investment calculator

Future Value Calculator

The Future Value Calculator projects one starting amount plus one level periodic deposit stream forward. It uses the entered period count, treats I/Y as the rate per period, applies beginning or end PMT timing, and reports future value, present-value equivalent, starting amount, total periodic deposits, total interest, first-period interest, and a timing note.

Result

Result summary: $1,000.00 plus $100.00 per period grows to about $3,108.93.
Future value: $3,108.93
Present value equivalent: $1,736.01
Starting amount: $1,000.00
Total periodic deposits: $1,000.00
Total interest: $1,108.93
First period interest: $60.00
What this means: End-period deposits are added after each period's interest.

Scenario nameNotes

Save this result, then use saved scenarios to switch between assumptions.

How the Future Value Calculator works

Use this calculator when the rate already matches the period count and you want a transparent accumulation estimate for a starting balance plus equal deposits. Use Present Value when discounting future money back to today, Finance for five-key TVM solves, Compound Interest for a no-deposit annual principal projection, Savings for monthly deposit-account style estimates, and official Investor.gov, SEC, FINRA, IRS, FCA, MoneyHelper, product, account, lender, accounting-standard, legal, or local regulator sources before making investment-product, annuity, retirement-income, tax, lending, accounting, inflation-adjusted, product-specific, legal, or jurisdiction-specific claims.

The app reads I/Y as the rate per period and converts it with r = interestRate / 100. It calculates G = (1 + r)^N, then sets the timing factor to 1 for end-of-period PMT or 1 + r for beginning-of-period PMT. The deposit factor is N when r is 0, otherwise ((G - 1) / r) * timingFactor. Future value equals startingAmount * G + periodicDeposit * depositFactor. Present-value equivalent is FV / G, except the implementation returns 0 when G is 0. Total periodic deposits equal PMT * N, total interest equals FV - startingAmount - total periodic deposits, and first-period interest uses startingAmount for end deposits or startingAmount + PMT for beginning deposits.

Future Value Calculator formula

This formula page covers the app's Future Value Calculator: one starting amount plus one level periodic-deposit stream projected forward with a constant rate per period. It reports future value, present-value equivalent, starting amount, total periodic deposits, total interest, first-period interest, and a timing note for beginning- or end-of-period deposits. It does not model irregular cash flows, variable rates, fees, taxes, inflation, investment products, account disclosures, lender disclosures, accounting measurements, annuity contracts, or personalised advice.

r = IY / 100; G = (1 + r)^N; d = beginning ? 1 + r : 1; DF = r === 0 ? N : ((G - 1) / r) * d; FV = PV * G + PMT * DF; PVE = G === 0 ? 0 : FV / G; TD = PMT * N; TI = FV - PV - TD; FPI = (beginning ? PV + PMT : PV) * r

The calculator compounds the starting amount forward, adds the compounded value of each equal periodic deposit, adjusts the deposit stream when payments are made at the beginning of each period, and then derives explanatory totals from the same projected balance.

Symbol	Meaning	How this page uses it
PV	Starting amount	The starting amount entered in the calculator. It is compounded from time 0 for the full period count.
FV	Future value	The projected ending balance from the starting amount plus periodic deposits under the entered rate and period assumptions.
N	Number of periods	The period count entered by the user. The app does not infer whether periods mean years, months, quarters, or another schedule.
IY	Interest rate percent	The Interest rate field. The formula treats it as a rate per period, not an APR, APY, annual-to-monthly conversion, or product quote.
r	Periodic rate	I/Y divided by 100 before compounding.
PMT	Periodic deposit	The equal deposit amount added every period. The calculator does not support changing, skipped, or irregular deposits.
d	Payment timing factor	1 for end-of-period deposits or 1 + r for beginning-of-period deposits.
DF	Deposit future-value factor	The future-value factor for the level deposit stream. It falls back to N when the periodic rate is 0.
PVE	Present-value equivalent	The projected future value discounted by the same growth factor. It is an explanatory app output, not a market valuation.
TD	Total periodic deposits	Periodic deposit times number of periods.
TI	Total interest	Future value minus starting amount minus total periodic deposits. It is a mechanical estimate, not a product yield, tax result, APR, or finance-charge disclosure.
FPI	First-period interest	Interest for the first period on the starting balance alone for end deposits, or on the starting balance plus the first deposit for beginning deposits.

Step by step

Read periods, starting amount, I/Y, periodic deposit, and payment timing from the calculator inputs.
Convert I/Y to a periodic decimal rate with r = IY / 100. This page treats I/Y as already matching the period count.
Calculate the growth factor G = (1 + r)^N for the starting amount.
Set the timing factor d to 1 for end-of-period deposits or 1 + r for beginning-of-period deposits.
When r is 0, use N as the deposit future-value factor because no deposit earns growth.
When r is not 0, calculate DF = ((G - 1) / r) * d for the equal deposit stream.
Calculate the future value as the starting amount times growth factor plus the periodic deposit times deposit factor: FV = PV * G + PMT * DF.
Calculate the present-value equivalent as PVE = FV / G, except the implementation returns 0 when G is 0 to avoid division by 0.
Calculate total periodic deposits as TD = PMT * N and total interest as TI = FV - PV - TD.
Calculate first-period interest on PV for end deposits, or PV + PMT for beginning deposits.
Round displayed currency outputs to two decimals after full-precision math.
Use official or primary sources before turning this generic future-value math into investment-return, annuity, retirement-income, tax, accounting, lending, legal, deposit-account, inflation-adjusted, product-specific, or jurisdiction-specific guidance.

Worked example

Default examples: end deposits, beginning deposits, and zero rate

These examples use the current app fixtures. I/Y is read as a rate per period, and the period count is used directly.

End-of-period deposits: PV = $1,000, PMT = $100, N = 10, and I/Y = 6 percent per period.
The growth factor is 1.06^10, or about 1.790848. The end-of-period deposit factor is about 13.180795.
The app calculates FV = $1,000 * 1.790848 + $100 * 13.180795 = $3,108.93 after rounding.
The present-value equivalent is $1,736.01, total periodic deposits are $1,000.00, total interest is $1,108.93, and first-period interest is $60.00.
Beginning-of-period deposits use the same inputs, but d = 1.06, so each deposit has one extra period of growth.
The beginning-deposit future value is $3,188.01, the present-value equivalent is $1,780.17, total interest is $1,188.01, and first-period interest is $66.00.
Zero-rate example: PV = $500, PMT = $250, N = 4, I/Y = 0 percent, and beginning timing.
Because r is 0, the deposit factor falls back to 4, so future value and present-value equivalent both equal $1,500.00.
The zero-rate fixture has $1,000.00 of total periodic deposits, $0.00 of total interest, and $0.00 of first-period interest.
The examples show future-value mechanics, not an investment recommendation, annuity quote, account quote, loan disclosure, tax answer, accounting measurement, guarantee, or product valuation.

The Future Value Calculator is useful for transparent projection of one starting balance plus one level deposit stream. It should not be used as proof of a real product value, legal disclosure, tax result, inflation-adjusted result, or personalised decision.

Assumptions and what this calculator ignores

Geographic scope: works globally. The math is currency-agnostic, so enter amounts in your own currency; local taxes, fees, and product rules are not included.

I/Y is the rate per period. If a user has an annual rate and monthly periods, they must convert the rate before entering it here.
N is used directly as the period count. The calculator does not infer whether periods are years, months, quarters, or another schedule. Deposits are equal every period, and payment timing changes only the deposit stream.
Scoped independent comparator checks pass 4 of 4 scoped fixtures for end-period deposits, beginning-period deposits, a zero-rate case, and a larger end-period case. Microsoft FV documentation is supplemental implementation context for rate, period count, payment, present value, future value, and payment timing. Investor.gov, SEC, FINRA, IRS, FCA, MoneyHelper, product documents, account disclosures, lender disclosures, accounting standards, inflation or official statistics sources, and local regulators are needed before regulated investment, annuity, retirement, tax, accounting, lending, legal, product-specific, inflation-adjusted, or jurisdiction-specific claims. Results are educational estimates, not financial, investment, tax, legal, lending, retirement, accounting, insurance, regulated-product, or personalised advice.

What this formula does not include

I/Y is treated as the rate per period. If a user has an annual rate but monthly periods, they must convert the rate before using this calculator.
Periods are used directly. The calculator does not infer whether N means years, months, quarters, or another schedule.
Periodic deposits are level and repeat every period. The calculator does not handle irregular cash-flow dates, skipped deposits, growing deposits, fees, taxes, or inflation.
Beginning-period timing changes the periodic deposit stream only; the starting amount still compounds for the full period count.
First-period interest and the timing note are app-only explanatory outputs. Scoped independent comparator checks compare future value, present-value equivalent, total periodic deposits, and total interest, but does not expose those two app-only fields.
Very unusual negative rates near -100 percent can make growth factors unstable. Treat those inputs as scenario-review cases, not realistic product pricing.
Total interest is future value minus starting amount and total deposits. It is not a lender finance charge, APR disclosure, account statement, tax calculation, investment return guarantee, inflation-adjusted purchasing-power result, or accounting fair value.
Scoped independent comparator checks currently pass 4 of 4 scoped fixtures for end-period deposits, beginning-period deposits, a zero-rate edge case, and a larger end-period scenario.
Microsoft FV documentation is useful implementation context for rate, period count, payment, present value, future value, and payment timing. It does not make this page an Excel-compatible sign-convention clone.
Investor.gov, SEC, FINRA, IRS, FCA, MoneyHelper, product documents, deposit-account disclosures, lender disclosures, accounting standards, inflation or official statistics sources, and local regulators are needed before adding regulated investment, annuity, retirement, tax, accounting, lending, legal, product-specific, inflation-adjusted, or jurisdiction-specific claims.
The result is an educational estimate from the entered assumptions, not financial, investment, tax, legal, lending, retirement, accounting, insurance, regulated-product, or personalised advice.

Common mistakes to avoid

Entering an annual rate while using monthly periods. This calculator does not convert annual I/Y to a monthly rate.
Treating beginning deposits as if they changed the starting amount timing. Beginning PMT changes the recurring deposit stream; the starting amount still compounds for the full period count.
Reading total interest, present-value equivalent, or first-period interest as an APR disclosure, account statement, tax calculation, inflation-adjusted value, accounting fair value, investment return guarantee, annuity quote, product valuation, legal answer, or personal recommendation.

Key terms

Rate per period: The I/Y input after dividing by 100 for one period. The calculator uses this rate directly; it does not convert annual rates to monthly rates.
Deposit future-value factor: The factor that compounds each equal periodic deposit to the end of the term. Beginning deposits use one extra 1 + r timing factor compared with end deposits.
Present-value equivalent: The projected future value discounted back by the same growth factor. It is an explanatory app output, not a market price, product quote, or accounting valuation.

Frequently asked questions

How is future value computed from a starting amount plus deposits?

Two components are added: the starting amount grows by (1 + r)^n, and the level deposit stream accumulates through the annuity factor ((1 + r)^n − 1) ÷ r, adjusted if deposits land at the beginning of each period. The default example projects $1,000 plus $100 per period at 6 percent over 10 periods. Total interest and first-period interest are itemized so the growth path is checkable.

What is the present-value equivalent shown with the result?

It discounts the projected future value back to today at the same rate - the mirror-image calculation. It answers 'what single amount today equals this whole plan'. Comparing it against the sum you actually put in (starting amount plus all deposits) shows how much of the future value is timing and compounding rather than contributions, which is a more honest read than the headline number alone.

Are the periods here years or months?

Whatever you make them - the calculator applies the rate per period as entered and never assumes a calendar. Ten periods at 6 percent can mean 10 years at an annual 6 percent, or 10 months at a monthly 6 percent (which would be an extreme rate). Keep the rate and the period unit consistent, and convert annual rates before modeling monthly deposits.

Methodology, sources, and disclaimer

This calculator is an original projection model combining single-amount growth with the level-deposit annuity factor at a per-period rate, reporting a present-value equivalent and first-period interest trace, validated by deterministic fixtures and rounding policy tests. It is not copied from a single source.

Fixtures pin the annuity-factor accumulation, both payment timings, and the PV-equivalent round trip. The result remains an educational estimate, not a product projection or a guaranteed balance.

Formula version 2026.05.22-generic-future-value. The version marks the calculation logic and validation fixture set used for this estimate.

Microsoft FV function documentation can be used as supplemental implementation context when copy compares rate, nper, pmt, pv, future value, and beginning/end payment timing with spreadsheet FV notation.
Investor.gov compound-interest materials can support plain investing-education context when copy explains how money and repeated contributions can grow under constant-rate assumptions.
Investor.gov, SEC, FINRA, IRS, FCA, MoneyHelper, product documents, deposit-account disclosures, lender disclosures, accounting standards, inflation or official statistics sources, and relevant local regulators should be used before copy frames generic future-value math as real investment returns, annuity contracts, retirement income, tax treatment, deposit-account outcomes, inflation-adjusted purchasing power, regulated investment values, lender disclosures, accounting-standard valuation, legal claims, product-specific guidance, or jurisdiction-specific guidance.

Results are educational estimates, not advice. Read the full disclaimer.

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