If P is the principal, r is the annual rate, n is the number of times compounded per year, and t is years:
Walk through
Step 1 of 5
Start
You deposit principal **P** at annual rate **r**, compounded **n** times a year.
Try it
$2,000 at 6% compounded monthly for 3 years
A = 2000(1 + 0.06/12)^(12·3) = 2000(1.005)³⁶ ≈ $2,393.46.
More frequent compounding helps, but with diminishing returns: at 6%, going from annual to monthly adds value; monthly to continuous barely moves the needle.
Your turn
If r/n = 0.01 and there are 24 periods, by what factor does the money grow?
Compound interest
Why?
Each compounding period multiplies by (1 + r/n). After n·t periods, you've multiplied that many times.
As n → ∞ (continuous compounding), A → P·e^(rt).