Compound Interest Calculator · Guide

Compound Interest Formula & Compounding Frequency

Compound interest applies growth to the existing balance, which means previous interest can become part of the amount earning future interest.

The lump-sum formula

For a principal P, nominal annual rate r, n compounding periods per year, and time t in years, A = P(1 + r/n)^nt.

What n means

Annual compounding uses n = 1, semiannual 2, quarterly 4, monthly 12, weekly 52, and daily 365.

Nominal annual rate versus APY

A nominal annual rate describes the stated rate before within-year compounding. APY is already an effective annual yield. Applying an extra compounding frequency to APY would double-count compounding.

Why daily can differ from monthly

With the same positive nominal annual rate, more frequent compounding raises the effective annual yield slightly because interest is credited into the growing balance more often.

Regular contributions

Each contribution enters at its scheduled time and then grows for the remaining horizon. A beginning-of-period contribution has one contribution period more growth time than an otherwise identical end-of-period contribution.

Worked example

$10,000 at a 4% nominal annual rate compounded daily for one year grows to about $10,408.08 under the calculator's fixed-rate model.

Why real results can differ

Actual accounts may use changing rates, fees, taxes, minimum balances, product-specific crediting rules, calendar day-count methods, or other terms that this generic fixed-rate projection does not model.