Compound Interest Guide

What compound interest means

Compound interest is interest earned on both the original amount and the interest already added. Over time, this creates exponential growth. The longer you leave money invested, the more powerful compounding becomes.

Simple vs compound interest

Simple interest is based only on the principal. Compound interest adds interest to the balance, then calculates interest on the new total. This difference becomes dramatic over long periods.

Core formula

The basic compound interest formula is: A = P(1 + r/n)^(nt). P is principal, r is annual rate, n is compounding frequency, and t is time in years. With regular contributions, the future value is the compound growth of the principal plus the annuity formula for the deposits.

Worked examples

Example: $5,000 at 6% compounded monthly for 10 years grows to about $9,100. If you add $200 per month, the total grows dramatically higher. Contributions often matter more than rate increases.

Why time beats rate

A 25-year timeline at a modest rate often beats a high rate over 10 years. This is why early saving is so important. The first years of compounding set the foundation for later growth.

Compounding frequency

Monthly compounding yields slightly more than annual compounding because interest is applied more often. The difference is small over short periods but can add up over decades.

Inflation and real returns

Inflation reduces purchasing power. A 6% return with 3% inflation yields a real return of about 3%. When planning long-term goals, consider inflation-adjusted outcomes.

Practical tips

• Automate contributions to maintain consistency.
• Increase contributions when income rises.
• Use conservative rates in projections.
• Track fees that reduce net returns.

Recommended calculators

• Compound Interest Calculator
• Investment Calculator
• Savings Calculator

Regular contributions

Contributions can matter more than the interest rate. A lower rate with steady contributions often beats a higher rate with no contributions. This is why retirement plans emphasize consistency.

The formula for a series of contributions is an annuity formula. It adds each deposit, compounded over the remaining time horizon.

The rule of 72

The rule of 72 estimates doubling time: 72 divided by the interest rate gives the approximate years to double. At 6%, it takes about 12 years. This is a quick way to understand the power of time.

Fees and taxes

Fees reduce effective returns. A 1% annual fee can cut long-term growth substantially. Taxes can also reduce compounding, depending on the account type. Use conservative net rates when planning.

Risk and return

Higher returns usually come with higher risk. Long-term projections should balance realistic returns with your risk tolerance. A calculator gives you scenarios, not guarantees.

Planning with inflation

If inflation averages 3%, a 6% nominal return is only 3% in real terms. Always ask what your money will be worth in future purchasing power, not just nominal dollars.

Compounding schedules in practice

Banks and investment products compound daily, monthly, or quarterly. The more frequent the compounding, the higher the effective annual yield. The difference is usually small per year but adds up over time.

Scenario planning

Use calculators to model a conservative, expected, and optimistic scenario. This helps you avoid overestimating growth and provides a realistic range for planning.

Compound interest in debt

Compounding can work against you with credit card balances or high-interest loans. Paying extra toward principal early reduces the compounding effect and saves money.

References

• Standard compound interest formula references in finance textbooks
• Federal Reserve educational materials on interest and savings