Compound Interest Calculator

What is compound interest?

Compound interest is interest calculated on a balance that already contains earlier interest. Every time interest is credited, the next period's interest is worked out on a larger base, so the balance climbs along a curve that gets steeper over time instead of a straight line.

The easiest way to see the effect is to set it against simple interest, which is paid only on the original deposit. At 5% simple interest, $10,000 earns $500 a year, so after ten years it has earned $5,000 and stands at $15,000. Compounded once a year, the same deposit reaches $16,288.95. The extra $1,288.95 is interest earned on interest, and the gap keeps widening the longer the money stays invested.

How to use the calculator

• Current principal / initial investment: the amount you start with. It must be greater than zero.
• Time duration: the length of the term, in years, half-years, quarters, months or days.
• Interest rate: the nominal yearly rate quoted by the bank or fund, before compounding is taken into account.
• Compound frequency: how often interest is added: annually, semiannually, quarterly, monthly or daily.
• Contribution (optional): a regular amount you add, per year, half-year, quarter, month or day. A negative number models regular withdrawals.
• Add contribution at: whether each contribution goes in at the start of a compounding period, so it earns interest straight away, or at the end.

The results show the value at the end of the term, the interest accrued (growth minus your own deposits), the effective yearly interest rate, the total of all contributions and the capital growth, which compares the final value with the starting amount.

The compound interest formula

For a single deposit with no further contributions, the final amount is:

A = P × (1 + r ÷ n)^{n × t}P is the principal, r the annual rate as a decimal (5% = 0.05), n the number of compounding periods per year and t the term in years.

Regular contributions turn the balance into a principal part plus an annuity part. With i = r ÷ n, k whole compounding periods and C the contribution per period, deposits made at the end of each period add:

A = P × (1 + i)^k + C × ((1 + i)^k − 1) ÷ i

Deposits made at the start of each period earn one extra period of interest, so the annuity part is multiplied by (1 + i). The effective yearly rate, which shows what the nominal rate is really worth once compounding is counted, is:

effective rate = (1 + r ÷ n)ⁿ − 1

Worked example with monthly deposits

Suppose you open an account with $10,000, the rate is 5% compounded monthly, you add $100 at the end of every month, and you leave everything in for 10 years.

1. The monthly rate is i = 0.05 ÷ 12 = 0.0041667 and there are k = 120 periods, so (1 + i)¹²⁰ = 1.647009.
2. The starting $10,000 grows to 10,000 × 1.647009 = $16,470.09.
3. The deposits grow to 100 × (1.647009 − 1) ÷ 0.0041667 = $15,528.23.
4. The final balance is 16,470.09 + 15,528.23 = $31,998.32.
5. You paid in 120 × $100 = $12,000, so the interest accrued is 31,998.32 − 10,000 − 12,000 = $9,998.32, of which $6,470.09 came from the original deposit and $3,528.23 from the monthly deposits.

The effective interest rate is (1 + 0.05 ÷ 12)¹² − 1 = 5.116%, a little above the quoted 5%. If the same deposits are made at the start of each month instead, the final balance becomes $32,063.02, which is $64.70 more.

Why the compounding frequency matters

The same nominal rate produces different results depending on how often interest is credited. The table shows $10,000 at 5% for ten years with no deposits:

Returns diminish quickly. Moving from annual to monthly compounding adds $181.14 over the decade, while moving from monthly to daily adds only $15.61. The rate itself and the length of the term matter far more than the compounding schedule.

How this calculator counts periods

• Only complete compounding periods earn interest. A term of 2.5 years with annual compounding earns interest for two periods, and 30 days with monthly compounding returns the original amount unchanged.
• Days are converted using a 365.2421-day year. For daily compounding a term of 100 days therefore counts as 99 full periods, not 100.
• Contributions are annualised and spread evenly over the compounding periods. A contribution of $1,200 per year and one of $100 per month give the same result, because both come to $1,200 a year.
• Total contributions use the full term, even when part of the last period is incomplete, so on a deposit-heavy plan with a fractional term the interest accrued row can even come out negative.

Rules of thumb and common mistakes

The rule of 72 estimates how long money takes to double: divide 72 by the annual rate. At 6% that is about 12 years (the exact figure is 11.9), and at 8% about 9 years (exactly 9.0).

• Confusing the quoted rate with the effective yield. Use the APY calculator to compare accounts that compound at different frequencies.
• Typing the rate as a decimal. Enter 5 for 5%, not 0.05.
• Forgetting that fees, taxes and inflation reduce real growth. The CD calculator lets you include a tax rate and an inflation rate.
• Assuming the rate is fixed for decades. Savings and money-market rates change, so treat long projections as scenarios rather than promises.

Compounding also works against borrowers: interest on a debt that is not repaid is added to what you owe. For repayment schedules, see the loan calculator, and to find what a lump sum is worth later, the future value calculator.

These results are estimates based on a constant rate and exact period counts. They are not financial advice, and real accounts may use different day-count conventions, fees and tax rules. See the disclaimer.