Compound Interest Explained

With simple interest, you earn a fixed amount each year based only on your original deposit. $10,000 at 7% simple interest earns $700 every year: $7,000 over ten years, no more.

With compound interest, each period's interest is added to the balance, and the next period's interest is calculated on that larger balance. Year one earns $700. Year two earns 7% of $10,700, which is $749. Year three earns 7% of $11,449, about $801. The increments grow every year, so the curve bends upward rather than rising in a straight line.

Early on the two approaches look similar. The difference shows up with time. After 10 years, $10,000 at 7% compounded annually is about $19,672 against $17,000 with simple interest. After 30 years it is about $76,123 against $31,000.

A = P × (1 + r / n)^{n × t}

• A is the final amount.
• P is the starting principal.
• r is the annual rate as a decimal (7% is 0.07).
• n is how many times per year interest is compounded.
• t is the number of years.

Worked example: $10,000 at 7% compounded annually for 30 years is 10,000 × 1.07³⁰ = about $76,123. You can reproduce any such figure in the compound interest calculator, which also lets you add regular deposits.

A little, but less than people expect. The more often interest is added, the slightly faster the balance grows, because interest starts earning interest sooner. Using the same $10,000, 7% and 30 years:

• Annual compounding: about $76,123
• Monthly compounding: about $81,165
• Daily compounding: about $81,645

Going from annual to monthly adds around $5,000. Going from monthly to daily adds only around $480. There is a ceiling: even continuous compounding at 7% gives only slightly more than daily.

When comparing savings accounts, look at the APY (annual percentage yield). It already includes the compounding effect. A 7% rate compounded monthly has an APY of about 7.23%. Two accounts with the same APY earn the same, regardless of how they compound internally.

Most people do not invest one lump sum; they add money over time. With monthly deposits, the formula becomes a sum, but the idea is the same: every deposit starts its own compounding clock.

Depositing $200 a month at 7% annual interest, compounded monthly, grows to roughly $244,000 after 30 years. You would have contributed $72,000 yourself; the other $172,000 or so is growth. Note that the first deposits did most of the work: they had 30 years to grow, while the final ones had almost none.

This is why starting early matters more than starting big. The same $200 a month started 10 years later (20 years of saving) grows to a little over $104,000 at the same rate, less than half. The savings goal calculator works in the opposite direction: enter a target and it shows the monthly amount you would need.

To estimate how long it takes money to double, divide 72 by the annual percentage rate. At 7%, 72 / 7 is about 10.3 years; the exact answer is about 10.2 years. At 4% it is about 18 years. It is a quick mental check, and it works best for rates between roughly 4% and 12%.

The same arithmetic works against you with debt. A credit card balance at 24% interest roughly doubles in three years if you make no payments. That is why paying down high-interest debt is often a better guaranteed return than most investments can promise.

• Returns are not guaranteed. A savings account rate is stated up front, but investment returns vary year to year. A calculator using a fixed 7% shows an illustration, not a forecast.
• Inflation reduces purchasing power. If prices rise 3% a year, a 7% nominal return is about a 4% real return. Over 30 years that difference is large, so consider running the calculator with an inflation-adjusted rate.
• Fees and taxes take a share. A fund charging 1% a year reduces the effective rate by about a percentage point, which compounds into a noticeable gap over decades. Taxes may also apply depending on the account type.
• Withdrawals interrupt compounding. Every amount you take out stops earning for the rest of the period.

The figures here are for education and not financial advice. Use the calculator to test several rates and time spans rather than relying on a single optimistic case.