Compound Interest Explained: How Your Savings Grow Over Time

Compound interest is often described as interest on interest. It is the reason small, regular savings can grow into large balances over time, and it is also why debt can spiral if left unpaid. Understanding how it works is one of the most useful pieces of financial knowledge you can have.

Simple interest versus compound interest With simple interest, you earn interest only on your original deposit. $1,000 at 5% simple interest earns $50 every year, so after ten years you have $1,500.

With compound interest, interest is added to the balance, and future interest is calculated on the new, larger balance. $1,000 at 5% compounded annually grows to $1,050 after one year, $1,102.50 after two, and about $1,629 after ten years. The extra $129 comes entirely from interest earning interest.

The compound interest formula The future value of a single deposit is:

• Future value = P × (1 + r/n)^(n × t)

Where P is the principal, r is the annual interest rate as a decimal, n is the number of compounding periods per year, and t is the number of years.

For regular monthly deposits, a second formula calculates the future value of the series of payments. Our savings calculator combines both so you can see the effect of a starting balance plus monthly contributions.

Compounding frequency Interest can compound annually, quarterly, monthly, or daily. More frequent compounding produces slightly higher returns. $10,000 at 5% for ten years grows to about $16,289 with annual compounding and about $16,470 with monthly compounding. The difference is real but smaller than the effect of rate, time, and contributions.

Time is the most powerful factor Consider two savers who each earn 6% per year:

• Saver A invests $200 per month from age 25 to 35, then stops. Total contributed: $24,000.
• Saver B invests $200 per month from age 35 to 65. Total contributed: $72,000.

By age 65, Saver A can end up with a balance comparable to Saver B despite contributing a third as much, because their money compounded for an extra decade. Starting early is often more important than starting big.

The rule of 72 To estimate how long money takes to double, divide 72 by the annual interest rate. At 6%, money doubles in about 12 years. At 9%, about 8 years. At 3%, about 24 years. The rule is an approximation but useful for quick mental math.

Compound interest on debt Compounding works against you when you borrow. Credit card balances with high annual rates can grow quickly if only minimum payments are made. The same maths that builds savings can make debt expensive, which is why paying down high-interest debt is often the best guaranteed return available.

Inflation and real returns A 5% return during a year with 3% inflation produces a real return of about 2%. When projecting long-term savings, consider using a lower real rate to understand future purchasing power.

Making compound interest work for you - Start saving as early as possible, even with small amounts. - Contribute regularly and automatically. - Reinvest interest rather than withdrawing it. - Choose accounts with competitive rates and low fees. - Avoid high-interest debt that compounds against you.

Try it yourself Open the savings calculator and enter a starting balance, monthly deposit, rate, and number of years. Then change just one input at a time. Increasing the time horizon usually has the most dramatic effect, which illustrates the power of compounding better than any explanation.

Summary Compound interest turns time into money. The longer your savings compound, the more your balance grows from interest alone. Start early, save consistently, and let the maths work for you.