Finance & Economics · Personal Finance
Compound Interest Calculator
Calculate the future value of an investment with compound interest. Supports annual, quarterly, monthly, and daily compounding.
Calculator
Formula
A is the future value, P is the principal (initial investment), r is the annual interest rate as a decimal, n is the number of compounding periods per year, and t is the number of years. The term (r/n) is the periodic interest rate, and nt is the total number of compounding periods.
Source: Standard compound interest formula. See: Ross, Westerfield & Jordan, Fundamentals of Corporate Finance, 12th ed.
How it works
The key insight behind compound interest is that your interest earns interest. In contrast to simple interest, where only the original principal earns returns, compound interest reinvests earnings back into the principal at each compounding period.
The compounding frequency has a meaningful but often misunderstood effect. Monthly compounding produces more than annual compounding because interest is being added — and then earning returns — 12 times per year rather than once. Daily compounding produces slightly more than monthly, but the incremental gain diminishes as frequency increases, converging towards continuous compounding in the limit.
The most important variable, by a wide margin, is time. Doubling the time period roughly doubles the number of compounding events, but because the exponent grows, the effect on final value is far more than proportional — this is the essence of exponential growth.
Worked example
An initial investment of $10,000 at 7% per year, compounded monthly over 20 years:
A = 10,000 × (1 + 0.07/12)^(12×20) = 10,000 × (1.005833...)^240 = $40,099.19
The interest earned is $40,099.19 − $10,000 = $30,099.19 — three times the original investment, generated purely through compounding without any additional contributions.
Limitations & notes
This calculator assumes a constant interest rate over the full period, which is rarely true for real investments. Market returns fluctuate, and the formula should be regarded as illustrative rather than predictive for equity investments.
Taxes, fees, and inflation are not accounted for. In most jurisdictions, investment gains are taxable, which can substantially reduce effective returns. Always model post-tax, post-fee returns for accurate financial planning.
Frequently asked questions
What is the difference between APR and APY?
APR (Annual Percentage Rate) is the simple annual interest rate without accounting for compounding. APY (Annual Percentage Yield) reflects the actual annual return after compounding is applied. For monthly compounding at 7% APR, the APY is (1 + 0.07/12)^12 − 1 ≈ 7.229%. APY is always equal to or greater than APR.
How often should interest compound to maximise returns?
More frequent compounding always produces higher returns, all else equal. However, the gain from increasing compounding frequency diminishes as frequency increases — the difference between monthly and daily compounding is minimal (roughly 0.01% per year at 7%). The difference between annual and monthly compounding is more meaningful.
What is the Rule of 72?
The Rule of 72 is a quick mental approximation: divide 72 by the annual interest rate to estimate the number of years required to double your investment. At 7% per year, money roughly doubles every 72 ÷ 7 ≈ 10.3 years. The exact answer is ln(2) ÷ ln(1.07) ≈ 10.24 years.
What interest rate should I use for long-term stock market projections?
The long-run historical real (inflation-adjusted) return of the US stock market is approximately 6.5–7% per year, with nominal returns around 9–10%. For conservative planning, many financial planners use 6–7% nominal or 4–5% real. These are historical averages — future returns may differ.
Does this calculator include regular contributions (DCA)?
This calculator covers lump-sum compound interest only. For scenarios with regular periodic contributions (dollar-cost averaging or savings plans), use the future value of an annuity formula: FV = PMT × [(1 + r/n)^(nt) − 1] ÷ (r/n), where PMT is the periodic payment amount.
Last updated: 2025-01-15 · Formula verified against primary sources.