Compound Interest Calculator: Daily/Monthly Growth
Use this compound interest calculator to project future value at any compounding frequency — daily, monthly, quarterly, or annual. Calculate compound interest on any principal at any rate, with effective APY shown.
$
%
yrs
Future value$0
Interest earned$0
Effective APY0.00%
Growth multiple1.0×
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How this calculator works
Compound interest pays interest on previously earned interest, not just on the principal. The future value depends on rate, time, and how often interest is added to the balance:
discrete: A = P(1 + r/n)nt
continuous: A = P × ert
continuous: A = P × ert
- P
- Principal (starting balance)
- r
- Annual rate as a decimal (7% → 0.07)
- n
- Compounding periods per year (12 = monthly)
- t
- Years
- e
- Euler's number, ≈ 2.71828 — the upper bound of compounding frequency
At 7%, the difference between annual and continuous compounding over 20 years is small — $38,697 vs $40,552 on a $10K principal. The bigger lever is time, not frequency.
Source: Standard compound-interest formula. APY definition — 12 CFR § 1030 (Regulation DD).
FAQ
What's continuous compounding?
The mathematical limit as compounding frequency approaches infinity. At a 7% APR, continuous gives an effective APY of e0.07 − 1 = 7.251%, compared to 7.229% for daily and 7.186% for monthly. Real banks never offer continuous; it's a theoretical upper bound used in academic finance and option pricing.
Does this calculator handle monthly contributions?
No — this is pure lump-sum compounding. For lump sum + monthly contributions (the typical retirement-savings scenario), use the Future Value Calculator or Roth IRA Calculator instead.
What is the difference between simple and compound interest?
Simple interest is calculated only on the original principal — same dollar amount each period. Compound interest is calculated on the principal PLUS accumulated interest, so it grows exponentially. On $10,000 at 5% over 20 years: simple earns $10,000; compound (annual) earns $16,533.
How often does compound interest compound?
Depends on the account. Most US savings accounts compound daily but credit it monthly. CDs vary — daily, monthly, or quarterly. Bonds and treasuries usually compound semi-annually. The shorter the compounding period, the higher the effective yield, but daily vs monthly differs by only ~0.01 percentage points.
What is the rule of 72 for compound interest?
Quick mental math: divide 72 by your annual return % = years to double. At 6% → 12 years; at 8% → 9 years. The rule is most accurate at returns of 6–10%. For exact: log(2) / log(1 + rate).
Does compound interest work in your favor on debt too?
Unfortunately, yes — but in reverse. Credit card debt at 22% APR compounds against you the same way investments compound for you. A $5,000 balance making minimum payments only takes 22 years to pay off and costs $7,000+ in interest. Compound interest accelerates in both directions.
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