The CFPB describes compound interest as earning interest on the money saved and on the interest earned along the way. Each time interest is credited (daily, monthly, quarterly or yearly), it joins the balance, and the next interest calculation uses that larger balance. Simple interest, by contrast, is always calculated on the original principal only. Compounding works in both directions: it grows savings and investments, and it grows unpaid debt such as a credit card balance.
Formula
A = P × (1 + r / n)^(n × t)
- A: the ending balance.
- P: the starting principal.
- r: the nominal annual interest rate as a decimal (5% = 0.05).
- n: the number of compounding periods per year (12 for monthly, 365 for daily).
- t: the number of years.
Interest earned is A − P. The yearly effect of compounding at a given rate and frequency is what an APY reports.
Example
The CFPB example: $1,000 at 5% interest compounded once a year grows to $1,050 after one year and $1,102.50 after two. The second year earns $52.50 instead of $50 because it earns interest on the first year's $50.
Over a longer period the gap widens. $10,000 at 5% for 10 years becomes:
- Simple interest: 10,000 + 10,000 × 0.05 × 10 = $15,000.00
- Compounded annually: 10,000 × 1.05^10 ≈ $16,288.95
- Compounded monthly: 10,000 × (1 + 0.05/12)^120 ≈ $16,470.09
The compound interest calculator runs these numbers for any rate, frequency and term, and the CD calculator, 401(k) calculator and dividend calculator apply the same principle to specific accounts.
Common mistakes
- Comparing accounts by interest rate alone. Use APY, which already reflects compounding frequency.
- Forgetting that a loan's APR does not include compounding, so the effective cost of a revolving balance is higher than the APR.
- Expecting compounding frequency to matter more than rate or time. Moving from monthly to daily compounding changes the result far less than a higher rate or a longer term.