How to Use the Compound Interest Calculator
From starting balance to a future-value estimate.
- Enter an initial amount (it can be zero) and optional contributions with a frequency and timing.
- Choose an assumed annual interest rate and how often interest is compounded (daily, monthly, quarterly, or yearly).
- Set the time in years and months. Optionally add a yearly contribution increase or an inflation rate under More options.
- Read the future value, deposits vs interest, APY, chart, and yearly breakdown. Results update as you type — no submit button.
The Compound Interest Formula
How to calculate compound interest for a lump sum, then contributions.
The standard compound interest formula is A = P(1 + r/n)^(nt). A is the future value, P is the principal, r is the annual rate as a decimal, n is the number of compounding periods per year, and t is time in years. Example: 10,000 at 5% compounded annually for 10 years is 10,000 × (1.05)^10 ≈ 16,288.95. The same amount compounded monthly is about 16,470.09.
When you add regular contributions, there is no single short formula that covers every frequency and timing mix, so this investment growth calculator (a future value calculator with deposits) adds each contribution on the months it falls due and grows the balance with an equivalent monthly factor derived from the nominal rate and compounding frequency.
Simple vs. Compound Interest
Same starting amount and rate — different growth paths.
With simple interest, 10,000 at 5% for 10 years earns 5,000 of interest and ends at 15,000. With compound interest at the same 5% compounded annually, the same starting amount ends near 16,288.95 because each year's interest is added to the base that earns later interest. The gap widens as time or the compounding frequency increases.
How Compounding Frequency Matters
Daily vs monthly vs yearly on the same assumed rate.
A daily compound interest calculator and a monthly compound interest calculator use the same nominal rate but different n in the formula. For 10,000 at 5% over 10 years with no contributions:
| Compounded | Approximate future value |
|---|---|
| Annually | 16,288.95 |
| Monthly | 16,470.09 |
| Daily (365) | 16,486.65 |
The difference between yearly and daily compounding here is under 200 on a 10,000 starting balance. Rate and time usually matter more than how often interest is credited.
The Rule of 72
A quick estimate of how long to double money at a steady rate.
Divide 72 by the assumed annual percentage return to estimate doubling time. At 6%, 72 ÷ 6 ≈ 12 years. That rule of 72 shortcut is an approximation; this page also shows years ≈ ln(2) ÷ ln(1 + APY), which uses the effective annual yield and still ignores contributions. Neither figure is a forecast.
What This Calculator Does Not Include
Honest limits of a future-value estimate.
Taxes, account fees, fund charges, and changing rates are not modeled. Real investment returns are not constant and can be negative. Inflation is only an optional estimate of today's-money purchasing power. Asking how much to save each month to reach a fixed goal belongs on the Savings Goal Calculator rather than this page.
Frequently Asked Questions
Formula, APY, compounding frequency, and the rule of 72.
How do I calculate compound interest?
Choose an assumed annual rate and compounding frequency, then apply A = P(1 + r/n)^(nt) for a lump sum, or add regular contributions month by month. This compound interest calculator runs that simulation live as you change the inputs.
What is the compound interest formula?
The basic compound interest formula is A = P(1 + r/n)^(nt), where A is the future value, P is the starting principal, r is the annual rate as a decimal, n is how many times interest compounds per year, and t is time in years. Regular contributions add a separate month-by-month term.
What is the difference between simple and compound interest?
Simple interest is earned only on the original principal. Compound interest is earned on the principal plus interest already credited, so the balance can grow faster over the same rate and time.
Does compounding more often make a big difference?
Daily or monthly compounding usually produces a slightly higher effective annual yield than yearly compounding at the same nominal rate. The gap is often small compared with the effect of the rate you assume and how long the money stays invested.
What is APY, and how is it different from the interest rate?
The interest rate is the nominal annual rate you enter. APY (effective annual yield) folds in compounding: APY = (1 + r/n)^n − 1. Comparing APYs is a clearer way to compare how often interest is credited.
How does the rule of 72 work?
The rule of 72 is a quick approximation: divide 72 by the annual percentage return to estimate years to double. This page also shows a more precise estimate using ln(2) ÷ ln(1 + APY), still ignoring contributions.
Does this calculator guarantee these returns?
No. The rate is an assumption you choose. Real investment returns vary, are not constant, and can be negative. Treat the future value as an illustration, not a prediction or promise.
Why does the future value change when contributions are made at the start of the period?
Contributions at the beginning of each period start earning interest sooner than contributions at the end. Over many periods that timing difference adds up, so the same contribution amount produces a higher ending balance when paid at the start.
Sources
Compound interest in plain language: Investor.gov (SEC) — What is compound interest?. Compounding and interest: CFPB — How does compound interest work?.
This calculator provides general information and illustrative estimates only. It is not financial or investment advice, and it does not predict future returns. Talk to a qualified financial adviser about your own situation.
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