Compound Interest Calculator: Future Value & Contributions
About this calculator The compound interest calculator takes a principal, a nominal annual interest rate, the number of compounding periods per year, a number of years and an optional monthly contribution, and accumulates them period by period—interest first, then the contribution—to give the future value at the end of the term and the total interest earned.
It answers a very specific class of question: if a sum of money compounds at a fixed rate and a fixed frequency for a number of years, what does it grow to; and what if a further amount is added every month? It is useful for understanding the effect of compounding frequency, comparing simple and compound interest, sizing a regular savings plan, or working backwards to ask how much per month is needed to reach a target.
What it does not do is equally clear: it does not provide or recommend any interest rate or product, it ignores taxes, inflation, fees and market volatility, and it does not forecast the return of any real asset. The rate you enter is your assumption; the output is simply the mathematical consequence of that assumption.
Important notice
This page is an educational and scenario-estimation tool. The “5%” in the examples is a demonstration figure only and does not represent any market rate or expected return. The results are for informational purposes only and do not constitute investment, tax or legal advice. The calculation convention follows the engine source code; convention date 2026-09-08.
How to use this calculator 01 Open the panel this page corresponds to the “Finance → Compound interest” sub-panel (/#/financial/compound). Defaults are principal 10,000, annual rate 5%, 10 years, compounding frequency 12, monthly contribution 0. 02 Fill in the five inputs principal, annual rate (%), years, compounding frequency per year, monthly contribution. Enter the rate as a percentage (5, not 0.05); enter the compounding frequency as the number of interest calculations per year (12 for monthly, 4 for quarterly). 03 Read the two results “Future value” and “Total interest” update live, rounded to two decimal places. 04 Check the result card and interpretation the card also shows “Total contributed” (principal plus all contributions) and “Effective annual rate” (shown when the frequency is greater than 1 and the rate is non-zero). A verified badge means the period-by-period accumulation and the closed-form formula agree; approximate means the number of periods is not an integer and only whole periods were counted. 05 Solve for a target (optional) enter an amount under “Target future value” and click “Solve”; the calculator uses a numerical search to return the required monthly contribution. If the principal alone already reaches the target at the given rate and term, it tells you no contribution is needed. Worked examples All three examples were produced by the engine’s compoundInterest routine by period-by-period accumulation and cross-checked against the closed form. Displayed amounts follow the interface convention of two decimal places; intermediate values keep more digits for checking.
Example 1: default inputs, monthly compounding, no contributions
Inputs: P = 10,000 P = 10{,}000 P = 10 , 000 r = 5 % r = 5\% r = 5% m = 12 m = 12 m = 12 t = 10 t = 10 t = 10 c = 0 c = 0 c = 0
Per-period rate i = 0.05 / 12 = 0.004166 6 ‾ i = 0.05/12 = 0.004166\overline{6} i = 0.05/12 = 0.004166 6 n = 12 × 10 = 120 n = 12 \times 10 = 120 n = 12 × 10 = 120
Growth factor ( 1 + i ) 120 = 1.0041 6 ‾ 120 ≈ 1.647009498 (1+i)^{120} = 1.0041\overline{6}^{\,120} \approx 1.647009498 ( 1 + i ) 120 = 1.0041 6 120 ≈ 1.647009498
Future value F V = 10,000 × 1.647009498 ≈ 16,470.09 FV = 10{,}000 \times 1.647009498 \approx 16{,}470.09 F V = 10 , 000 × 1.647009498 ≈ 16 , 470.09
Total interest I = 16,470.09 − 10,000 = 6,470.09 I = 16{,}470.09 - 10{,}000 = 6{,}470.09 I = 16 , 470.09 − 10 , 000 = 6 , 470.09
Interface shows: future value 16,470.09 , total interest 6,470.09 , effective annual rate 5.1162% .
Example 2: the same 5% at different compounding frequencies
Hold P = 10,000 P = 10{,}000 P = 10 , 000 r = 5 % r = 5\% r = 5% t = 10 t = 10 t = 10 c = 0 c = 0 c = 0 m m m
Frequency m m m
Per-period rate i i i
Periods n n n
Future value
Total interest
EAR
1 (annual)
0.05
10
16,288.95
6,288.95
5.0000%
12 (monthly)
0.0041667
120
16,470.09
6,470.09
5.1162%
365 (daily)
0.00013699
3,650
16,486.65
6,486.65
5.1267%
For comparison: simple interest
—
—
15,000.00
5,000.00
—
Going from annual to monthly compounding adds 181.14; going from monthly to daily adds only 16.56. The gain from higher frequency diminishes, and the limit is continuous compounding, P e r t = 16,487.21 P e^{rt} = 16{,}487.21 P e r t = 16 , 487.21
Example 3: monthly compounding with a 500 monthly contribution
Inputs: P = 10,000 P = 10{,}000 P = 10 , 000 r = 5 % r = 5\% r = 5% m = 12 m = 12 m = 12 t = 10 t = 10 t = 10 c = 500 c = 500 c = 500
i = 0.004166 6 ‾ i = 0.004166\overline{6} i = 0.004166 6 n = 120 n = 120 n = 120 C = 500 × 12 / 12 = 500 C = 500 \times 12/12 = 500 C = 500 × 12/12 = 500 Principal part: 10,000 × 1.647009498 = 16,470.09 10{,}000 \times 1.647009498 = 16{,}470.09 10 , 000 × 1.647009498 = 16 , 470.09
Contribution part: annuity factor ( 1 + i ) 120 − 1 i = 0.647009498 0.004166 6 ‾ ≈ 155.282279 \dfrac{(1+i)^{120}-1}{i} = \dfrac{0.647009498}{0.004166\overline{6}} \approx 155.282279 i ( 1 + i ) 120 − 1 = 0.004166 6 0.647009498 ≈ 155.282279 77,641.14 77{,}641.14 77 , 641.14
Future value F V = 16,470.09 + 77,641.14 = 94,111.23 FV = 16{,}470.09 + 77{,}641.14 = 94{,}111.23 F V = 16 , 470.09 + 77 , 641.14 = 94 , 111.23
Total contributed = 10,000 + 500 × 120 = 70,000 = 10{,}000 + 500 \times 120 = 70{,}000 = 10 , 000 + 500 × 120 = 70 , 000 I = 94,111.23 − 70,000 = 24,111.23 I = 94{,}111.23 - 70{,}000 = 24{,}111.23 I = 94 , 111.23 − 70 , 000 = 24 , 111.23
Interface shows: future value 94,111.23 , total interest 24,111.23 , total contributed 70,000.00 .
A note on conventions
With the same 500 per month but the compounding frequency changed to 1 (annual), the engine combines the 12 monthly payments into a single 6,000 deposit at year end, and the future value falls to 91,756.30 —2,354.93 less than with monthly compounding. This is not an error; it is a direct consequence of the “contributions are credited at the end of each compounding period” convention described under Assumptions.
The inputs of the three examples above can be entered directly into the calculator to reproduce them. Change any one input (for example, the term from 10 to 20 years) and the future value becomes 27,126.40 (with no contributions).
Principles and derivation From simple to compound interest
Simple interest is charged on the principal only: after t t t P r t P\,r\,t P r t P ( 1 + r t ) P(1+rt) P ( 1 + r t ) P ( 1 + i ) P(1+i) P ( 1 + i ) P ( 1 + i ) 2 P(1+i)^2 P ( 1 + i ) 2 n n n P ( 1 + i ) n P(1+i)^n P ( 1 + i ) n
Figure 1: monthly compounding versus simple interest over 10 years (data from the engine’s year-by-year balances) Why the contribution term is a geometric series
A deposit of C C C n − 1 n-1 n − 1 C ( 1 + i ) n − 1 C(1+i)^{n-1} C ( 1 + i ) n − 1 C ( 1 + i ) n − 2 C(1+i)^{n-2} C ( 1 + i ) n − 2
C [ ( 1 + i ) n − 1 + ( 1 + i ) n − 2 + ⋯ + 1 ] = C ⋅ ( 1 + i ) n − 1 i C\left[(1+i)^{n-1} + (1+i)^{n-2} + \cdots + 1\right] = C\cdot\frac{(1+i)^n - 1}{i} C [ ( 1 + i ) n − 1 + ( 1 + i ) n − 2 + ⋯ + 1 ] = C ⋅ i ( 1 + i ) n − 1 This is the future-value factor of an ordinary annuity (annuity-immediate, payments at the end of each period). If payments are made at the beginning instead (annuity-due), each deposit compounds for one extra period and the whole term is multiplied by ( 1 + i ) (1+i) ( 1 + i )
Nominal annual rate (APR) versus effective annual rate (EAR)
In “5% per year, compounded monthly”, the 5% is a nominal annual rate: by convention it is simply the per-period rate i i i m m m
E A R = ( 1 + r m ) m − 1 EAR = \left(1+\frac{r}{m}\right)^{m} - 1 E A R = ( 1 + m r ) m − 1 A nominal 5% compounded monthly corresponds to an EAR of 5.1162%; daily, 5.1267%; continuously, e 0.05 − 1 = 5.1271 % e^{0.05}-1 = 5.1271\% e 0.05 − 1 = 5.1271%
The Rule of 72
To ask “how many years to double”, the exact answer is n = ln 2 / ln ( 1 + i ) n = \ln 2 / \ln(1+i) n = ln 2/ ln ( 1 + i ) ln 2 / ln 1.05 = 14.21 \ln 2/\ln 1.05 = 14.21 ln 2/ ln 1.05 = 14.21 72 / 5 = 14.4 72/5 = 14.4 72/5 = 14.4
Relationship to net present value
The compound growth formula F V = P V ( 1 + i ) n FV = PV(1+i)^n F V = P V ( 1 + i ) n P V = F V / ( 1 + i ) n PV = FV/(1+i)^n P V = F V / ( 1 + i ) n net present value calculator discounts each period’s cash flow back to today and sums them, using the very same factor. Once you understand compounding, you understand all of the mathematics behind discounting.
Assumptions
Fixed rate : the per-period rate i = r / m i = r/m i = r / m Equal periods, settled at period end : interest is added to the principal at the end of each compounding period; contributions are also credited at that point, after interest, and earn nothing in the period they arrive.Monthly contributions scaled by 12 / m 12/m 12/ m : with m m m c × 12 / m c \times 12/m c × 12/ m m = 12 m = 12 m = 12 m = 1 m = 1 m = 1 Whole periods only : the engine runs ⌊ m t ⌋ \lfloor m\,t \rfloor ⌊ m t ⌋ approximate.Frictionless : no taxes, fees, inflation, exchange rates or early-withdrawal penalties.Currency-neutral : principal, contributions and results share one currency unit; the calculator performs no currency conversion. Scope and limitations
Can calculate savings at a fixed rate, regular fixed contributions, order-of-magnitude estimates for education or retirement targets, and comparisons between compounding frequencies.
Approximate only products whose rate changes (floating, stepped or dividend-based) can only be modelled as scenarios with an assumed average rate, and different scenarios may diverge widely.
Cannot calculate the contractual return of any real financial product. Fees, taxes, compounding and payment-date rules and early-redemption terms all change the real outcome; refer to the contract.
Does not provide rates, compare products or recommend institutions; results are not return forecasts.
Numerical precision amounts are computed in IEEE 754 double precision and displayed to two decimal places. Over extremely long terms (hundreds of years) or at extremely high frequencies, accumulated rounding may appear in the last digit; this is a display-precision matter, not a formula error. Common mistakes
Entering 5% as 0.05 : the annual rate field takes a percentage. Entering 0.05 gives an annual rate of 0.05%, and the 10-year future value is only 10,050.12.Treating the per-period rate as the annual rate : 5% compounded monthly is 0.41667% per month, not 5% per month. If you enter 5 as the annual rate and a frequency other than 1, make sure a nominal annual rate is what you intend.Comparing offers with different frequencies by nominal rate : at the same nominal 5%, monthly compounding actually yields 0.1162 percentage points more than annual. Compare across frequencies using EAR.Forgetting your own convention : whether contributions are made at the beginning or end of the period, and whether monthly payments are combined, accounts for the 2,354.93 difference in Example 3. If another tool gives a different number, compare conventions before comparing formulas.Entering the number of years or months as the frequency : compounding frequency means “how many times per year interest is calculated”. Entering 120 does not mean “10 years × 12 months”; it means 120 times per year.Mistaking total interest for a rate of return : total interest is an absolute amount, magnified by term and principal. To compare the efficiency of options, look at EAR or annualised return.Ignoring inflation : the future value is a nominal amount. At 3% inflation, 16,470 in ten years buys roughly what 12,255 buys today. Typical use cases Teaching: an intuitive feel for exponential growth Change the term from 10 to 20 and then 30 years and watch the future value accelerate rather than merely double; then change the frequency from 1 to 12 to 365 and watch the gains diminish. This is the most everyday illustration of exponential functions and limits.
Solving for a savings target Given a target amount, an acceptable term and an assumed rate, use “Solve for target” to find the monthly contribution required, then adjust the term or the target to see which variable the result is most sensitive to.
Comparing two ways of quoting interest One offer says “5% annualised, compounded monthly”; another says “5.1% annualised, compounded annually”. Use EAR to decide which is actually higher (the first is 5.1162%, the second 5.1%).
Isomorphic problems in engineering and science Population growth, radioactive decay (a negative rate), bacterial culture and equipment depreciation all follow x n = x 0 ( 1 + i ) n x_n = x_0(1+i)^n x n = x 0 ( 1 + i ) n
FAQ What should I enter for compounding periods per year? Follow the interest rules: 1 for annual, 4 for quarterly, 12 for monthly, 365 for daily. If unsure, use 12 as a baseline, then try 1 and 365 to see the range—for rates around 5% the spread is usually under 1.3%.
Why is the contribution future value from my annuity formula higher than here? Most often a difference in convention: many textbook problems use beginning-of-period payments (annuity-due), while this calculator uses end-of-period payments; or the other source compounds monthly while you chose annual compounding here, which combines the monthly payments at year end. Both points are covered under Assumptions.
What happens with a negative rate? The formula still holds: ( 1 + i ) n (1+i)^n ( 1 + i ) n
Why are future value and total interest shown to only two decimal places? Amounts are displayed to the cent, following currency convention. Internally the calculation is double-precision with no intermediate rounding; if you need more digits, recompute with the closed-form formula from the examples.
What do verified and approximate on the result card mean? verified means the period-by-period accumulation agrees with the closed form within a relative error of 10 − 9 10^{-9} 1 0 − 9 approximate means years × frequency is not an integer and the engine counted whole periods only. They describe mathematical consistency, not any guarantee of a real return.
Can this calculator work out loan repayments? No. A loan is a “borrow first, repay later” cash flow and needs the present-value annuity formula (or the workbench “Finance → Loan” panel). The compound interest calculator handles “deposit first, withdraw later”. The two share the same discount factor but run in opposite directions.
References and further reading
compoundInterest (period-by-period compounding, end-of-period contributions) and aprToEar in the CalcX engine source src/engine/finance.ts; every figure on this page was recomputed by that engine.Brealey, R. A., Myers, S. C., Allen, F., & Edmans, A. Principles of Corporate Finance , 14th ed. McGraw Hill, 2022. Chapter 2, “How to Calculate Present Values”, gives the standard derivations of future value, annuities and continuous compounding.
Wikipedia, Compound interest （访问日期：2026-09-08）—the compound interest formula, continuous compounding and history.
Wikipedia, Effective interest rate （访问日期：2026-09-08）—converting between nominal and effective rates.
Wikipedia, Rule of 72 （访问日期：2026-09-08）—the doubling-time approximation and its error analysis.
Data effective date: 2026-09-08 (this page contains no market rate data; the date refers to when the engine formulas and explanatory text were verified).
Privacy All inputs and calculations run inside your browser and are never uploaded to a server. The text on this page is static content; it neither contains nor records any user input.
Sources & review
Reviewed by CalcX 编辑组
Updated 2026-09-09 Open Compound Interest Calculator: Future Value & Contributions in CalcX