Compound interest

Before you rely on it

What to check

Two things to pin down: compounding frequency, and whether contributions land at the start or end of each period.

The common error

Where people go wrong with compound interest

Assuming the minimum payment makes progress. On a high-rate revolving balance it can cover interest and almost nothing else, leaving the balance roughly where it started after a year of payments.

Worked through

Compound interest in plain numbers

Put $10,000 in an account paying 5% a year, compounded annually. After one year you have $10,500. In year two, interest is earned on $10,500, not on $10,000, so you gain $525 and reach $11,025. After ten years the balance is $16,288.95. With simple interest, which pays only on the original $10,000, ten years would give $15,000; the $1,288.95 difference is interest earned on interest. Give it twenty years and the compound balance is $26,532.98 against $20,000 simple; the longer the time, the more the second-order effect dominates, which is why starting early matters so much.

Easily confused

Compound interest and its neighbours

Compound interest is the opposite of simple interest, which never adds accrued interest back into the base; it is also easy to confuse with the effective annual rate, the yearly outcome of compounding at a given frequency, and with exponential growth in general. The same mechanism works against you on debt: a credit card balance that compounds daily grows by interest on interest. Whether it helps or hurts depends on which side of the account you sit. Savers want more frequent compounding, and borrowers want less.

In real decisions

Where compound interest turns up

Compounding explains retirement projections, savings targets, loan costs and the growth of investments; the rule of 72 gives a quick estimate: divide 72 by the annual rate and you get roughly the years to double, so 6% doubles money in about twelve years. Students, savers and planners use it to see what regular deposits become; borrowers use it to see how a balance grows if unpaid. Financial calculators and spreadsheets apply it in one line, given rate, time and deposits.

Know the edges

Where compound interest stops being reliable

Real returns are rarely steady, and the formula assumes a fixed rate. Fees, taxes and inflation reduce what compounding delivers. For investments, average returns overstate what a volatile path produces. For savings, the stated rate may change. Long projections stretch small assumptions into big numbers, so test the result at a lower rate as well; the math is exact; the inputs are guesses.

Quick answers

What people ask about compound interest

What is the rule of 72? A quick estimate of doubling time. Divide 72 by the annual percentage rate. At 6% money doubles in about 12 years, at 9% in about 8.

Does compounding work against me on debt? Yes. Unpaid interest is added to the balance and charged interest itself, which is why card debt grows quickly. Paying more than the minimum breaks the cycle.