Compound Interest Calculator

What compound interest is

Compound interest is interest earned on interest. Simple interest pays a fixed amount on the original principal each period; compound interest adds each period's earnings to the balance so the next period earns on a larger base. Over short periods the difference is minor. Over decades it dominates everything else.

The formula for a lump sum is A = P(1 + r/n)^(nt), where P is the principal, r is the annual rate, n is the number of compounding periods per year, and t is time in years. With regular contributions you add the future value of an annuity, which is what the calculator above computes — and if contributions are made at the start of each period rather than the end, each one earns a period more, so the annuity term is multiplied by (1 + r/n).

Why time matters more than the amount

Compounding is exponential, so the years at the end of a long horizon contribute far more growth than the years at the start. This produces a result that consistently surprises people: an investor who contributes for ten years and then stops often ends up ahead of one who starts ten years later and contributes for thirty.

Consider $10,000 growing at 7%. After 10 years it is about $19,700. After 20 years, roughly $38,700. After 30 years, about $76,100. The third decade alone adds more than the first two combined — with no additional contributions. The same effect shows in regular saving: the table below puts the identical $200 a month to work from three different starting ages.

Compounding frequency and the rule of 72

More frequent compounding produces slightly more growth. At 6%, annual compounding gives an effective annual rate of exactly 6%, monthly gives about 6.17%, and daily about 6.18%. The gain from annual to monthly is real but modest, and the difference between daily and continuous compounding is negligible. This is why the effective annual rate, which normalizes for frequency, is the right basis for comparing accounts — and why the calculator can translate a rate at one frequency into its equivalent at another.

For quick mental math, the rule of 72 estimates doubling time: divide 72 by the annual percentage rate. At 6%, money doubles in roughly 12 years; at 9%, in about 8. It is an approximation, most accurate between about 6% and 10%, and the calculator shows the exact figure alongside it.

How good is the rule of 72?

Good enough for a conversation, and slightly off at the extremes. It overstates doubling time at low rates and understates it at high ones; at typical investment returns the error is a few months.

What the projection leaves out

A constant growth rate is a modeling convenience, not a description of markets. Real returns arrive unevenly, and the order of good and bad years matters if you are withdrawing money. Two other factors reduce real-world results: inflation, which erodes purchasing power by roughly 2% to 3% per year historically, and taxes on interest, dividends, and realized gains in taxable accounts.

Fees deserve particular attention because they compound against you. A 1% annual fee sounds small but consumes roughly a quarter of a portfolio's growth over 30 years. Comparing a 0.05% index fund with a 1% actively managed fund over a long horizon is often a larger decision than the choice between individual investments.