Finance · Interest and investing
Compound a balance and see the EAR
Grow a single principal at a nominal annual rate with a chosen compounding frequency, including continuous compounding. The page also reports the effective annual rate. There are no recurring deposits on this form.
Calculate
How the calculator works
Discrete compounding uses A = P(1 + r/n)^{n t}. Continuous compounding uses A = P e^{r t}. The effective annual rate converts the schedule into a once-a-year equivalent: (1 + r/n)^n − 1, or e^r − 1 when continuous. Interest = A − P. Fees, tax, and monthly deposits are omitted (deposits have their own calculator).
Formula and method
A = P (1 + r/n)^{n t}r is the nominal annual rate as a decimal, n the number of compoundings per year, t time in years.
A = P e^{r t} (capitalisation continue)Limit as n goes to infinity. Same r and t; usually a slightly higher A than daily 365.
EAR = (1 + r/n)^n − 1 (ou e^r − 1 en continu)
Effective annual rate: what a once-yearly compound would need to match this schedule.
Nominal versus effective is the point of the EAR line. A 4% nominal compounded monthly is not the same as 4% compounded annually. Daily uses n = 365, not 365.25 and not Bank-of-365 vs 360 conventions. Markets are not a fixed r. Inflation and tax are absent unless you already netted them out of r.
Worked example
$10,000 at 4% for 10 years, monthly
P = $10,000, r = 4%, t = 10, monthly.
- A = 10,000 × (1 + 0.04/12)^{120} ≈ $14,908.33.
- Interest ≈ $4,908.33.
- EAR = (1 + 0.04/12)^{12} − 1 ≈ 4.07%.
About $14,908.33, EAR ≈ 4.07%. Annual compounding would yield about $14,802.44.
Input notes
- Starting principal
- Starting dollars. This page does not add a monthly contribution.
- Annual nominal rate
- Nominal annual percent. 4 means 4%, not 0.04 typed as 4% by mistake — type 4 for four percent.
- Time
- Time t, including a decimal (0.5 for six months).
- Compounding
- Sets n, or continuous. Daily is 365 periods, not “business days.”
Assumptions and limits
Assumptions
- Constant nominal rate, no deposits or withdrawals.
- Discrete n as listed, or continuous exponential.
- Daily n = 365.
Limits
- Not a forecast of stocks, bonds, or bank specials.
- No APY marketing rounding rules beyond EAR as defined.
- No tax lot or inflation adjustment.
How to read the result
EAR lets you compare a monthly account with an annual one at the same nominal print rate. Higher n raises A slightly for the same r. If you will add $300 a month, this page understates the future value; use the contributions calculator.
Common mistakes
Confusing nominal 4% with EAR 4%.
They match only for annual compounding. Monthly 4% nominal has EAR a bit above 4%.
Using simple interest I = Prt and calling it compound.
Simple interest does not pay interest on interest. That is the other calculator.
Related calculations
- Simple interestInterest is proportional to principal, rate, and time. It does not itself earn interest. Use this only when a contract is actually simple, not as a stand-in for savings compounding.
- Savings with monthly depositsProjects a starting balance and constant monthly deposits, credited at month-end, with an annual nominal rate converted as monthly = annual / 12. It is a fixed-rate scenario, not a market forecast.
- CAGRCAGR is the fictional constant annual rate that would take a starting value to an ending value in n years. It smooths the trip: a crash and a rebound disappear into one number.
- ExponentEvaluate aᵇ. Integers, decimals, negative exponents (reciprocals), and 1/2 (square root, base ≥ 0) are possible, within the reals and floating-point limits.
- Inflation and purchasing powerAn amount, a constant annual rate, a period. Compound forward, or bring a later sum back to today’s purchasing power.
- ROIROI here is a simple ratio of gain (or loss) to cash put in. It does not know whether the outcome took a month or a decade. CAGR is the tool that uses years.
Frequently asked questions
What is EAR on this page?
The annual equivalent of the compounding schedule: (1+r/n)^n − 1, or e^r − 1 if continuous.
APY in US bank ads is closely related but can use legal rounding. Here EAR is the mathematical conversion of the n you picked. It is not a guaranteed bank yield.
Does more frequent compounding always pay a lot more?
It pays more, often modestly, at consumer rates.
At 4% for 10 years, monthly versus annual on $10,000 is on the order of a hundred dollars, not thousands. The gap grows with r and t.
Is continuous compounding used in savings accounts?
Rarely for retail deposits. It is the smooth limit of the discrete formula.
Some textbooks and a few products quote it. This option is here so you can see P e^{rt} next to monthly or daily, not as a product recommendation.
Where do monthly deposits go?
On the savings-with-contributions calculator, not here.
This form is a single principal. Adding cash each month is a different recurrence: grow, then deposit.
Author and update
Written by Rédaction HexaCalc (editorial team). Content last updated: August 25, 2026. No third-party medical or financial review is claimed.
This calculation uses a standard mathematical identity. See also the methodology.
Interest that does not compound
Simple interest is I = P × r × t. Use it when a contract truly does not credit interest on interest.
Calculate simple interestCompound-interest projection at a constant nominal rate. This is a calculator, not financial, tax, or credit advice, and not a loan or investment offer. Lenders and brokers apply their own rounding, fees, insurance, and APR. Check the actual contract and disclosures.
Category: Finance