Toolarithm

Finance Calculator

Future Value Calculator

Project a starting amount, regular deposits and their future growth.

Project your future balance

Separate your funding from investment growth.

Formatting only; no exchange conversion.

Rate convention and horizon

An effective annual quote already includes compounding. Nominal rates use exponential interpolation between compounding dates; this is a planning model rather than an account crediting rule.

Use an exact horizon from zero to 100 years. Fractional years are entered as whole additional months.

Recurring contributions

Changes the deposit after each full year's count of contributions. A negative value reduces later deposits.

Only completed intervals receive recurring deposits, for either timing choice. An incomplete final interval grows existing funding without a new deposit. Weekly and biweekly mean 52 and 26 equal intervals per year.

One-time additional deposit
Optional comparisons

Your projected future value

Nominal future value
$76,454.76
Total money funded
$51,000.00
Growth / loss
$25,454.76
Effective annual return
6.1678%6.1678\%
Recurring deposits funded
$36,000.00
Horizon
120  months120\;\text{months}

Funding includes the starting amount, actual recurring deposits and the one-time deposit. Growth can be negative. Inflation changes purchasing power rather than cash in the account.

Where the future value comes from

Starting amount after growth
$27,290.95
Recurring deposits after growth
$49,163.80
One-time deposit after growth
$0.00
Additional one-time funding
$0.00
FV≈27290.95101+49163.80404+0≈76454.75505\mathrm{FV}\approx27290.95101+49163.80404+0\approx76454.75505

The mathematical substitution is rounded for display; calculations and exports retain more precision. Currency components are rounded independently and can differ slightly when added. The component values include each deposit's modeled growth, while total funding includes only money put in.

Inputs saved with this plan

Starting amount entered
15000
Annual percentage entered
6
Rate convention
nominal
Nominal compounding
monthly
Whole years
10
Additional whole months
0
Contribution frequency
monthly
Deposit per interval entered
300
Annual deposit change percentage
0
Deposit timing
end
One-time amount entered
0
Purchasing-power adjustment enabled
false
Rate comparison enabled
false
Currency
USD
Projection view
annual

Future value projection schedule

Every year-end and the exact final horizon are included. Period amounts aggregate the intervals since the previous displayed checkpoint. The Start row includes any month-zero one-time deposit. No recurring deposit is implied at a zero horizon. With no recurring plan, detailed rows use monthly growth intervals.

Future value projection ledger
IntervalYearsOpeningRecurring depositsOne-time depositPeriod growth / lossClosing balanceCumulative fundingCumulative growth / loss
Start0$15,000.00$0.00$0.00$0.00$15,000.00$15,000.00$0.00
Interval 121$15,000.00$3,600.00$0.00$1,025.84$19,625.84$18,600.00$1,025.84
Interval 242$19,625.84$3,600.00$0.00$1,311.15$24,536.98$22,200.00$2,336.98
Interval 363$24,536.98$3,600.00$0.00$1,614.06$29,751.04$25,800.00$3,951.04
Interval 484$29,751.04$3,600.00$0.00$1,935.65$35,286.69$29,400.00$5,886.69
Interval 605$35,286.69$3,600.00$0.00$2,277.07$41,163.76$33,000.00$8,163.76
Interval 726$41,163.76$3,600.00$0.00$2,639.56$47,403.32$36,600.00$10,803.32
Interval 847$47,403.32$3,600.00$0.00$3,024.40$54,027.72$40,200.00$13,827.72
Interval 968$54,027.72$3,600.00$0.00$3,432.98$61,060.70$43,800.00$17,260.70
Interval 1089$61,060.70$3,600.00$0.00$3,866.76$68,527.46$47,400.00$21,127.46
Interval 12010$68,527.46$3,600.00$0.00$4,327.29$76,454.76$51,000.00$25,454.76

Model: fixed annual rate, equal contribution intervals, retained returns, exponential interpolation between nominal compounding dates. Annual deposit changes apply after each full year's number of contributions. No taxes, fees, withdrawals, variable returns or per-interval cent rounding. Supported projected monetary values are capped at one trillion in the selected currency. CSV includes complete interval and annual ledgers for both enabled rates. Print retains the displayed primary view; choose every modeled interval for a complete PDF.

What Can You Create?

Build a future-value projection around actual funding choices

A lump-sum growth estimate

Turn off recurring deposits to follow an existing amount through the selected horizon. Add a separately timed one-time deposit when useful, and inspect how much of the ending value comes from the initial amount versus that additional funding.

A recurring contribution plan

Choose equal weekly, biweekly, twice-monthly, monthly, quarterly, semi-annual or annual contributions independently of nominal compounding. Beginning and end timing use the same completed-interval count. Optional annual deposit changes make the cash-flow policy more explicit than assuming one unchanged amount forever.

A purchasing-power and rate comparison

Keep nominal account value separate from an optional inflation-adjusted estimate. Compare another annual rate while holding the funding policy constant, so a higher return assumption is not confused with the effect of putting in more money.

Future value formulas and a step-by-step example

For a numerical nominal annual percentage aa and annual compounding count mm, the annual log-growth factor is LL. An effective annual quote yy is already a decimal annual return. Continuous nominal compounding uses its exponential convention.

L={mln⁡ ⁣(1+a100m),nominal periodica100,nominal continuousln⁡(1+y),effective annual,FVP=PeLTL=\begin{cases}m\ln\!\left(1+\dfrac{a}{100m}\right),&\text{nominal periodic}\\[5pt]\dfrac{a}{100},&\text{nominal continuous}\\[5pt]\ln(1+y),&\text{effective annual}\end{cases},\qquad \mathrm{FV}_{P}=Pe^{LT}

With ff equal contribution intervals per year, the interval growth rate is i=eL/f−1i=e^{L/f}-1. For a constant deposit CC and nn complete intervals, an ordinary annuity at its last complete interval has the following value. A remaining tail grows that value further without adding a recurring deposit.

An={C(1+i)n−1i,i≠0Cn,i=0,Anbeginning=An(1+i)A_n=\begin{cases}C\dfrac{(1+i)^n-1}{i},&i\ne0\\[5pt]Cn,&i=0\end{cases},\qquad A_n^{\text{beginning}}=A_n(1+i)

The beginning factor can reduce value when the interval return is negative; it does not always increase it. With changing deposits, the calculator weights each annual contribution block by the time it remains invested rather than treating every deposit as one initial lump sum.

Ck=C(1+s)⌊(k−1)/f⌋,FVC=∑k=1nCkeL(T−tk)C_k=C(1+s)^{\lfloor(k-1)/f\rfloor},\qquad \mathrm{FV}_{C}=\sum_{k=1}^{n}C_k e^{L(T-t_k)}

Here ss is the annual deposit-change rate as a decimal. End deposits use tk=k/ft_k=k/f and beginning deposits use tk=(k−1)/ft_k=(k-1)/f, with the same completed-interval count for either choice.

Step 1: Grow the initial amount

Start with 1,000 dollars, a nominal annual rate of 10%10\%, annual compounding and a two-year horizon. The starting amount grows to 1,210 dollars. This is only the initial component; later deposits must be valued according to their own funding dates.

FVP=1000(1.10)2=1210\mathrm{FV}_{P}=1000(1.10)^2=1210

Step 2: Add recurring and one-time funding

Deposit 100 dollars at the end of each year, with no annual increase, plus a separate 200-dollar deposit in month twelve. The first recurring deposit grows for one more year and the second has no remaining growth. The one-time deposit also grows for one year, yielding 220 dollars.

FVC=100(1.10)+100=210,FVone-time=200(1.10)=220\mathrm{FV}_{C}=100(1.10)+100=210,\qquad \mathrm{FV}_{\text{one-time}}=200(1.10)=220FV=1210+210+220=1640,F=1000+200+200=1400,G=1640−1400=240\mathrm{FV}=1210+210+220=1640,\qquad F=1000+200+200=1400,\qquad G=1640-1400=240

Moving the same two recurring deposits to the beginning of their complete intervals changes their combined future value to 231 dollars. Total funding stays 1,400 dollars, but the final balance becomes 1,661 dollars because those deposits earn an additional interval of positive growth.

FVC,beginning=100(1.10)2+100(1.10)=231,FVbeginning=1661\mathrm{FV}_{C,\text{beginning}}=100(1.10)^2+100(1.10)=231,\qquad \mathrm{FV}_{\text{beginning}}=1661

Step 3: Keep purchasing power separate

If the illustrative annual inflation assumption is 5%5\%, the original end-deposit scenario has a purchasing-power value of about 1,487.53 dollars in today's money. The nominal account balance remains 1,640 dollars; inflation is not an additional withdrawal.

FVreal=1640(1.05)2≈1487.53\mathrm{FV}_{\text{real}}=\frac{1640}{(1.05)^2}\approx1487.53
Why Users Love This Tool

Understand the sources of the projected balance

Separate funding from its growth

  • Starting principal, recurring cash deposits and a one-time contribution remain distinct.
  • Each funding component has its own future-value contribution based on time invested.
  • Signed losses remain visible at negative rates, with an explicit zero-rate case.
  • Tiny nonzero growth is typeset rather than hidden behind a rounded zero currency amount.

Use reproducible assumptions

  • Whole years plus additional whole months preserve the selected horizon exactly.
  • Effective annual quotes do not receive a second nominal compounding adjustment.
  • Only completed contribution intervals receive deposits; an unfinished tail is explicit.
  • No per-interval currency rounding, taxes, fees or changing market returns are implied.
Perfect For

Useful for future expenses and long-term accumulation questions

Savers testing a contribution policy

See how an initial amount and a recurring funding habit combine over the same horizon. An annual deposit increase can represent a planned budget change, but the tool does not assume your income actually rises. Check total funding alongside the future balance to assess the commitment behind the result.

Households comparing future purchasing power

A future nominal amount may buy less than the same number today. Use the optional inflation assumption to view a separate purchasing-power estimate, and keep that estimate distinct from cash in the account. The model does not predict the cost of a particular purchase or the path of consumer prices.

Students studying time value of money

Compare a starting lump sum with a stream of ordinary or beginning-of-interval deposits. The worked example traces funding and growth into a final value before applying a purchasing-power adjustment. The full interval ledger makes the timing assumptions inspectable beyond a single formula or a handful of early checkpoints.

How It Works

How it works in three quick steps.

1

Set the starting amount, rate and exact horizon

Enter present value and an annual rate quote. Choose nominal compounding or an effective annual return, then enter whole years and additional whole months without silently rounding a fractional year.

2

Build the contribution policy and optional adjustments

Choose an independent contribution frequency and beginning or end timing. Add an annual deposit increase or decrease and an optional one-time deposit. Enable purchasing-power adjustment or a second annual rate if useful.

3

Review funding, growth and the complete schedule

Separate deposited money from signed investment growth, inspect all annual checkpoints or every interval, and compare matching cash flows at the alternative rate. Download complete CSV ledgers or select the desired primary view for print and PDF.

Download & Print

Keep the assumptions and the full growth schedule

Download complete CSV ledgers

Export every modeled interval and every annual checkpoint for the primary and optional alternative rate. The file keeps source settings, opening balances, new funding, signed period growth, cumulative amounts and purchasing power when enabled. It does not truncate the schedule to the first few years.

Choose the print or PDF detail

The print layout retains results, original inputs and the selected primary projection view while removing editing controls and the supporting guide. Choose every modeled interval before printing for a detailed PDF, or retain annual checkpoints for a shorter record. Landscape orientation helps fit the funding and growth columns.

Copy or share an editable scenario

Copy the projection with its assumptions or save a link that restores active settings and the schedule view. Financial inputs are readable in the fragment, so treat a personal scenario accordingly. Currency selection changes formatting, including whole-yen display, without changing the amount through an exchange conversion.

FAQ

Frequently Asked Questions

What is the future value of an investment?
Future value estimates what a starting amount and scheduled additional funding become at a later horizon under a specified growth model. This tool separates your starting money, recurring deposits and one-time funding from the returns attributed to them. A higher future value can come from putting in more money as well as earning more growth, so review both total funding and signed growth before comparing two plans.
Should I enter a nominal rate or an effective annual return?
A nominal annual rate needs a compounding convention to determine its effective annual growth. An effective annual return or APY already includes that annual compounding effect, so the nominal frequency controls are inactive for that quote. Choose the convention that matches the figure you are modeling. The calculator interpolates growth exponentially between nominal compounding boundaries; it does not reproduce a bank's statement dates, daily balances or interest-crediting rules.
Can contribution frequency differ from compounding frequency?
Yes. You can model monthly deposits with annual nominal compounding, weekly deposits with a monthly nominal quote, or other supported combinations. The annual growth factor is translated into equivalent growth over each equal contribution interval. Weekly and biweekly mean fifty-two and twenty-six equal intervals per year rather than actual dated payments. This convention makes the timing reproducible while keeping the contribution schedule independent of the rate quote.
How are beginning deposits and incomplete intervals handled?
Both timing choices fund the same number of completed contribution intervals. Beginning deposits are made at the start of those completed intervals, while end deposits follow their growth. Any remaining partial interval grows existing money without adding a recurring deposit, even with beginning timing. A zero horizon therefore has no recurring funding. This explicit convention avoids silently creating a deposit for an unfinished interval when the selected horizon and frequency do not align.
How does the annual contribution change work?
The entered contribution is used for the first full year's number of scheduled deposits. After that count, the next year's deposits change by the specified percentage, and the process repeats. This changes contributions rather than the investment return or inflation rate. Negative percentages reduce future deposits; a complete reduction stops deposits after the first block. The schedule and total funding show the resulting amounts without rounding each deposit to currency cents.
When does the one-time additional deposit enter the projection?
Choose a whole month from today through the final horizon. Month zero enters at the start and grows for the full horizon; a deposit in the final month is included with no remaining growth. A one-time deposit can occur inside a contribution interval and grows only from its selected month. It remains separate from recurring deposits and their annual increases, so its cash amount and its future value can be inspected independently.
Does inflation reduce the balance shown in the account?
The nominal future value is the modeled account balance. Enabling inflation adds a separate purchasing-power estimate expressed in today's money by deflating that balance over the selected horizon. It does not remove cash from the account or alter the deposit schedule. Negative inflation assumptions are also supported as a mathematical scenario. This adjustment is distinct from taxes, management fees and investment volatility, which are outside this model.
Can I model a negative return or a zero interest rate?
Yes. Signed annual rates above the supported lower bound can produce losses, and those losses remain visible instead of being relabeled as zero interest. At a zero rate, future value equals the money actually funded over the horizon. The calculation also uses stable growth functions near zero so a very small nonzero return is not lost merely by subtracting nearly equal powers. Values below currency display precision use accessible scientific notation.
What does the alternative rate comparison hold constant?
The alternative keeps the same initial amount, contribution frequency, deposit timing, annual contribution change, one-time deposit and horizon. It also uses the same nominal or effective quote convention and inflation assumption. Only the annual rate changes. Comparing both growth and final value helps isolate that rate assumption from funding changes. Each scenario is a constant-rate planning estimate, rather than a simulation of changing market returns or a promise of investment performance.
Can I save every interval rather than only the first few years?
The annual view includes every completed year and the exact final horizon. Select every modeled interval to inspect the full primary ledger, including an incomplete final tail when present. CSV always exports complete interval and annual ledgers for both enabled rates, along with active settings at their entered precision. Print and Save as PDF retain the currently selected primary view; choose every interval before printing when you want the complete detailed schedule.
About This Tool

About this future-value and funding planner

A future balance combines two different sources: money placed into the plan and growth earned while that money remains invested. Toolarithm's Future Value Calculator keeps those sources visible. It begins with a present amount, then values recurring deposits and a separately timed one-time contribution over an exact whole-month horizon. The component breakdown helps explain why a larger future balance can reflect a larger funding commitment rather than a better investment return. The same distinction carries into the projection schedule and saved calculation.

Contribution policy deserves as much attention as the rate assumption. Weekly, biweekly, monthly and annual deposits do not enter at the same modeled times, and beginning deposits have a different growth window from end deposits. This tool uses equal intervals and funds only completed intervals under either timing choice. Any final unfinished fraction grows existing funding without inventing another recurring deposit. Annual contribution changes apply after each full year's scheduled deposit count, keeping the cash-flow policy separate from both investment growth and inflation.

The optional alternative rate isolates a growth assumption while retaining the same funding policy. Inflation adjustment answers a different question by translating the nominal final balance into today's purchasing power. Neither option predicts a path of market returns or reproduces an account provider's interest-crediting dates. The calculation retains precision rather than posting rounded cents every interval, and it excludes taxes, fees and withdrawals. Use the result as a transparent planning model, compare assumptions that matter to your situation, and retain actual account terms and records when reconciling an estimate with real savings or investment activity.

Editorial Transparency

Who maintains this page

Ownership and review

Written and maintained by the Toolarithm editorial team. No review date is shown without a maintained editorial record. No independent professional review is claimed.

Methodology

Formulas are checked with worked examples and boundary cases. Timing, compounding, payment, and rounding assumptions remain visible; results are educational estimates, not financial advice.

Read the editorial methodology

Dates and sources

Review dates change only after a substantive method or content check.

Keep building

Explore more calculators

Calculators hub