Compound Interest Calculator

What Is Compound Interest?

Compound interest is interest calculated on both the initial principal and the accumulated interest from previous periods. Unlike simple interest — which only earns on the original deposit — compound interest earns on a growing base. This "interest on interest" effect is why Albert Einstein is often (apocryphally) quoted as calling it the eighth wonder of the world.

Every savings account, bond, mortgage, and investment portfolio is shaped by compound interest. Understanding the formula, the compounding frequency, and the effect of regular contributions gives you a real edge when comparing financial products, planning retirement, or paying down debt.

Compound Interest Formula Explained

The standard compound interest formula is:

Where each variable means:

• A — the future value (what your investment grows to)
• P — the principal (the initial amount invested or deposited)
• r — the annual interest rate expressed as a decimal (e.g. 5% = 0.05)
• n — the number of times interest is compounded per year (12 for monthly, 365 for daily)
• t — the time in years

The total interest earned is simply A − P. The formula scales naturally: a higher n means interest compounds more frequently, increasing the effective rate above the nominal annual rate.

How to Calculate Compound Interest Step by Step

Take $2,000 invested at 4% compounded quarterly for 5 years:

1. Identify: P = $2,000, r = 0.04, n = 4 (quarterly), t = 5
2. Compute the period rate: r/n = 0.04/4 = 0.01
3. Compute total periods: n×t = 4×5 = 20
4. Apply the formula: A = $2,000 × (1.01)^20
5. Calculate: (1.01)^20 ≈ 1.22019
6. A = $2,000 × 1.22019 = $2,440.38
7. Total interest = $2,440.38 − $2,000 = $440.38

The Power of Compounding Frequency

The same nominal interest rate produces different results depending on how often it compounds. More frequent compounding always yields a higher effective annual rate (EAR). The EAR is the true yearly return after accounting for intra-year compounding:

Compound Interest with Regular Contributions

Adding regular monthly contributions dramatically amplifies the compounding effect. Consider two investors, both earning 7% annually compounded monthly:

• Investor A deposits $10,000 as a lump sum and makes no further contributions. After 30 years: ~$81,165.
• Investor B starts with $0 but deposits $200 every month. After 30 years: ~$243,994.

Investor B deposits only $72,000 total, but earns $171,994 in interest — more than double what Investor A earns despite starting with nothing. Consistency beats a single large deposit when time is on your side.

This calculator models contributions by simulating each month individually, which gives the most accurate result regardless of the compounding frequency selected. Each month the accrued interest is added to the balance and the contribution is deposited at the end of the period.

Compound Interest vs Simple Interest

Simple interest is calculated only on the original principal: I = P × r × t. On $1,000 at 5% for 10 years, simple interest yields $500 — exactly $147 less than the $647 earned through monthly compounding. The difference grows exponentially: over 30 years at 5%, simple interest earns $1,500 while monthly compounding earns $3,467.

Simple interest is rare in practice. It appears in some short-term loans and bond coupon payments. Most savings accounts, mortgages, student loans, and investment products use compound interest, which is why understanding it is essential for any financial planning.

Compound Interest Calculator FAQ

What is the compound interest formula?

A = P × (1 + r/n)^(n×t). P is your starting principal, r is the annual rate as a decimal (5% = 0.05), n is the number of compounding periods per year, and t is time in years. Total interest is A minus P.

How does compound interest differ from simple interest?

Simple interest only earns on the original principal each period. Compound interest earns on the principal plus all previously earned interest, so the base grows with each period. Over long time horizons the difference is enormous — compounding grows exponentially while simple interest grows linearly.

What does compounding frequency mean?

Compounding frequency is how many times per year interest is calculated and added to your balance. Monthly (n=12) means interest is credited 12 times per year; daily (n=365) means 365 times. More frequent compounding slightly raises the effective annual return because each period's interest starts earning sooner.

What is the effective annual rate (EAR)?

The EAR is the true yearly return after accounting for compounding within the year. Formula: EAR = (1 + r/n)^n − 1. A 5% nominal rate compounded monthly gives EAR = (1 + 0.05/12)^12 − 1 = 5.116%. Banks advertise the nominal rate; the EAR is what your money actually earns. Use the EAR when comparing accounts with different compounding frequencies.

How much does $10,000 grow at 7% compounded monthly for 20 years?

Using A = 10,000 × (1 + 0.07/12)^(12×20) = 10,000 × (1.005833)^240 ≈ 10,000 × 4.0387 = $40,387. Total interest earned is $30,387 — three times the original investment from 20 years of compounding alone.

What is the Rule of 72?

The Rule of 72 is a mental shortcut: divide 72 by the annual interest rate to estimate how many years it takes to double your money. At 6%, 72 ÷ 6 = 12 years. At 9%, 72 ÷ 9 = 8 years. It works best for rates between 2% and 20% and assumes annual compounding. For more frequent compounding the doubling time is slightly shorter.

Does adding monthly contributions make a big difference?

Yes — often more than increasing the rate. Adding $200 per month to a $1,000 starting balance at 6% for 20 years produces a final balance of ~$95,101 versus ~$3,310 without contributions. The contributions matter because they compound too: early contributions grow for the full remaining period, late contributions only for a few years. Starting early amplifies this effect significantly.