Compound Interest Calculator

Compound Interest Formula

Where: P = Principal, r = Annual rate (decimal), n = Compounds per year, t = Years

The Power of Compounding

Compound interest earns interest on interest, causing wealth to grow exponentially over time.

How Compound Interest Works

Compound interest is interest calculated on both the original principal and all previously earned interest. Each period's growth is added to the balance, and the next period grows from that larger base. This "interest on interest" is why compound growth accelerates over time while simple interest plods along in a straight line.

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

Worked example: Invest $5,000 at 6% compounded monthly for 5 years. Monthly rate: 0.06/12 = 0.005; periods: 12 × 5 = 60. A = 5,000 × (1.005)⁶⁰ ≈ 5,000 × 1.34885 = $6,744.25. Interest earned: $1,744.25. Under simple interest the same deposit would earn only 5,000 × 0.06 × 5 = $1,500.

How Compounding Frequency Changes the Result

More frequent compounding means interest starts earning its own interest sooner. For $10,000 at 7% over 10 years:

The jump from annual to monthly is worth about $425; from monthly to daily only about $40 — frequency has diminishing returns. In the limit as n → ∞, compounding becomes continuous: A = Pe^rt, giving $20,137.53 here — barely above daily compounding.

Nominal Rate vs. Effective Annual Rate

A "6% nominal rate compounded monthly" does not mean you earn exactly 6% per year. The effective annual rate (EAR) captures what compounding actually delivers:

For 6% nominal compounded monthly: (1.005)¹² − 1 ≈ 6.17%. This is the number to use when comparing accounts with different compounding frequencies — always compare EAR to EAR, never nominal to nominal.

The Rule of 72

To estimate how long money takes to double at a given rate, divide 72 by the percentage rate. At 7%: 72/7 ≈ 10.29 years (exact: ln(2)/ln(1.07) ≈ 10.24 years). The rule also works in reverse: to double money in 8 years, you need roughly 72/8 = 9% per year.

Why Time Beats Rate

Because growth is exponential, extra years matter more than extra rate. Compare $10,000 at 7% compounded annually:

The second decade earns nearly triple the interest of the first ($19,025 vs $9,672) — the last years of compounding do most of the work. Starting early beats chasing a slightly higher rate.

Real vs. Nominal Growth

The formula gives nominal growth — before inflation. If prices rise 3% while your money compounds at 7%, your real purchasing-power growth is roughly 7% − 3% = 4% per year. Long-horizon planning should always be done in real terms.

Common Mistakes to Avoid

• Comparing nominal rates across frequencies: 6% monthly beats 6.1% annual? No — compare the effective annual rates.
• Using the percent in the formula: r must be the decimal (0.07), and n × t is the total number of periods, not the years.
• Ignoring inflation: A 5% nominal return at 4% inflation is barely 1% real growth.
• Underestimating fees: A 1% annual fee on a 7% return wipes out far more than one-seventh of the final balance, because the fee compounds too.
• Stopping early: Withdrawing resets the compounding clock — the biggest gains come in the final years.

Contributions Supercharge Compounding

The calculator above covers lump sums, but real investing usually adds regular contributions. Each contribution then compounds for the remaining time. The future value of equal end-of-period contributions is:

Worked example: Invest $200 at the end of every month at 7% (compounded monthly) for 30 years. Monthly rate: 0.07/12 ≈ 0.005833; periods: 360. FV = 200 × ((1.005833³⁶⁰ − 1)/0.005833) ≈ 200 × 1,219.97 = $243,994.20. Total contributed: $72,000 — compounding supplied the other $171,994. Starting ten years later (20 years of contributions) would reach only about $104,185, showing again why time dominates.

The Hidden Cost of Fees

Fees compound against you exactly like returns compound for you. Compare $10,000 over 30 years at 7% versus 6% (a 1% annual fee):

A fee that looks like "just 1%" consumed nearly a quarter of the final balance. Verify: 10,000 × 1.07³⁰ ≈ $76,122.55 ✓

Compounding and Debt

Compounding cuts both ways. A credit card charging 24% APR compounded monthly has an effective annual rate of (1 + 0.24/12)¹² − 1 ≈ 26.82% — almost 3 points above the quoted APR. Unpaid balances grow on the same exponential curve that builds wealth, which is why high-rate debt should be cleared before investing.

How Much Must You Save Monthly to Reach $1 Million?

Flip the contributions formula around to solve for the required payment:

Worked example: To reach $1,000,000 in 30 years at 7% compounded monthly: PMT = 1,000,000 × 0.005833 / (1.005833³⁶⁰ − 1) ≈ 5,833.33 / 7.1165 ≈ $819.69 per month. Total contributed: about $295,088 — compounding provides the remaining $704,912.

The Latte Factor, Quantified

Small daily spending compounds like everything else. Saving $5 a day ($150/month) instead of spending it, at 7% compounded monthly for 40 years: FV = 150 × ((1.005833⁴⁸⁰ − 1)/0.005833) ≈ $393,722. Total contributed: $72,000. Whether the "latte" is coffee or any $150/month habit, four decades of compounding turn it into nearly $400,000.

Nominal APR vs. What You Actually Pay on Debt

The higher the rate, the wider the gap between the quoted APR and the effective rate — another reason to clear high-rate balances first.

Key Takeaways

• Compound interest grows on the previous balance, so growth accelerates — the final years contribute the most.
• Compounding frequency helps, but with diminishing returns: daily barely beats monthly.
• Always compare the effective annual rate, not the quoted nominal rate, when frequencies differ.
• The Rule of 72 (72 ÷ rate) estimates doubling time in seconds.
• Time in the market beats timing the market: starting a decade earlier roughly doubles the outcome.
• Fees and high-rate debt compound against you with the same force — minimize both.

How the Calculator Computes Your Result

1. Takes your principal P, annual rate (converted from percent to decimal), years t, and compounding frequency n.
2. Computes the final amount with A = P(1 + r/n)^nt.
3. Reports total interest earned as A − P, so you can see exactly how much compounding contributed.