Compound Interest Calculator

Calculate compound interest on savings and investments. See future value with monthly contributions, compare compounding frequencies, and view year-by-year growth.

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How Compound Interest Works

Compound interest is often called the "eighth wonder of the world." Unlike simple interest (calculated only on the principal), compound interest earns interest on your accumulated interest — creating exponential growth over time.

The Compound Interest Formula

A = P(1 + r/n)^nt

A = final amount
P = initial principal
r = annual interest rate (as decimal)
n = number of times interest compounds per year
t = number of years

With Monthly Contributions

When adding regular contributions, the formula extends to include the future value of an annuity:

A = P(1 + r/n)^nt + PMT × [((1 + r/n)^nt - 1) / (r/n)]

Where PMT = periodic contribution amount.

Example

$10,000 invested at 7% annually for 20 years with $200/month contributions:

Initial investment: $10,000
Total contributions: $48,000 ($200 × 240 months)
Total interest earned: ~$66,000
Final balance: ~$124,000

Your money more than doubled through compound interest alone.

The Rule of 72

A quick way to estimate how long it takes to double your money: divide 72 by the annual return rate.

At 6%: 72/6 = 12 years to double
At 8%: 72/8 = 9 years to double
At 10%: 72/10 = 7.2 years to double
At 12%: 72/12 = 6 years to double

Compounding Frequency

Interest can compound annually, semi-annually, quarterly, monthly, or daily. More frequent compounding produces slightly higher returns. On $10,000 at 5% for 10 years:

Annually: $16,288.95
Monthly: $16,470.09
Daily: $16,486.65

The difference between monthly and daily compounding is small ($16.56 on $10K over 10 years), but between annual and monthly it's more noticeable ($181.14).

Compound Interest Works Against You Too

The same compounding that grows savings works against you with debt. Credit card balances at 20-25% APR compound monthly, doubling your debt in about 3-4 years if unpaid. A $5,000 balance at 24% APR paying only minimums takes 20+ years and costs $8,000+ in interest.

Inflation's Impact on Real Returns

Inflation erodes the purchasing power of your returns. If your investments earn 7% but inflation is 3%, your real return is approximately 4%. Over 30 years, $100,000 at 7% nominal grows to $761,000 — but in today's purchasing power (at 3% inflation), that's equivalent to about $313,000. Always consider real (inflation-adjusted) returns when planning long-term.

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Frequently Asked Questions

What is the compound interest formula?

A = P(1 + r/n)^(nt), where P is the principal, r is the annual rate as a decimal, n is the number of compounding periods per year and t is the number of years. A is the final balance. Regular monthly contributions add a second term for the growth of each deposit.

What is the difference between simple and compound interest?

Simple interest is paid only on the original principal, so the balance grows by the same amount every year. Compound interest is paid on the principal plus all interest already earned, so growth speeds up over time. Over decades the gap between the two becomes very large.

How long does it take to double money at 8 percent?

About 9 years. The Rule of 72 estimates doubling time by dividing 72 by the annual rate, so 72 / 8 = 9 years. The exact figure with annual compounding is 9.01 years. At 6 percent the rule gives 12 years, and at 9 percent it gives 8 years.

How much does starting to invest 5 years later cost?

Starting 5 years later on a 7 percent plan with the same monthly contributions ends with roughly 30 to 40 percent less than a plan that runs 5 years longer. The earliest contributions compound for the longest time, so time in the market matters more than the size of each deposit.