What is the compound interest formula?

A = P(1 + r/n)^(nt). P = principal (starting amount), r = annual interest rate (as a decimal), n = compounding frequency per year, t = time in years. A is the final balance including interest.

How do you calculate compound interest by hand?

Take 10,000 at 5% compounded monthly for 10 years. Divide the rate by 12 (0.05 / 12 = 0.0041667), add 1, raise it to the power 120 (12 x 10) to get about 1.647, and multiply by 10,000. The final balance is 16,470.09, so the interest earned is 6,470.09.

How do you solve the formula for time?

Rearrange A = P(1 + r/n)^(nt) to t = ln(A/P) / (n x ln(1 + r/n)). With annual compounding at 5%, money doubles in ln 2 / ln 1.05, about 14.2 years.

What does n stand for in the formula?

n is the number of times interest is added each year. The calculator offers annual (n = 1), quarterly (n = 4), monthly (n = 12) and daily (n = 365) compounding.

Compound interest formula calculator

Calculate compound interest using the standard formula A = P(1 + r/n)^(nt), where P is the principal, r is the annual rate, n is the number of times interest compounds per year, and t is the time in years. This calculator shows your final balance, total interest earned, and a full year-by-year breakdown. All calculations run locally in your browser.

Principal (starting amount)

Annual interest rate (%)

Compound frequency

Time period: 10 years

1 yr50 yrs

Formula: A = P(1 + r/n)^(nt), where P = principal, r = annual rate, n = compounds/year, t = years

Final amount after 10 years

16,288.95

Total interest earned: 6,288.95
Principal: 10,000.00
Annual rate: 5%
Compounding: Annual

Calculations are estimates for informational purposes only. Consult a financial professional for advice.

Year	Balance	Interest this year
1	10,500.00	500.00
2	11,025.00	525.00
3	11,576.25	551.25
4	12,155.06	578.81
5	12,762.82	607.75
6	13,400.96	638.14
7	14,071.00	670.05
8	14,774.55	703.55
9	15,513.28	738.73
10	16,288.95	775.66

How it works

The compound interest formula is A = P(1 + r/n)^(nt), where P is the principal, r is the annual interest rate as a decimal, n is the number of compounding periods per year, and t is the number of years. The year-by-year table recalculates each row using this formula with increasing t values. All arithmetic runs in JavaScript in your browser.

Processing runs in your browser

All calculations happen locally in your browser tab. Our servers are not involved at any point.

Calculations are estimates for informational purposes only. Consult a financial professional for advice.

Related operations

For working out a quick percentage of a value, try the percentage calculator. To convert fractional rates into decimals, use the fraction calculator. To compare this growth with an investment's actual return, try the ROI calculator.

Frequently asked questions

What is the compound interest formula?: A = P(1 + r/n)^(nt). P = principal (starting amount), r = annual interest rate (as a decimal), n = compounding frequency per year, t = time in years. A is the final balance including interest.
How do you calculate compound interest by hand?: Take 10,000 at 5% compounded monthly for 10 years. Divide the rate by 12 (0.05 / 12 = 0.0041667), add 1, raise it to the power 120 (12 x 10) to get about 1.647, and multiply by 10,000. The final balance is 16,470.09, so the interest earned is 6,470.09.
How do you solve the formula for time?: Rearrange A = P(1 + r/n)^(nt) to t = ln(A/P) / (n x ln(1 + r/n)). With annual compounding at 5%, money doubles in ln 2 / ln 1.05, about 14.2 years.
What does n stand for in the formula?: n is the number of times interest is added each year. The calculator offers annual (n = 1), quarterly (n = 4), monthly (n = 12) and daily (n = 365) compounding.

Last reviewed September 30, 2026

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