Compound Interest Calculator
Calculate compound interest with monthly, quarterly, or annual compounding. See how your investment grows over time with our free calculator.
Future Value
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How to Use the Compound Interest Calculator
Enter your initial principal, annual interest rate, investment period, compounding frequency, and optional monthly contribution. The calculator shows your final value, total contributions, interest earned, and a year-by-year growth table.
Compound Interest Formula
A = P(1 + r/n)^(nt) + PMT ร [((1+r/n)^(nt) โ 1) / (r/n)] A = final amount, P = principal, r = annual rate (decimal), n = compounding periods/year, t = years, PMT = periodic contribution
Frequently Asked Questions
- The compound interest formula is A = P(1 + r/n)^(nt), where P = principal, r = annual rate (decimal), n = compounding periods per year, t = years. Total interest = A โ P. For $10,000 at 8% for 10 years compounded monthly: A โ $22,196.
- Compound interest is interest calculated on both the initial principal and the accumulated interest from previous periods. Unlike simple interest (which only accrues on the principal), compound interest grows exponentially โ you earn 'interest on interest.'
- The more frequently interest compounds, the more you earn (or owe). Ranking by growth: daily > monthly > quarterly > annually. For a $10,000 investment at 8% for 10 years: annual compounding = $21,589; daily compounding = $22,253. The difference matters more at higher rates and longer terms.
- Simple interest = P ร r ร t (always on original principal). Compound interest = P(1 + r/n)^(nt) โ P (grows exponentially). Over 10 years at 8%, $10,000 earns $8,000 in simple interest but over $12,000 in compound interest โ that's the power of compounding.
- For monthly compounding, set n = 12: A = P(1 + r/12)^(12t). Monthly interest rate = annual rate รท 12. The effective annual rate (EAR) with monthly compounding at 8% nominal = (1 + 0.08/12)^12 โ 1 โ 8.30%.
- The Rule of 72 is a quick way to estimate how long it takes to double your money: Years to double โ 72 รท interest rate. At 8%: 72 รท 8 = 9 years. At 6%: 72 รท 6 = 12 years. At 12%: 72 รท 12 = 6 years. It's surprisingly accurate for rates between 2โ20%.
- To find the rate: r = (A/P)^(1/t) โ 1. If $5,000 grew to $8,000 in 7 years: r = (8000/5000)^(1/7) โ 1 = 1.6^(0.1429) โ 1 โ 6.9% annual rate.
- The power of compounding is most visible over long periods. $10,000 invested at 8%: after 10 years = $21,589; after 20 years = $46,610; after 30 years = $100,627; after 40 years = $217,245. Starting early is more powerful than contributing more later.
- Future Value with contributions: FV = P(1+r/n)^(nt) + PMT ร [((1+r/n)^(nt) โ 1) / (r/n)]. P = initial investment, PMT = periodic contribution, r = annual rate, n = compounding periods, t = years. Our calculator handles this automatically.
- With monthly contributions: A = P(1 + r/12)^(12t) + PMT ร [((1+r/12)^(12t) โ 1) / (r/12)]. Example: $10,000 initial + $200/month at 7% for 20 years = approximately $143,000. Monthly contributions dramatically boost final wealth.