stock-heavy portfolio). Set the time horizon to your years until retirement, and the monthly contribution to your total monthly savings. The final balance is your projected nest egg — in today's dollars if you used a real rate, or in future dollars if you used a nominal rate.

A standard rule of thumb is the "4% rule" for safe withdrawals: in retirement, you can withdraw 4% of your starting balance annually, adjusted for inflation, and have roughly 95% confidence it lasts 30 years. So a $1 million projection translates to about $40,000/year of sustainable spending — useful for sanity-checking whether your savings rate is on track.

Compounding frequency: monthly vs daily vs annually

The difference between annual and daily compounding is real but small. On a 7% rate over 30 years, annual compounding turns $10,000 into $76,123; daily compounding turns it into $81,646. About 7% more. Past monthly, the extra precision is negligible — banks advertise "daily compounding" because it sounds better, not because the difference matters in real outcomes.

The biggest threats to your projection

Compound interest calculators show smooth exponential curves. Real life does not.

• Sequence-of-returns risk: losing 30% in year 1 vs year 25 are very different events for a retirement portfolio. Two portfolios with the same average return can land in dramatically different places depending on order.
• Fees: a 1% expense ratio over 30 years reduces your final balance by roughly 20%. Choose low-cost index funds (0.03–0.10% expense ratio) over actively managed funds (0.5–1.5%) unless you have a very specific reason.
• Withdrawals during downturns: selling assets to fund expenses during a market crash locks in losses. The standard defence is a 6-month cash buffer outside the investment account.
• Inflation: 3% inflation halves purchasing power in 24 years. Real returns (after inflation) are what actually buy you groceries in retirement.

Related calculators

• Mortgage Calculator — model your monthly payment and see how much total interest each loan term costs.
• Loan Calculator — compare the cost of borrowing against the cost of investing instead.
• Percentage Calculator — quick math for returns and savings rates.