Compound Interest Calculator

Compound interest is the eighth wonder of the world, according to a famous quote often attributed to Albert Einstein. Unlike simple interest, which is calculated only on the initial principal, compound interest is calculated on the principal plus all previously accumulated interest.

The fundamental formula is: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal, r is the annual interest rate, n is the number of compounding periods per year, and t is the time in years.

The power of compound interest lies in exponential growth. The longer your money remains invested, the more dramatic the growth becomes. An initial investment can double, triple, or even multiply tenfold given sufficient time and a reasonable interest rate.

Time is the most crucial factor in compound interest. An investor who starts at 25 with $200/month will accumulate significantly more than someone who starts at 35 with $400/month, despite contributing less total money.

Consider two investors: Investor A starts at 25, contributes $5,000/year for 10 years, then stops (total: $50,000). Investor B waits until 35 and contributes $5,000/year for 30 years (total: $150,000). At 65, with 7% annual returns, Investor A often has more money despite contributing three times less.

This phenomenon, called the 'time value of money,' demonstrates why every year of delay can cost tens of thousands of dollars in future wealth. Starting early, even with small amounts, is almost always better than waiting to invest larger sums.

Compounding frequency refers to how often interest is calculated and added to your principal. Common frequencies include daily, monthly, quarterly, semi-annually, and annually.

More frequent compounding results in higher effective yields. For example, a 6% annual rate compounded monthly yields 6.17% effective annual rate, while daily compounding yields 6.18%. The difference becomes more significant with higher rates and longer time periods.

Continuous compounding represents the theoretical maximum, where interest is calculated and added infinitely often. While no real investment offers true continuous compounding, many high-yield savings accounts and money market funds compound daily, approaching this theoretical maximum.

Regular contributions supercharge compound growth through dollar-cost averaging. By consistently adding money regardless of market conditions, you buy more shares when prices are low and fewer when prices are high.

The timing of contributions matters. Contributing at the beginning of each period (annuity due) rather than the end (ordinary annuity) results in approximately one period's extra growth on each contribution. Over decades, this can add 2-4% to your final total.

Even modest monthly contributions can have dramatic effects. $200/month at 7% becomes approximately $241,000 after 30 years, of which $169,000 is compound interest. Without contributions, a single $72,000 lump sum at the same rate would only reach about $548,000.

Inflation silently erodes the purchasing power of your savings. A nominal return of 7% with 3% inflation yields only a 4% real return. Understanding this distinction is crucial for long-term financial planning.

Historical U.S. inflation has averaged about 3% annually, though it varies significantly. The Federal Reserve targets 2% inflation, but recent years have seen both lower (1-2%) and higher (5-9%) rates.

To maintain purchasing power, your investments must earn returns above the inflation rate. This is why holding too much cash can actually lose money in real terms, even though the nominal balance appears stable or growing slightly.

The Rule of 72 is a simple way to estimate doubling time: divide 72 by your interest rate to approximate how many years it takes to double your money. At 6% interest, money doubles in approximately 12 years (72/6 = 12).

This rule works best for interest rates between 6% and 10%. For higher rates, use 70 instead of 72. For lower rates, use 69.3 (the natural logarithm of 2 × 100).

Related rules: The Rule of 114 estimates tripling time (114/rate = years to triple). The Rule of 144 estimates quadrupling time. These mental shortcuts help quickly evaluate investment opportunities without a calculator.

Stock market (S&P 500): Historically returns approximately 10% annually before inflation, or 7% after inflation. However, returns vary dramatically by decade, from -1% (2000s) to +17% (1990s).

Bonds: High-quality bonds have historically returned 5-6% annually. Government bonds are safer but yield less; corporate bonds offer higher returns with increased risk.

Savings accounts and CDs: Currently yield 4-5% for high-yield accounts, though this varies with the Federal Reserve's interest rate policies. Historically, savings rates have ranged from 0.1% to over 10%.

Real estate: National appreciation averages 3-4% annually, roughly matching inflation. However, rental income can add 4-8% additional return, making real estate potentially comparable to stocks.

Maximize tax-advantaged accounts first. 401(k)s, IRAs, and Roth accounts allow compound growth without annual tax drag, which can cost 0.5-1.5% per year in taxable accounts.

Reinvest all dividends and distributions automatically. Taking cash instead of reinvesting can reduce long-term returns by 40% or more over a 30-year period.

Minimize fees ruthlessly. A 1% annual fee might seem small, but over 30 years it can reduce your final balance by 25% or more. Index funds typically charge 0.03-0.20%, while actively managed funds charge 0.5-2%.

Stay invested through market volatility. Investors who remained fully invested in the S&P 500 from 1990-2020 earned 7.5% annually. Missing just the 10 best days reduced returns to 3.4%. Time in the market beats timing the market.