What is the compound interest formula?

A = P(1 + r ÷ n)nt, where P is the principal, r the annual rate as a decimal, n the compounding periods per year and t the number of years. Interest = A − P.

How do I calculate compound interest monthly?

Use n = 12: divide the annual rate by 12 and raise (1 + r/12) to the power 12 × years.

What is the difference between simple and compound interest?

Simple interest is paid only on the original principal; compound interest is also paid on interest already earned, so it grows faster over time.

How often should interest compound?

More often is better for savers, but the gain from monthly to daily compounding is very small.

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

Home › Finance Formulas › Compound Interest Formula A = P(1 + r/n)^nt

Compound Interest Formula Calculator

Compound interest is interest calculated on the principal plus the interest already earned. The standard formula A = P(1 + r ÷ n)^nt gives the final amount A when a principal P earns a nominal annual rate r, compounded n times a year, for t years. The interest earned is A − P.

Formula

A = P × (1 + rn)^nt Interest = A − P

Where

A: final amount (principal + interest)
P: principal (initial deposit)
r: nominal annual rate, as a decimal
n: compounding periods per year
t: time in years

Calculator

Principal (P)

Annual rate (r) (%)

Compounding (n)

Years (t)

Result and step-by-step solution

Final amount

16,470.09

Interest earned: 6,470.09 on 10,000.00 over 10 years, compounded monthly.

Rate per period
rn = 0.0512 = 0.00416667
Number of periods
n × t = 12 × 10 = 120
Growth factor
(1 + 0.00416667)¹²⁰ = 1.6470095
Final amount
A = 10,000.00 × 1.6470095 = 16,470.09

Year-by-year balance

Year	Balance	Total interest
1	10,511.62	511.62
2	11,049.41	1,049.41
3	11,614.72	1,614.72
4	12,208.95	2,208.95
5	12,833.59	2,833.59
6	13,490.18	3,490.18
7	14,180.36	4,180.36
8	14,905.85	4,905.85
9	15,668.47	5,668.47
10	16,470.09	6,470.09

How to use the formula

The formula has two parts: the periodic rate r ÷ n, and the number of periods nt. The calculator shows both before computing the growth factor, and prints a year-by-year table so you can see the balance accelerate: the interest earned in the last year is much larger than in the first, because it is earned on a bigger balance.

The default example puts 10,000 in an account at 5% compounded monthly for 10 years. The balance reaches 16,470.09, so the interest is 6,470.09; simple interest would have paid only 5,000. This page handles a single deposit. For regular contributions, combine it with the future value of an annuity, or use the site’s compound interest calculator with monthly additions.

Frequently asked questions

What is the compound interest formula?: A = P(1 + r ÷ n)^nt, where P is the principal, r the annual rate as a decimal, n the compounding periods per year and t the number of years. Interest = A − P.
How do I calculate compound interest monthly?: Use n = 12: divide the annual rate by 12 and raise (1 + r/12) to the power 12 × years.
What is the difference between simple and compound interest?: Simple interest is paid only on the original principal; compound interest is also paid on interest already earned, so it grows faster over time.
How often should interest compound?: More often is better for savers, but the gain from monthly to daily compounding is very small.

Last reviewed: September 26, 2026. Calculations run in your browser and were checked against numpy-financial, SciPy and published spreadsheet examples.