Compound Interest Calculator

What this calculator does

This calculator projects the future value of an investment that earns compound interest. You can enter an initial principal, a monthly contribution, an annual return rate, a time horizon, and a compounding frequency. The result shows the final balance, the total amount you contributed, and how much of the balance came from interest alone.

How compound interest works

With simple interest, you earn a fixed amount each period based only on the original principal. With compound interest, each period's interest is added to the balance, so the next period's interest is calculated on a slightly larger number. Over time this snowballs.

The standard formula for a single lump sum is:

FV = P × (1 + r/n)^(n × t)

• P — the initial principal
• r — the annual interest rate (as a decimal)
• n — the number of compounding periods per year
• t — the time horizon in years

When you also add regular contributions, you're effectively buying a stream of small lump sums. The future value of those contributions is the future value of an ordinary annuity: PMT × ((1 + r/n)^(n × t) − 1) / (r/n).

A worked example

Suppose you start with $10,000, contribute $500 per month, and earn 7% annually compounded monthly for 30 years. Your contributions total $190,000 ($10,000 + $500 × 360). Your ending balance is roughly $691,000 — meaning compound growth alone added more than $500,000 on top of what you put in.

Tips and common mistakes

• Time matters more than the rate. Doubling the time horizon often beats a meaningfully higher return. Start as early as possible.
• Use realistic returns. The long-run U.S. stock-market average is roughly 7% real (after inflation). Modeling 12%+ for decades will produce numbers you can't bank on.
• Account for taxes and fees. A 1% annual fee or tax drag compounds against you the same way returns compound for you.
• Inflation reduces purchasing power. $1 million in 30 years is not $1 million today. Either model a real return rate (nominal minus inflation) or treat the result as nominal dollars.

Frequently asked questions

What is compound interest?

Compound interest is interest you earn on both your original principal and the interest that has previously accumulated. Over long periods, this snowball effect produces dramatically higher returns than simple interest, which only earns on the original amount.

How is compound interest calculated?

The standard formula for a lump sum is FV = P(1 + r/n)^(nt), where P is the principal, r is the annual rate (as a decimal), n is the number of compounding periods per year, and t is the number of years. With regular contributions you add the future value of an annuity: PMT × [((1+r/n)^(nt) − 1) / (r/n)].

Why does compounding frequency matter?

More frequent compounding means interest is credited and starts earning interest sooner. The difference between annual and daily compounding at the same rate is small but real over decades; the practical effect is captured by APY (which assumes a given compounding frequency) versus the nominal rate.

What is the difference between APR and APY?

APR (annual percentage rate) is the nominal annual rate without accounting for compounding within the year. APY (annual percentage yield) is the effective annual rate after compounding is applied. For comparing savings or investment products, APY is the apples-to-apples number.

What is the rule of 72?

The rule of 72 is a quick mental shortcut: divide 72 by your annual rate of return to estimate how many years it takes to double your money. At 7%, that's about 10.3 years; at 9%, about 8 years. It's an approximation, not a substitute for the actual formula.

Why does starting earlier make such a big difference?

Compounding rewards time exponentially. A $5,000 contribution at age 25 has 40 years to grow at compound rates; at age 45, it has only 20. Most of the final balance in a long-term retirement portfolio comes from gains in the last decade, which only happens if the money has been working for decades before that.