Future Value Calculator

Future value planner

See what today's money could grow to

Enter a starting balance, a fixed annual rate, and time. Add regular deposits if you plan to keep saving. Your result, growth chart, and schedule use the same assumptions.

1Enter your plan
2Calculate the total
3Review each year

Your assumptions

Build the projection

Display currency

Will you make regular deposits?Yes, include depositsGrow the starting amount and add the same amount each period.No, starting amount onlyProject one lump sum with no later deposits.

Starting amountMoney available before the first compounding period.Annual interest rateA fixed nominal yearly rate; enter 6 for 6%.Time periodHow long the money remains in the projection.Compounding & deposit frequencyInterest and regular deposits use the same period.Deposit each periodThe same amount is added at the selected frequency.

When is each deposit made?Beginning deposits receive one extra period of modeled growth.

End of periodCommon savings exampleBeginning of periodEarns for one more period

The example uses a fixed 6% nominal rate, annual compounding, and ten $100 year-end deposits.

Growth over time

Balance vs. money deposited

The solid line is the projected balance. The dashed line is the amount you have put in.

Projected balanceMoney deposited

Year-by-year detail

How the balance changes

Each row reconciles the opening balance, deposits, modeled interest, and ending balance.

Future value accumulation schedule
Through	Start balance	Deposits	Interest	End balance
Year 1	$0.00	$1,000.00	$50.00	$1,050.00
Year 2	$1,050.00	$1,000.00	$102.50	$2,152.50
Year 3	$2,152.50	$1,000.00	$157.63	$3,310.13
Year 4	$3,310.13	$1,000.00	$215.51	$4,525.63
Year 5	$4,525.63	$1,000.00	$276.28	$5,801.91
Year 6	$5,801.91	$1,000.00	$340.10	$7,142.01
Year 7	$7,142.01	$1,000.00	$407.10	$8,549.11
Year 8	$8,549.11	$1,000.00	$477.46	$10,026.56
Year 9	$10,026.56	$1,000.00	$551.33	$11,577.89
Year 10	$11,577.89	$1,000.00	$628.89	$13,206.79
19 intermediate rows hidden
Year 30	$65,438.85	$1,000.00	$3,321.94	$69,760.79

Integrated time-value solver

Solve FV, PV, PMT, rate, or periods

Use the projection above when the annual rate and horizon are known and you want a growth chart and schedule. Use this five-key solver when exactly one time-value variable is unknown. I/Y is the rate for one selected period; N and PMT must use that same period.

Five-key TVM solver

Choose one value to calculate

Select the missing key, then enter only the other four values. Rates and period counts always use the same period basis.

Step 1

What do you want to calculate?

FVFind the ending value after the entered periods and recurring payments.

Results

Your calculated value

Future Value (FV)$3,108.93

Based on 10 years at 6% per year, with payments at the end of each period.

PMT × N: -$1,000.00
Growth factor: 1.7908×
Equation check: Balances to 0

Currency changes formatting only. The underlying equation uses signed currency units and keeps full precision until display.

Educational time-value arithmetic only; this is not a rate quote, approval, appraisal, or investment forecast.

Cash-flow comparison

PV, PMT, and FV magnitudes

Bar lengths use absolute magnitudes; labels preserve the entered or solved signs.

-$1,000.00

PMT

-$100.00

$3,108.93

Complete result

Five-key value table

The calculated key is highlighted; every rate and count uses the same selected period.

Key	Meaning	Value
N	Number of periods	10 years
I/Y	Rate per year	6%
PV	Present value	-$1,000.00
PMT	Periodic payment	-$100.00
FVCalculated	Future value	$3,108.93

Future value, without the fog

See what you put in, what compounds, and what you may end with

Future value is the projected balance at a specific later point. It combines the money already invested, regular contributions, and the growth produced by a declared rate. The page also reverses the same periodic relationship to solve PV, PMT, I/Y, or N, while keeping every assumption and cash-flow direction visible.

Ending amount: FV after the final period
Cash added: PV + every PMT
Modeled growth: FV − total cash added

Start with the question

What does future value tell you?

It answers: “If these dollars stay invested, the same contribution arrives each period, and the entered rate repeats, what balance follows after N periods?”

That makes future value a forward projection. Present value asks the reverse question: what amount today is equivalent to a stated future amount? The integrated five-key solver also reverses for a level payment, periodic rate, or period count. Keep the valuation date and period basis visible so those ideas are never mixed.

Reproduce the review example

$1,000 now, then $100 at each year-end

Use 10 annual periods at 6%, with each $100 contribution made at the end of its year. This is an ordinary-annuity timing convention.

Example inputsAll periods are annual

Number of periods: 10 years
Starting amount (PV): $1,000
Rate per period: 6%
Periodic contribution: $100 / year
Contribution timing: End of year

Projected future value$3,108.93after 10 years

Starting principal: $1,000.00
10 contributions: $1,000.00
Modeled growth: $1,108.93

Starting principal
Contributions
Growth

Screenshot-style check: $1,000 + ($100 × 10) = $2,000 contributed; $3,108.93 − $2,000 = $1,108.93 of modeled growth.

Opening amount at year 10$1,000 × 1.06¹⁰ = $1,790.85

Future value of year-end deposits$100 × ((1.06¹⁰ − 1) ÷ 0.06) = $1,318.08

Combined future value$1,790.85 + $1,318.08 = $3,108.93

Keep every period on one basis

Formula and variables

Level contributions with matching rate periodsFV = PV(1 + i)^N + PMT × (((1 + i)^N − 1) ÷ i) × (1 + i)^type

Use type = 0 for end-of-period payments and type = 1 for beginning-of-period payments. If i = 0, use FV = PV + PMT × N.

Variables used by the worked example
Symbol	Meaning	Plain-language definition	Example
`FV`	Future value	The balance at the end of the last period.	$3,108.93
`PV`	Present value	The amount already invested at time zero.	$1,000
`PMT`	Periodic contribution	The same amount added once per period.	$100
`i`	Rate per period	The decimal return applied in each matching period.	0.06
`N`	Number of periods	How many equal growth periods the scenario covers.	10
`type`	Contribution timing	0 for end of period; 1 for beginning of period.	0

Monthly example: an annual nominal rate of 6% with monthly periods uses i = 0.06 ÷ 12 and N = years × 12. An APY already reflects compounding, so do not divide it by 12 as though it were a nominal rate without converting it first.

Reverse the same periodic relationship

When to use the five-key TVM solver

The projection workbench expects a nominal annual rate, frequency, and years so it can draw a schedule. The five-key solver is for a different question: exactly one of FV, PV, PMT, I/Y, or N is unknown, and the other four already share one period basis.

Choose one missing key and enter the other four
Solve	Enter	Result meaning
`FV`	PV, PMT, I/Y, N	Ending value after the final period
`PV`	FV, PMT, I/Y, N	Equivalent signed value at time zero
`PMT`	PV, FV, I/Y, N	Equal signed payment each period
`I/Y`	PV, FV, PMT, N	One bounded nonnegative rate per period
`N`	PV, FV, PMT, I/Y	Number of matching periods

Cash-flow directionmoney paid out = negative · money received = positive

Period alignmentI/Y is per period · N counts those periods · PMT repeats each period

Substitution checkPV(1+i)ᴺ + PMT factor + FV ≈ 0

A solved rate is not automatically an annual rate, APR, APY, or IRR. Rate solving is bounded to one unique nonnegative root from 0% through 100% per period. Multiple-sign-change or irregular cash flows need a dated cash-flow model. Inflation is separate too: nominal FV does not show future purchasing power, so compare it with a clearly sourced inflation scenario rather than silently subtracting a rate.

One switch, one extra growth period

Beginning vs. end of period

The opening $1,000 is present for all 10 years in both cases. Only the recurring $100 deposits move.

End of period

Interest first, then add $100

The first deposit grows for nine years; the tenth arrives at the result date and earns no interest in this model.

$3,108.93ordinary annuity · type 0

Beginning of period

Add $100, then apply interest

Every contribution receives one more growth period, so the PMT portion is multiplied by 1.06.

$3,188.01annuity due · type 1

Audit the result, not just the headline

How to read the chart and schedule

Read a stacked growth chart

Total height is the ending balance at that point.
Principal and contributions are dollars you supplied.
Growth is the modeled return earned so far.

Read the detail schedule

Year	Start	Interest	Deposit	End
1	$1,000.00	$60.00	$100.00	$1,160.00
2	$1,160.00	$69.60	$100.00	$1,329.60
3	$1,329.60	$79.78	$100.00	$1,509.38
…	…	…	…	…
9	$2,583.59	$155.02	$100.00	$2,838.61
10	$2,838.61	$170.32	$100.00	$3,108.93

For an end-of-year contribution, end = start + interest + deposit. The next row should begin with the prior row's ending balance.

What the number leaves out

Limits to keep beside the result

The rate is constant

Actual investment returns move up and down, and deposit rates can change. A smooth line is a scenario, not a forecast or promise.

Cash flows are regular

The formula assumes the same contribution arrives at the selected point in every period. Irregular deposits need dated cash-flow modeling.

Fees, tax, and inflation are outside the total

Unless separately modeled, the result is nominal and before fees and taxes. It does not show future purchasing power.

Account rules can differ

Day-count methods, crediting dates, minimum balances, contribution limits, penalties, and withdrawals may change a real account result.

Quick answers

Future value calculator FAQ

What is future value?

Future value is the amount a present balance and any later cash flows would reach at a stated future point under the entered rate and timing assumptions. It is an ending amount, not today’s purchasing power.

Why does contribution timing change the answer?

A beginning-of-period contribution is present for one extra growth period. With the example inputs, beginning-of-year deposits produce $3,188.01 instead of $3,108.93—a difference of $79.08—with no change to the $2,000 contributed.

Should I enter an interest rate or an APY?

Use the rate definition requested by the calculator. A nominal annual rate and an APY are not interchangeable: APY already reflects compounding. Keep the rate period, contribution period, and number of periods on one consistent basis.

What happens when the rate is 0%?

There is no modeled growth, so future value is simply the opening amount plus all net contributions. The zero-rate form is FV = PV + PMT × N.

Can this page solve for PV, PMT, rate, or periods?

Yes. The integrated five-key solver lets you choose FV, PV, PMT, I/Y, or N as the missing value. Enter only the other four values and keep I/Y, N, and PMT on the same period basis.

Why does the five-key solver use negative cash flows?

Signs identify direction from one viewpoint. Money paid out is negative and money received is positive, so PV, PMT, and FV can balance in one equation. The result table preserves those signs and reports the substitution residual.

Why can the schedule differ by a cent from a hand calculation?

A reliable calculator keeps full precision internally and rounds only displayed currency. Adding rounded interest rows can create a small cents difference; a larger mismatch usually points to rate, frequency, or timing inputs that do not match.

Can a future value calculator predict investment performance?

No. It shows conditional arithmetic under a fixed rate. It does not assign probabilities, model market volatility or sequence risk, choose an investment, or guarantee that the ending balance will occur.

Continue the calculation

Important limitations

These educational calculations assume a constant rate and equal periodic cash flows. They do not include fees, taxes, inflation, market volatility, changing rates, missed or irregular cash flows, day-count rules, or product terms. The periodic-rate solve is limited to one unique nonnegative root from 0% through 100% per period; no result is a quote, APR, IRR, valuation, recommendation, or guarantee.

Review the stated scope, calculation method, assumptions, supported inputs, and effective dates, and obtain qualified advice before using a high-stakes result.

This formula passed its registered engineering tests and is published under an explicit site-owner policy authorization. No independent expert, QA, editorial, legal, or third-party review is claimed. Verify consequential results with a qualified professional.

This subject may affect health, finance, tax, legal, or other consequential decisions. It has not received an independent domain-expert review; consult a qualified professional before relying on it.

Future value, without the fog

See what you put in, what compounds, and what you may end with

Ending amount: FV after the final period
Cash added: PV + every PMT
Modeled growth: FV − total cash added

Start with the question

What does future value tell you?

It answers: “If these dollars stay invested, the same contribution arrives each period, and the entered rate repeats, what balance follows after N periods?”

Reproduce the review example

$1,000 now, then $100 at each year-end

Use 10 annual periods at 6%, with each $100 contribution made at the end of its year. This is an ordinary-annuity timing convention.

Example inputsAll periods are annual

Number of periods: 10 years
Starting amount (PV): $1,000
Rate per period: 6%
Periodic contribution: $100 / year
Contribution timing: End of year

Projected future value$3,108.93after 10 years

Starting principal: $1,000.00
10 contributions: $1,000.00
Modeled growth: $1,108.93

Starting principal
Contributions
Growth

Screenshot-style check: $1,000 + ($100 × 10) = $2,000 contributed; $3,108.93 − $2,000 = $1,108.93 of modeled growth.

Opening amount at year 10$1,000 × 1.06¹⁰ = $1,790.85

Future value of year-end deposits$100 × ((1.06¹⁰ − 1) ÷ 0.06) = $1,318.08

Combined future value$1,790.85 + $1,318.08 = $3,108.93

Keep every period on one basis

Formula and variables

Level contributions with matching rate periodsFV = PV(1 + i)^N + PMT × (((1 + i)^N − 1) ÷ i) × (1 + i)^type

Use type = 0 for end-of-period payments and type = 1 for beginning-of-period payments. If i = 0, use FV = PV + PMT × N.

Variables used by the worked example
Symbol	Meaning	Plain-language definition	Example
`FV`	Future value	The balance at the end of the last period.	$3,108.93
`PV`	Present value	The amount already invested at time zero.	$1,000
`PMT`	Periodic contribution	The same amount added once per period.	$100
`i`	Rate per period	The decimal return applied in each matching period.	0.06
`N`	Number of periods	How many equal growth periods the scenario covers.	10
`type`	Contribution timing	0 for end of period; 1 for beginning of period.	0

Reverse the same periodic relationship

When to use the five-key TVM solver

Choose one missing key and enter the other four
Solve	Enter	Result meaning
`FV`	PV, PMT, I/Y, N	Ending value after the final period
`PV`	FV, PMT, I/Y, N	Equivalent signed value at time zero
`PMT`	PV, FV, I/Y, N	Equal signed payment each period
`I/Y`	PV, FV, PMT, N	One bounded nonnegative rate per period
`N`	PV, FV, PMT, I/Y	Number of matching periods

Cash-flow directionmoney paid out = negative · money received = positive

Period alignmentI/Y is per period · N counts those periods · PMT repeats each period

Substitution checkPV(1+i)ᴺ + PMT factor + FV ≈ 0

One switch, one extra growth period

Beginning vs. end of period

The opening $1,000 is present for all 10 years in both cases. Only the recurring $100 deposits move.

End of period

Interest first, then add $100

The first deposit grows for nine years; the tenth arrives at the result date and earns no interest in this model.

$3,108.93ordinary annuity · type 0

Beginning of period

Add $100, then apply interest

Every contribution receives one more growth period, so the PMT portion is multiplied by 1.06.

$3,188.01annuity due · type 1

Audit the result, not just the headline

How to read the chart and schedule

Read a stacked growth chart

Total height is the ending balance at that point.
Principal and contributions are dollars you supplied.
Growth is the modeled return earned so far.

Read the detail schedule

Year	Start	Interest	Deposit	End
1	$1,000.00	$60.00	$100.00	$1,160.00
2	$1,160.00	$69.60	$100.00	$1,329.60
3	$1,329.60	$79.78	$100.00	$1,509.38
…	…	…	…	…
9	$2,583.59	$155.02	$100.00	$2,838.61
10	$2,838.61	$170.32	$100.00	$3,108.93

For an end-of-year contribution, end = start + interest + deposit. The next row should begin with the prior row's ending balance.

What the number leaves out

Limits to keep beside the result

The rate is constant

Actual investment returns move up and down, and deposit rates can change. A smooth line is a scenario, not a forecast or promise.

Cash flows are regular

The formula assumes the same contribution arrives at the selected point in every period. Irregular deposits need dated cash-flow modeling.

Fees, tax, and inflation are outside the total

Unless separately modeled, the result is nominal and before fees and taxes. It does not show future purchasing power.

Account rules can differ

Day-count methods, crediting dates, minimum balances, contribution limits, penalties, and withdrawals may change a real account result.

Quick answers

Future value calculator FAQ

What is future value?

Why does contribution timing change the answer?

Should I enter an interest rate or an APY?

What happens when the rate is 0%?

There is no modeled growth, so future value is simply the opening amount plus all net contributions. The zero-rate form is FV = PV + PMT × N.

Can this page solve for PV, PMT, rate, or periods?

Yes. The integrated five-key solver lets you choose FV, PV, PMT, I/Y, or N as the missing value. Enter only the other four values and keep I/Y, N, and PMT on the same period basis.

Why does the five-key solver use negative cash flows?

Why can the schedule differ by a cent from a hand calculation?

Can a future value calculator predict investment performance?

Continue the calculation

Build the projection

Balance vs. money deposited

How the balance changes

What do you want to calculate?

Enter the four known values

Your calculated value

PV, PMT, and FV magnitudes

Five-key value table

What does future value tell you?

$1,000 now, then $100 at each year-end

Formula and variables

When to use the five-key TVM solver

Beginning vs. end of period

Interest first, then add $100

Add $100, then apply interest

How to read the chart and schedule

Read a stacked growth chart

Read the detail schedule

Limits to keep beside the result

The rate is constant

Cash flows are regular

Fees, tax, and inflation are outside the total

Account rules can differ

Future value calculator FAQ

Related internal tools

Important limitations

Build the projection

Balance vs. money deposited

How the balance changes

What do you want to calculate?

Enter the four known values

Your calculated value

PV, PMT, and FV magnitudes

Five-key value table

What does future value tell you?

$1,000 now, then $100 at each year-end

Formula and variables

When to use the five-key TVM solver

Beginning vs. end of period

Interest first, then add $100

Add $100, then apply interest

How to read the chart and schedule

Read a stacked growth chart

Read the detail schedule

Limits to keep beside the result

The rate is constant

Cash flows are regular

Fees, tax, and inflation are outside the total

Account rules can differ

Future value calculator FAQ

Related internal tools