How Compound Interest Works: Growth, Time and the Rule of 72

Compound interest is the process where interest earns interest. A sum of money grows by a fixed percentage each period, and the interest from earlier periods is added to the balance so that it also earns interest in later periods. The effect is small at first and very large over long horizons. It is the single most important mechanism behind retirement savings, bond returns and long-term debt costs.

This post explains the formula, shows how the numbers grow with a simple table, introduces the Rule of 72 as a mental shortcut, and covers the practical lessons for saving and borrowing.

Simple interest versus compound interest

Simple interest pays a fixed amount based only on the original sum, called the principal. If you deposit 1,000 at 7 percent simple interest, you earn 70 each year. After 10 years you have 1,700, because the 70 per year never changes.

Compound interest works differently. The interest is added to the balance, and the next period's interest is calculated on the new, larger balance. The same 1,000 at 7 percent compounded annually earns 70 in year one, then 74.90 in year two because the second year's interest is calculated on 1,070. The gap between the two methods widens every year.

The formula

The standard formula for a single deposit with annual compounding is:

FV = P × (1 + r)^n

Here FV is the future value, P is the principal, r is the annual interest rate written as a decimal, and n is the number of years. Each year the balance is multiplied by the same factor, (1 + r). After n years it has been multiplied by that factor n times, which is why the exponent does so much of the work.

Many accounts compound more often than once a year, such as monthly or daily. More frequent compounding raises the effective annual yield a little. The difference between annual and monthly compounding at a 7 percent nominal rate is small, about 7.23 percent effective versus 7.00 percent, so the rate you are quoted matters more than the compounding frequency.

A worked comparison

The table below shows what a single 1,000 deposit grows to at 7 percent per year, compounded annually. These figures are calculated directly from the formula and are illustrative, not a forecast for any real product.

Years	Balance at 7%	Growth from start
0	1,000.00	0
10	1,967.15	+967
20	3,869.68	+2,870
30	7,612.26	+6,612

Notice the pattern. The first ten years roughly double the money. The next ten years roughly double it again. The final decade adds more than the first two decades combined in absolute terms. Most of the total growth happens late, which is why time is the strongest input in the formula.

The Rule of 72

The Rule of 72 is a quick way to estimate how long an investment takes to double. Divide 72 by the annual interest rate in percent. At 6 percent the money doubles in about 12 years. At 8 percent it doubles in about 9 years. At 12 percent it doubles in about 6 years.

The rule comes from the natural logarithm of 2, which is about 0.693. Dividing 69.3 by the rate gives the exact doubling time for continuous compounding, and 72 is used because it has many small divisors and is a close approximation for typical rates between roughly 6 and 10 percent. The rule is accurate enough for planning and fails badly for very high or very low rates.

Why starting early matters more than contributing more

Two savers can end up with very different results from the same formula. Consider two people who each earn a 7 percent annual return. Anna invests 200 per month from age 25 to 35, then stops and leaves the money alone until age 65. Ben invests 200 per month from age 35 to 65. Anna contributes 24,000 in total, which is 10 years of payments. Ben contributes 72,000, which is 30 years of payments.

Under these assumptions Anna finishes with more money, because her first contributions had 40 years to compound while Ben's had 30 at most. The example is a simplified model with no fees, taxes, or inflation, but it shows the principle clearly: an early dollar is worth more than a later dollar, even when the later saver contributes more in total.

Compounding works against borrowers

The same mechanism applies to debt. Credit card balances often compound monthly at high annual rates. A balance of 5,000 at 24 percent annual interest, compounded monthly, grows by about 2 percent per month before any payments. If only the minimum is paid, the balance can shrink very slowly, and the total interest paid can exceed the original purchase.

This is why the order of payments matters. Paying down the highest-rate debt first reduces the factor that multiplies your balance each period. Paying a fixed monthly amount that is larger than the interest charge is the only way the principal truly falls.

Inflation and real returns

Nominal returns are the numbers on a statement. Real returns subtract inflation. If an account earns 4 percent and prices rise by 3 percent, the real growth in purchasing power is roughly 1 percent. The compounding formula works the same way with real rates, which is why savers focus on real returns over long periods. A nominal return of 7 percent with inflation at 3 percent doubles purchasing power in about 18 years, not 10.

Taxes reduce returns in a similar way. A tax-advantaged account lets the full balance compound, while a taxable account loses part of each year's gain to tax before it can compound. Over decades this difference can be large.

Practical lessons

Start saving as early as your budget allows, even in small amounts. Automate contributions so that compounding begins before you decide to spend the money. Use low-cost, diversified funds because fees compound against you the same way returns compound for you. A 1 percent annual fee on a 7 percent return cuts the effective growth rate by a seventh, which compounds into a large gap over thirty years.

Pay attention to the rate on debt as well as savings. A 20 percent card rate is a compounding force working against you, and clearing it often produces a guaranteed return equal to that rate.

Key takeaways

Compound interest is interest earned on interest. The formula FV = P × (1 + r)^n shows that time sits in the exponent, so small differences in years produce large differences in outcome.

The Rule of 72 gives a fast estimate of doubling time. Dividing 72 by the rate in percent works well for typical rates and is useful for comparing options in your head.

Early contributions usually beat larger late contributions because they have more periods to grow. Fees, taxes and inflation all reduce the effective rate, so their effects also compound and deserve attention. The same mechanism that builds savings can rapidly grow debt, so repaying high-rate balances is one of the most reliable financial returns available.