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Future Value Calculator (TVM)

Project the future value of a lump sum plus recurring contributions using the time value of money formula with six compounding frequencies and annuity-due or ordinary-annuity timing.

FINANCE

Future value (FV) tells you what a sum of money today will be worth at a future date once interest compounds on the principal and on any periodic contributions. It is the foundational calculation in time value of money (TVM) and underpins retirement projections, savings-goal math, and bond pricing.

The calculator combines two pieces: the lump-sum future value FV = PV × (1 + r/n)^(nt) and, if you contribute periodically, the annuity future value FV = PMT × (((1 + r/n)^(nt) − 1) / (r/n)), with an extra (1 + r/n) multiplier when contributions arrive at the beginning of each period (annuity-due) rather than the end (ordinary annuity). Continuous compounding collapses the lump term to FV = PV × e^(rt). Worked example: $10,000 present value plus $500/month deposited at the end of each month, earning 7% APR compounded monthly for 20 years. Periodic rate r/n = 0.07/12 = 0.005833, periods nt = 240. Lump portion = 10,000 × (1.005833)^240 ≈ $40,387. Annuity portion = 500 × ((1.005833^240 − 1) / 0.005833) ≈ $260,463. Future value ≈ $300,850 with total contributions of $130,000 and total interest of about $170,850 - more than half the ending balance comes from compounding rather than your deposits, which is why starting early matters so much.

Disclaimer: Returns shown are nominal and do not automatically adjust for inflation or taxes. For tax-advantaged accounts (Roth IRA, 401(k), HSA) the FV displayed is approximately what you will see at withdrawal. For taxable accounts, apply your marginal or capital-gains rate to the interest portion. To get a real (inflation-adjusted) future value, subtract your inflation assumption from the rate before computing.

Future Value Calculator (TVM)

Compute the future value of a present sum plus optional periodic contributions using the time value of money formula. Supports annual, semiannual, quarterly, monthly, daily, and continuous compounding.

Present Value ($)

Annual Interest Rate (%)

Number of Years

Compounding Frequency

Periodic Payment / PMT ($)Recurring contribution made each compounding period. Set to 0 for a single lump sum.

Payment Timing

End of period (ordinary annuity)Beginning of period (annuity-due)

Future Value

$300,851

Total Contributions$130,000

Total Interest Earned$170,851

Effective Annual Yield4.28%

Total accumulated value at the end of the horizon, including reinvested interest.

Year-by-Year Accumulation

Year	Start Balance	Contributions	Interest	End Balance
1	$10,000	$6,000	$919	$16,919
2	$16,919	$6,000	$1,419	$24,339
3	$24,339	$6,000	$1,956	$32,294
4	$32,294	$6,000	$2,531	$40,825
5	$40,825	$6,000	$3,148	$49,973
6	$49,973	$6,000	$3,809	$59,782
7	$59,782	$6,000	$4,518	$70,299
8	$70,299	$6,000	$5,278	$81,578
9	$81,578	$6,000	$6,094	$93,671
10	$93,671	$6,000	$6,968	$106,639
11	$106,639	$6,000	$7,905	$120,544
12	$120,544	$6,000	$8,910	$135,455
13	$135,455	$6,000	$9,988	$151,443
14	$151,443	$6,000	$11,144	$168,587
15	$168,587	$6,000	$12,383	$186,971
16	$186,971	$6,000	$13,712	$206,683
17	$206,683	$6,000	$15,137	$227,820
18	$227,820	$6,000	$16,665	$250,486
19	$250,486	$6,000	$18,304	$274,790
20	$274,790	$6,000	$20,061	$300,851

Understanding Time Value of Money

Time value of money says a dollar today is worth more than a dollar tomorrow because today's dollar can be invested and earn return. The future value formula FV = PV(1 + r/n)^(nt) compounds the present value PV at periodic rate r/n over nt periods. When you add recurring contributions PMT, the annuity portion FV = PMT × (((1+r/n)^(nt) − 1)/(r/n)) sums each deposit's individual growth. If contributions land at the beginning of each period (annuity-due), every deposit earns one extra period of interest, so the annuity term gets multiplied by (1 + r/n).

Compounding frequency matters but with diminishing returns. At 7% annual, a $10,000 lump sum over 20 years grows to $38,697 with annual compounding, $40,387 monthly, and $40,552 continuous - the gap from monthly to continuous is only ~40 basis points of total return. The continuous case FV = PV × e^(rt) is the mathematical ceiling; nothing compounds "faster." For typical rates 3-10%, jumping from annual to monthly compounding moves the needle a few percent, but going from daily to continuous is almost invisible.

Future value is the workhorse calculation behind retirement planning (will my 401(k) hit my target?), savings goals (how big is my down-payment fund in 5 years?), bond pricing (par value compounded by yield), and reverse-engineering net present value (discount future cash flows back to today). It's also the basis for the Rule of 72: years to double ≈ 72 / rate%, derived from solving 2 = (1+r)^t.

Returns shown are nominal and do not automatically adjust for inflation or taxes. For tax-advantaged accounts (Roth IRA, 401(k), HSA) the FV shown is roughly what you'll see at withdrawal. For taxable accounts, apply your marginal or capital gains rate to the interest portion. To get a real (inflation-adjusted) future value, subtract your inflation assumption from the rate before computing.

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Frequently Asked Questions

What is future value in finance?

Future value is the worth of a current sum of money at a specified date in the future, given an assumed rate of return. It answers 'if I invest X today (and optionally add PMT each period) at rate r, how much will I have after t years?' FV is the mirror image of present value, which discounts a future amount back to today.

How does compounding frequency change the result?

More frequent compounding means interest is credited and starts earning interest sooner, so FV rises with frequency - but with sharply diminishing returns. At 7% over 20 years on $10,000, annual compounding yields about $38,697, monthly yields about $40,387, and continuous yields about $40,552. Going from annual to monthly is a meaningful bump; going from daily to continuous is barely a rounding difference.

What is the difference between FV and PV?

Present value (PV) discounts a future cash flow back to today by dividing by (1 + r)^t. Future value (FV) projects a current amount forward by multiplying by (1 + r)^t. They are algebraic inverses: PV = FV / (1 + r)^t and FV = PV × (1 + r)^t. NPV (net present value) sums multiple discounted future cash flows minus the initial outlay.

What discount rate should I use?

Use the expected nominal return on a comparable investment. For broad US equity exposure, historical nominal returns run about 9-10% annually; for a 60/40 portfolio about 6-7%; for high-yield savings or short Treasuries about the current rate (4-5% in May 2026); for corporate bonds the yield to maturity. If you want a real (inflation-adjusted) answer, subtract expected inflation (about 2-3%) from your nominal rate.

Does future value account for inflation?

Not by default. The FV shown is in nominal dollars - the actual dollar figure you would see on a statement. To get real (inflation-adjusted) future value, plug in a real rate of return: nominal rate minus expected inflation. For example, 7% nominal minus 2.5% inflation gives a 4.5% real rate, which translates today's purchasing power into the future.

Future Value Calculator (TVM)

Future Value Calculator (TVM)

Year-by-Year Accumulation

Understanding Time Value of Money

Frequently Asked Questions

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