# Compound Interest Calculator Model compound growth of savings or investments with regular deposits, interest rate, and time horizon to project future value. --- - **Canonical URL:** https://dothecalculation.com/calculators/compound-interest-calculator - **Category:** Financial calculators - **Publisher:** Do The Calculation (https://dothecalculation.com) - **Cost:** Free, no account or sign-up required - **Privacy:** Runs entirely in the browser; inputs are never sent to a server - **Methodology:** https://dothecalculation.com/methodology - **Reviewed by:** Sheharyar Shahid, Data Analyst & Advanced Excel Specialist (DAE) (https://dothecalculation.com/about/team/sheharyar-shahid) --- ## Compound Interest Calculator — Future Value With Monthly Deposits Model how time, interest rates, and compounding frequencies turn initial balances and regular deposits into long-term wealth. - Compounding frequency comparisons (daily to annual) - Future value and interest splits - Dynamic growth curve visualization ## The Mathematics of Compounding Growth Compound interest is interest calculated on the initial principal and also on the accumulated interest of previous periods. Known mathematically as exponential growth, it stands in contrast to simple interest, where interest is earned strictly on the original principal. The power of compounding is driven by frequency. When interest is credited to an account, it becomes part of the principal base for the next compounding period. The shorter the compounding interval (e.g., daily instead of annually), the faster your wealth accumulates. ## How to Use This Calculator Enter your initial (starting) amount, a monthly contribution, the annual interest rate, and the number of years you plan to invest. The calculator compounds your balance monthly, adding your contribution each period, and returns the future value, total contributions made, and total interest earned. ## Worked Example: $10,000 Starting, $300/Month at 6% for 10 Years Initial amount $10,000, monthly contribution $300, annual interest rate 6%, time horizon 10 years (120 months). Total contributions: $10,000 (starting) + $300 × 120 = $46,000. Future value after monthly compounding: ≈ $67,357.77. Interest earned: $67,357.77 − $46,000 ≈ $21,357.77 — meaning interest contributed nearly as much to the final balance as the contributions themselves did (roughly 46% of the total), even though the account started with a modest $10,000 and only a moderate 6% rate. ## The Compound Interest Formulas To calculate the future value of a principal sum compounded over time, apply the standard compounding formula: $$A = P \left(1 + \frac{r}{n}\right)^{nt}$$ Where: * \(A\) is the future value of the investment, including interest. * \(P\) is the principal investment amount. * \(r\) is the annual interest rate (decimal). * \(n\) is the number of times interest is compounded per year. * \(t\) is the time the money is invested in years. When regular monthly deposits are added to the principal, the calculator combines this formula with the future value of an ordinary annuity formula: $$A = P \left(1 + \frac{r}{n}\right)^{nt} + PMT \times \frac{\left(1 + \frac{r}{n}\right)^{nt} - 1}{\frac{r}{n}}$$ Where \(PMT\) is the monthly contribution amount. This reveals how consistent, small deposits amplify compound growth over decades. ## The Impact of Compounding Frequency Compounding frequency determines how often interest is calculated and added to your balance. The most common intervals are daily, monthly, quarterly, and annually. Daily compounding yields the highest return because interest starts earning interest the very next day. While the difference between daily and monthly compounding may seem minor on small sums, it scales significantly over long timelines and large balances. This is why credit cards charge daily compounding on debt, while savings accounts often offer monthly or daily compounding on deposits. ## The Rule of 72: A Quick Mental Shortcut To estimate how long it takes to double your money under compound interest, use the **Rule of 72**. Divide 72 by your annual interest rate to find the approximate doubling period in years: $$\text{Years to Double} \approx \frac{72}{\text{Annual Rate}}$$ For example, an investment earning a consistent 8% annual return will double in value approximately every \(72 / 8 = 9\text{ years}\). This mental model highlights the accelerating curves of compound growth. ## Related Calculators For a shorter-term goal with a fixed target date, try the [savings calculator](/calculators/savings-calculator); for a full portfolio contribution and growth breakdown, use the [investment calculator](/calculators/investment-calculator) or model retirement-specific assumptions with the [retirement calculator](/calculators/retirement-calculator). ## Frequently asked questions ### What is compound interest? Compound interest is interest calculated on the initial principal plus the accumulated interest from previous periods. It represents earning interest on interest. ### What is the formula for compound interest? The base formula is A = P(1 + r/n)^(nt), where A is future value, P is principal, r is annual rate, n is compounding frequency, and t is time in years. ### What is the difference between simple and compound interest? Simple interest is calculated strictly as a percentage of the original principal. Compound interest is calculated on the principal plus all previously accumulated interest, leading to exponential growth. ### What does compounding frequency mean? Compounding frequency is the number of times interest is calculated and added to the principal balance per year (e.g., 12 for monthly, 365 for daily). ### How does daily compounding differ from monthly compounding? Daily compounding calculates and adds interest to the balance 365 times a year, while monthly compounding does so 12 times, resulting in slightly higher returns for daily compounding over time. ### What is APY (Annual Percentage Yield)? APY is the real annual rate of return, taking into account the effect of compound interest. It is always higher than the nominal interest rate when compounding occurs more than once a year. ### What is the Rule of 72? The Rule of 72 is a quick shortcut to estimate when an investment will double. Divide 72 by the annual interest rate to find the approximate doubling period in years. ### Does this calculator account for inflation? No. The calculator models nominal growth. To adjust for inflation, subtract the estimated inflation rate (e.g., 2-3%) from your annual rate input. ### How do monthly deposits affect compound growth? Monthly deposits add new capital to the principal base regularly, giving the compounding math a larger amount to compound each month and accelerating wealth building. ### Are savings account rates simple or compound? Almost all bank savings accounts and CDs apply compound interest, usually compounding daily or monthly and crediting interest to your account monthly. ## Related concepts - **APY** — Annual Percentage Yield: the true annual rate of return reflecting compounding effects. - **Rule of 72** — A mathematical shortcut to estimate the years required to double an investment. - **Ordinary Annuity** — A series of equal periodic payments made at the end of each period, compounding over time. ## Related guides - [Compound Interest: Formula, Examples, and Calculator](https://dothecalculation.com/blog/finance/compound-interest-deep-dive) — Learn how compound interest works, calculate growth with monthly deposits, compare assumptions, and avoid common projection mistakes. - [Simple vs Compound Interest: Linear Growth vs Interest on Interest](https://dothecalculation.com/blog/finance/simple-vs-compound-interest) — Compare simple interest and monthly compound interest, learn when each model fits, and use worked examples aligned to the calculators. ## Related calculators - [Investment Calculator](https://dothecalculation.com/calculators/investment-calculator) — Project compound growth of your investments with regular contributions, interest rate, and time horizon to estimate future value. - [CAGR Calculator](https://dothecalculation.com/calculators/cagr-calculator) — Calculate the compound annual growth rate between a starting and ending value to measure investment performance over time. - [Interest Calculator](https://dothecalculation.com/calculators/interest-calculator) — Calculate simple and compound interest scenarios instantly to see how principal, rate, and time affect your total earnings. - [Savings Calculator](https://dothecalculation.com/calculators/savings-calculator) — Forecast savings account growth and calculate the monthly deposits needed to reach a specific financial goal by a target date. - [Simple Interest Calculator](https://dothecalculation.com/calculators/simple-interest-calculator) — Calculate simple interest, the final amount owed, and total repayment amount based on your principal, rate, and loan term. - [Dividend Calculator](https://dothecalculation.com/calculators/dividend-calculator) — Calculate dividend yield, projected annual income, and future portfolio value with DRIP dividend reinvestment over time. --- _This tool is for educational purposes only. Compounding schedules, investment returns, inflation indices, retirement nest egg timelines, and asset appreciation targets depend on personal budget profiles, tax brackets, market volatility, and macroeconomic policies. Always consult a certified financial planner (CFP) or tax advisor before finalizing long-term investment strategies._ --- _Source: [Do The Calculation](https://dothecalculation.com/calculators/compound-interest-calculator). Quote freely with attribution and a link to this page._