Calculate Compound Interest Growth

Compound interest is interest earned on both the principal amount and any previously earned interest. Unlike simple interest, compound interest grows exponentially over time, making it a powerful tool for long-term investments and savings. The interest you earn each period is added to your principal, so you earn interest on your interest.

The compound interest formula is: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal, r is the annual interest rate (as a decimal), n is the number of times interest is compounded per year, and t is the time in years. For example, $1,000 at 5% compounded annually for 10 years becomes $1,000(1 + 0.05/1)^(1×10) = $1,628.89.

Simple interest is calculated only on the principal amount, while compound interest is calculated on both the principal and any previously earned interest. Simple interest grows linearly, while compound interest grows exponentially. For example, $1,000 at 5% simple interest for 10 years earns $500 total, while compound interest earns $628.89.

The more frequently interest is compounded, the more you'll earn. Daily compounding provides the highest returns, followed by monthly, quarterly, and annually. Most savings accounts compound daily or monthly. For example, $1,000 at 5% for 10 years: annually = $1,628.89, monthly = $1,647.01, daily = $1,648.66.

The Rule of 72 is a quick way to estimate how long it takes for an investment to double. Divide 72 by the annual interest rate to get the approximate number of years. For example, at 6% interest, it takes about 12 years to double your money (72 ÷ 6 = 12). At 8%, it takes about 9 years (72 ÷ 8 = 9).

Compound interest works against you with debt. Credit cards and loans use compound interest, meaning you pay interest on both the principal and accumulated interest. This is why it's important to pay off high-interest debt quickly. For example, a $1,000 credit card balance at 18% APR can grow to over $1,800 in just 4 years if only minimum payments are made.

Continuous compounding is when interest is calculated and added to the principal an infinite number of times per year. The formula is A = Pe^(rt), where e is Euler's number (approximately 2.718). While theoretical, it's used in some financial models and provides the maximum possible compound growth.

For regular contributions, use the future value of an annuity formula: FV = PMT × [(1 + r)^n - 1] / r, where PMT is the regular payment, r is the interest rate per period, and n is the number of periods. Add this to the compound interest on your initial principal for the total future value.

The effective annual rate is the actual interest rate earned when compounding is considered. EAR = (1 + r/n)^n - 1, where r is the nominal rate and n is compounding frequency. For example, 5% compounded monthly has an EAR of (1 + 0.05/12)^12 - 1 = 5.12%.

Inflation reduces the real value of compound interest returns. To calculate real returns, subtract the inflation rate from the nominal interest rate. For example, if you earn 6% interest but inflation is 2%, your real return is only 4%. This is why it's important to consider inflation when planning long-term investments.