Toolarithm

Finance Calculator

Compound Interest Calculator

Project compound growth with monthly deposits. Save or share your full annual projection.

Live calculator

Compound interest inputs

Money already saved before the first monthly deposit.

Nominal yearly percentage, not APY. Negative rates model a constant loss.

Decimal years are rounded to the nearest whole month; the modeled duration appears below.

A fixed deposit each month. Use zero for a single starting deposit.

Daily uses a fixed 365-period year.

Labels amounts only. This does not convert money or apply local tax rules.

Future value

$59,163.80

Starting principal
$10,000.00
Total deposits
$40,000.00
Recurring deposits
$30,000.00
Interest earned
$19,163.80
Effective APY
6.16778%6.16778\%
Modeled duration
120 months

The selected nominal rate is converted to equivalent monthly growth. Deposits are applied at the chosen start or end of each month. Total deposits include the starting principal. Taxes, fees, inflation, and withdrawals are excluded.

Compound interest growth compared with total depositsThe gold line shows the projected balance and the dashed gray line shows cumulative deposits. Exact values for every checkpoint are in the annual projection table below.Start120 months
Gold: projected balanceDashed gray: total deposits

Complete annual projection

All 10 checkpoints are included. Deposits and interest are cumulative; a partial final year uses its modeled month count.

Compound interest annual projection
YearBalanceDepositsInterest / loss
1$13,700.67$13,000.00$700.67
2$17,629.59$16,000.00$1,629.59
3$21,800.83$19,000.00$2,800.83
4$26,229.35$22,000.00$4,229.35
5$30,931.01$25,000.00$5,931.01
6$35,922.66$28,000.00$7,922.66
7$41,222.18$31,000.00$10,222.18
8$46,848.56$34,000.00$12,848.56
9$52,821.97$37,000.00$15,821.97
10$59,163.80$40,000.00$19,163.80
What Can You Create?

Build clear compound growth scenarios

Savings growth projections

Estimate how a starting balance and monthly deposits could grow over time when interest compounds at a daily, monthly, quarterly, semiannual, or annual schedule.

Investment scenario checks

Compare rate assumptions and contribution habits before building a deeper spreadsheet or talking through long-term investing goals with an advisor.

Time horizon comparisons

Adjust years and contributions to see how patience, consistency, and compounding can change the final balance across different planning windows.

Why Users Love This Tool

Fast answers with the assumptions still visible

Clear financial outputs

  • Future value is shown as the primary result, with deposits, interest earned, and effective annual yield separated for faster review.
  • The complete annual projection includes every year and the final partial year, with cumulative deposits and interest shown beside the balance.
  • Choose a display currency, download the complete CSV schedule, or print the current assumptions and projection to a PDF using your browser.
  • Inputs update the calculation immediately, making it easy to compare several contribution and rate assumptions in one sitting.

Transparent assumptions

  • The calculator asks for compounding frequency because nominal rates can produce different effective annual yields.
  • Monthly contributions can be applied at the beginning or end of the month, which matters when contributions also earn interest.
  • The model separates principal, recurring deposits, and earned interest so users can see where growth is coming from.
  • The page includes practical guidance and FAQs so users understand when compounding assumptions are useful and when they are only estimates.
Perfect For

Compound interest planning for study and decisions

Students and teachers

Use the calculator to demonstrate exponential growth, compounding periods, contribution timing, and the difference between deposits and interest earned.

Personal planners

Run quick assumptions for emergency funds, savings goals, investment accounts, and long-term contribution habits before refining a plan.

Small business owners

Estimate the growth of reserves, sinking funds, or interest-bearing cash balances with a clear view of deposits and accumulated interest.

How It Works

How it works in three quick steps.

1

Enter the starting balance

Add the initial principal, annual interest rate, number of years, and any monthly contribution you expect to make during the projection period.

2

Choose compounding assumptions

Select daily, monthly, quarterly, semiannual, or annual compounding, then choose whether monthly deposits happen at the beginning or end of each month.

3

Review the growth result

Review future value, cumulative deposits, interest earned, effective APY, and the modeled month count. Check the complete annual projection, then copy a summary, share the scenario link, download CSV, or print to PDF.

Formula

Compound interest formulas, including monthly deposits

The calculator converts nominal annual compounding to equivalent monthly growth, then applies each monthly deposit at its selected timing. The equations below describe exactly that model. They do not reproduce an account’s daily posting calendar, variable rates, or bank-specific rounding rules.

Working formulas

Growth of the starting principal

A=P(1+rn)ntA=P\left(1+\frac{r}{n}\right)^{nt}

This expression excludes recurring deposits. It describes the original principal growing at a constant nominal annual rate. To match the live result, use the modeled duration after the calculator rounds the entered time to whole months.

Effective annual yield as a percentage

APY=[(1+rn)n−1]×100%\mathrm{APY}=\left[\left(1+\frac{r}{n}\right)^n-1\right]\times100\%

APY expresses one year of growth as a percentage, including the effect of compounding. The calculator derives an equivalent monthly growth rate from this annual yield before applying the monthly contribution schedule. Contributions affect the projected balance, while this yield describes the rate assumption.

Equivalent monthly rate

i=(1+rn)n/12−1i=\left(1+\frac{r}{n}\right)^{n/12}-1

Use this monthly rate even when compounding is daily, quarterly, semiannual, or annual. It preserves the selected annual yield while placing deposits on one consistent monthly timeline.

End-of-month deposits

A=P(1+i)m+C(1+i)m−1iA=P(1+i)^m+C\frac{(1+i)^m-1}{i}

The deposit part is an ordinary annuity: the final deposit has no time left to earn interest. This expression applies when the monthly rate is nonzero.

Beginning-of-month deposits

A=P(1+i)m+C(1+i)(1+i)m−1iA=P(1+i)^m+C(1+i)\frac{(1+i)^m-1}{i}

Every recurring deposit earns one extra month of growth relative to an end-of-month deposit. This expression also supports a negative monthly rate, so earlier deposits can lose more value in a constant-loss scenario.

Zero-rate case and total interest

i=0:A=P+Cm,I=A−(P+Cm)i=0:\quad A=P+Cm,\qquad I=A-(P+Cm)

At a zero rate, timing and compounding frequency have no effect. Total deposits include the original principal; earned interest is the final balance minus all deposits. A negative difference represents modeled loss.

Symbols

AA - balance from the starting principal
The accumulated value of the initial principal after the modeled duration, excluding recurring deposits.
PP - starting principal
The initial balance entered before any recurring monthly contributions are added.
rr - nominal annual rate as a decimal
Divide the entered percentage by 100. For example, 6%6\% means r=6100=0.06r=\frac{6}{100}=0.06.
nn - compounding periods per year
Use 365 for daily, 12 for monthly, 4 for quarterly, 2 for semiannual, or 1 for annual compounding.
tt - modeled duration in years
The calculator rounds the entered duration to whole months. Divide that modeled month count by 12 to obtain the time used when checking the principal growth expression.
CC - monthly deposit
The fixed recurring deposit, in the same currency as the starting principal.
mm - whole months
The modeled month count is m=round⁡(12tentered)m=\operatorname{round}(12t_{\mathrm{entered}}) and the modeled years are t=m/12t=m/12. A duration of zero months earns no interest and adds no monthly deposits.
ii - monthly equivalent rate
The selected annual yield expressed as one month of growth, calculated without rounding intermediate balances to cents.
II - cumulative interest or loss
The projected balance minus starting principal and all recurring deposits.
Worked example

Calculate one year of growth step by step

Start with P=10,000P=10{,}000, contribute C=250C=250 at each month’s end, and use a nominal annual rate of 6%6\% compounded monthly for m=12m=12 months. These are illustrative assumptions rather than a quoted account rate.

  1. 1. Convert the annual percentage

    r=6/100=0.06,n=12r=6/100=0.06,\qquad n=12

  2. 2. Find monthly growth

    i=(1+0.06/12)12/12−1=0.005i=(1+0.06/12)^{12/12}-1=0.005

  3. 3. Grow principal and monthly deposits

    A=10,000(1.005)12+250(1.005)12−10.005≈13,700.67A=10{,}000(1.005)^{12}+250\frac{(1.005)^{12}-1}{0.005}\approx13{,}700.67

  4. 4. Separate deposits from interest

    D=10,000+250(12)=13,000,I≈700.67D=10{,}000+250(12)=13{,}000,\qquad I\approx700.67

  5. 5. Check the effective annual yield

    APY=[(1.005)12−1]×100%≈6.1678%\mathrm{APY}=[(1.005)^{12}-1]\times100\%\approx6.1678\%

For the same example with beginning-of-month deposits, the final value is approximately 13,716.0913{,}716.09. With a zero rate it is exactly 13,00013{,}000. Comparing these checks helps separate contribution timing from growth and avoids confusing deposits with earnings.

Download & Print

Save, share, and print your compound interest result

Copy a clean summary

Copy the future value, deposits, interest, and input assumptions for your notes. Share scenario copies a link with the inputs in its fragment; anyone receiving that link can read the included financial amounts.

Print the result

Choose Print / Save PDF, then select your printer or the browser’s Save as PDF destination. The print layout includes the scenario assumptions and every annual checkpoint, with navigation and unrelated page content removed.

Record assumptions

Download CSV to save the full schedule with the currency, principal, nominal rate, requested years, modeled months, monthly deposit, compounding frequency, and timing. Spreadsheet values retain calculation precision; visible money amounts are rounded for readability.

FAQ

Frequently Asked Questions

What does a compound interest calculator do?
A compound interest calculator estimates how money can grow when interest is added back to the balance and then earns more interest in future periods. This Toolarithm calculator also includes optional monthly contributions, compounding frequency, and contribution timing. That makes it useful for savings goals, investment examples, classroom lessons, and early planning scenarios where the growth path matters as much as the final balance.
How is compound interest different from simple interest?
Simple interest calculates interest only on the original principal, while compound interest calculates interest on the principal plus previously earned interest. Over longer periods, compounding can create much larger balances because interest begins to earn interest. This is why the compound interest calculator is better for savings and investment projections, while the simple interest calculator is better for fixed formula examples and non-compounding agreements.
Which compounding frequency should I choose?
Choose the frequency that matches the account, investment, or example you are modeling. Savings accounts often compound daily or monthly, while some classroom examples use annual compounding for simplicity. More frequent compounding can increase the effective annual yield when the nominal rate is the same. If you do not know the exact schedule, monthly compounding is a reasonable estimate for quick planning, but it should not replace the terms from a real account disclosure.
Why does contribution timing change the result?
Contribution timing matters because money contributed at the beginning of a month has more time to earn interest than money contributed at the end of the month. The difference can be small over short periods, but it becomes more visible when contributions are large, rates are higher, or the projection spans many years. This calculator lets you test both assumptions so the projection better matches how you actually save.
Can I use this calculator for investment returns?
You can use the compound interest calculator to model investment return assumptions, but the result is only an estimate. Real investments can rise and fall, returns are rarely constant, and taxes, fees, inflation, withdrawals, and risk are not included. The calculator is best for comparing broad scenarios and understanding the effect of time and contributions. For real investment decisions, use it as a planning aid alongside professional advice and actual account information.
Does the calculator include taxes, inflation, or fees?
No. The current calculator focuses on the core compound interest formula, recurring monthly contributions, compounding frequency, and contribution timing. Taxes, inflation, account fees, changing rates, withdrawals, and market volatility are not included. Keeping the model focused makes the formula easier to understand and faster to use, but users should adjust their expectations when applying the result to real savings accounts, investments, or long-term financial plans.
How are decimal years and partial years handled?
The calculator works on a monthly timeline. It multiplies your entered years by twelve and rounds to the nearest whole month, then shows that modeled duration beside the result. Each completed year receives a checkpoint, and a shorter final year receives its own row. For example, one and a half years produces eighteen monthly deposits and an additional checkpoint after the first annual row. Use the displayed month count when reproducing the calculation.
Why can this projection differ from my bank statement?
This tool converts the selected compounding schedule into an equivalent monthly growth rate and assumes identical monthly deposits. A real account may accrue interest on actual daily balances, use changing rates, post deposits on specific dates, round posted interest, or charge fees. Those details can change the credited amount even when the advertised rate looks similar. Match the account’s nominal rate and timing first, and use its disclosure or statements for an exact reconciliation.
About This Tool

Why compound interest projections need careful inputs

Compound interest is powerful because each period builds on the balance that came before it. That makes it useful for modeling savings accounts, investment assumptions, education examples, business reserves, and any scenario where earned interest remains in the account. It also means the result is sensitive to inputs. A small change in rate, time horizon, compounding frequency, or contribution timing can create a noticeably different future value. Toolarithm's compound interest calculator keeps those assumptions visible so the final number is easier to understand. Instead of showing only one answer, it separates starting principal, recurring contributions, earned interest, and effective annual yield.

The calculator is designed for planning and learning rather than pretending every future rate will be exact. Real accounts may include variable interest rates, taxes, fees, withdrawals, inflation, contribution limits, and market risk. Those factors are not included in this focused model. What the tool does well is answer a practical first question: if these inputs are true, what happens to the balance over time? Users can change the rate, adjust monthly deposits, test beginning-of-month versus end-of-month contributions, and review the complete annual projection before saving or printing the result. That makes the page useful for personal planning, classroom demonstrations, quick comparisons, and conversations that need a clear starting estimate before deeper financial analysis.

Method and educational reference

The formulas above document Toolarithm’s fixed-rate monthly model. For an independent introduction to principal, recurring contributions, time, and compounding, see the SEC’s Investor.gov compound interest calculator. Different tools can use different deposit and posting conventions; this reference does not certify this calculator’s implementation.

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