Compound Interest Calculator

A compound interest calculator shows how an initial balance grows when interest earned in each period is added to the balance and earns interest in the next period. This recursive growth is what Einstein supposedly called "the eighth wonder of the world." Whether he actually said that is debatable; the math is not.

Enter your starting balance, expected annual rate, time horizon, and how often the account compounds (monthly, daily, etc.). The result shows your final balance and the portion that came from interest rather than your original deposit.

Where compound interest shows up

The same formula governs almost every long-horizon money mechanic in everyday life:

• Savings accounts and CDs, banks compound interest daily or monthly and credit it to your balance.
• Stock and bond returns, reinvested dividends and interest compound across decades, which is what produces the famous long-run equity return numbers.
• Retirement accounts, 401(k)s, IRAs, and Roth IRAs all compound tax-deferred (or tax-free, in the Roth case), which is why starting contributions in your 20s vs your 40s produces dramatically different end balances.
• Loan and credit-card balances, running a balance compounds in the bank's favor, not yours. Credit-card interest at 22% compounded monthly is what turns a manageable balance into an unmanageable one.
• Inflation, prices compound at whatever the inflation rate is, which is why $100 in 1995 doesn't buy what $100 buys today.

Why time matters more than rate

The single most important insight from compound interest is that time is exponentially more valuable than rate. Compounding is a multiplicative process: each year multiplies the previous balance by (1 + r). Over n years the total multiplier is (1 + r)^n. Doubling rate is a linear improvement; doubling time is an exponential one.

Consider two savers, both earning the same 7% annual return:

• Saver A invests $5,000/year from age 25 to 35 (10 years), then stops.
• Saver B invests $5,000/year from age 35 to 65 (30 years).

Saver A puts in $50,000 total. Saver B puts in $150,000, three times as much. By age 65, Saver A ends up with about $602,000, while Saver B ends up with about $510,000. The early starter wins by a wide margin despite contributing a third as much, because each of A's early dollars has 30+ years to compound while B's first dollars only have 30 and B's last dollars have just 1.

This is why the standard advice, start early, even if you can only contribute a small amount, is mathematically correct, not just folksy.

Compounding works in both directions

The same mechanic that makes savings grow also makes debt grow. A credit-card balance at 22% APR with monthly compounding has a multiplier of (1 + 0.22/12)^12 ≈ 1.244, a 24.4% effective annual yield, in the bank's favor. Carrying a $5,000 balance and only making minimum payments (typically 2% of balance, around $100/month, mostly interest) can take 30+ years to pay off and cost more than $10,000 in interest.

The asymmetry: compounding gains over decades requires patience. Compounding losses over a few years can come fast. Pay off high-interest debt before optimizing investment returns.

The compound interest formula is A = P × (1 + r/n)^(n × t) where:

• A is the final amount
• P is the principal (starting balance)
• r is the annual rate as a decimal (7% → 0.07)
• n is how many times per year interest compounds
• t is the time in years

More frequent compounding produces slightly higher returns, but the difference between monthly (n = 12) and daily (n = 365) is small, fractions of a percent over decades. Continuous compounding (the theoretical limit) gives A = P × e^(rt), just barely higher than daily.

Compounding frequency, side by side

Take $10,000 at 7% over 30 years and vary only the compounding frequency:

The jump from annual to monthly matters (about $5,000 over 30 years). The jump from monthly to daily is rounding error (about $464). Beyond daily there's effectively no improvement at all. When comparing real accounts, the bank's published APY already bakes in the compounding frequency, which means you can compare APYs directly without thinking about how often the bank actually credits interest.

The Rule of 72 (and where it comes from)

The Rule of 72 is the most useful mental shortcut for compound interest: divide 72 by your interest rate to estimate how many years it takes your balance to double. At 6%, money doubles every 12 years. At 9%, every 8 years. At 12%, every 6.

The math underneath: doubling means (1 + r)^t = 2. Taking the natural log of both sides gives t × ln(1 + r) = ln(2). For small r, `ln(1

• r) ≈ r, so t ≈ ln(2) / r ≈ 0.693 / r. In percentage terms that's 69.3 / rate%, but 72 is used in practice because it has more integer divisors (2, 3, 4, 6, 8, 9, 12) and the slight overestimate cancels with the small-r` approximation error in the typical 4–10% range.

Adding regular contributions

The pure formula A = P × (1 + r/n)^(nt) only handles a lump sum that sits and grows. Most real-world saving involves regular contributions on top, for which the future value of an annuity formula applies:

FV = PMT × [((1 + r/n)^(nt) − 1) / (r/n)]

Add the lump-sum future value (P × (1 + r/n)^(nt)) to the contribution future value above, and you have the total balance. This is what the investment calculator, retirement calculator, and savings goal calculator compute internally, same compound interest math with a contribution stream layered on top.