What compound interest is
Simple interest pays you only on the money you put in. Compound interest also pays you on the interest you've already earned, because each credit is added to the balance and earns interest from then on. Early on the effect is barely visible; after a decade or two, interest-on-interest can be larger than all of your deposits combined — that's the upward bend in the chart above.
The formulas
A single deposit P at annual rate r, compounded n times a year for t years:
A = P × (1 + r/n)^(n·t) continuous: A = P × e^(r·t) APY = (1 + r/n)^n − 1
Monthly deposits D are added using the equivalent monthly rate i = (1 + r/n)^(n/12) − 1, so any compounding frequency works with monthly deposits:
Deposits at end of month: FV = D × ((1 + i)^(12t) − 1) / i Deposits at start of month: FV × (1 + i)
Worked example
Start with $5,000, add $200 a month, earn 4.5% compounded monthly for 15 years.
The starting deposit grows to 5,000 × (1.00375)^180 ≈ $9,808. The 180 monthly deposits grow to 200 × ((1.00375)^180 − 1) / 0.00375 ≈ $51,283. Together that's $61,090.71 — from $41,000 of your own money, so $20,090.71 is interest. The APY at monthly compounding is 4.594%.
Assumptions and limitations
- The rate stays fixed for the whole period. Savings rates change; stock returns vary from year to year and can be negative.
- No taxes, fees or withdrawals are modeled, and results are in future (nominal) dollars, not adjusted for inflation.
- Daily compounding uses a 365-day year.
Background: Investor.gov (U.S. SEC), Compound interest.
Frequently asked questions
How often should interest compound?
More often is better for savers, but the difference shrinks quickly. At 5% a year, annual compounding yields 5.00%, monthly 5.12% and daily 5.13%. Continuous compounding is the mathematical limit at 5.13%. The rate itself and the time invested matter far more than the frequency.
What is the difference between APR and APY?
APR is the nominal annual rate before compounding. APY (annual percentage yield) is what you actually earn in a year once compounding is included. Banks advertise savings accounts by APY; if you only have the APY, enter it with annual compounding.
What is the Rule of 72?
A shortcut for doubling time: divide 72 by the annual rate. At 6%, money doubles in about 72 ÷ 6 = 12 years. It is an approximation that works best for rates between about 4% and 12%.
Should deposits be at the start or end of the month?
Deposits at the start of each period earn one extra period of interest, so they grow slightly more. Automatic transfers on payday are usually close to "start" if interest is credited at month-end. The difference is small for typical savings rates.
Does this include taxes or inflation?
No. Interest in a regular savings or brokerage account is usually taxable each year, which slows growth, and inflation reduces what the final balance can buy. The retirement calculator lets you see the result in today's dollars.
CalcNest results are estimates based on the inputs and assumptions above, not financial, tax or lending advice. A lender's official Loan Estimate or your account statement is the final word.