Future Value Calculator

Number of Periods (N) Starting Amount (PV) Interest Rate per period (I/Y %) Periodic Deposit (PMT) PMT Timing

Future Value Calculator

The Future Value (FV) Calculator tells you what an investment or series of payments will be worth at a future date after earning compound returns. Use it to answer practical questions such as: “If I put $1,000 in the bank today at 6% annual interest, how much will I have in 10 years?” or “If I save $100 every month, how much will I accumulate?” The tool handles single lump sums, periodic deposits (annuities), growing payments, and continuous compounding, and it lets you choose compounding frequency and payment timing.

Understanding future value is essential for planning goals (retirement, college, large purchases), comparing investment options, and setting realistic savings targets. Want the reverse calculation? Try our Present Value Calculator to find what a future amount is worth in today’s dollars.

What Is Future Value?

Future Value (FV) is the amount an investment will grow to at a specified future date, given an interest rate and compounding rules. It converts today’s money into tomorrow’s money by applying growth (interest) over time. Where present value asks, “What is this future sum worth today?” FV asks, “If I invest today (or make regular deposits), how much will I have later?”

Key points in plain language:

Single lump sum vs. series of deposits: FV can describe the accumulation of a one-time deposit (e.g., $1,000 today) or a stream of regular payments (e.g., $100 monthly).
Compounding matters: Interest that is earned on interest (compounding) accelerates growth. The more frequent the compounding (monthly, daily, continuous), the higher the FV for the same nominal annual rate.
Nominal vs. real returns: FV computed with a nominal rate gives future money; if you want future purchasing power, compute with a real rate (nominal adjusted for inflation).
Why it matters: FV is the backbone of goal-setting: how much to save each period, how large the current capital will grow, and whether an investment meets your future target.

Graphically, FV is an upward-sloping curve: over time, the invested amount grows faster as compounding has more periods to act. When payments are periodic, the FV profile grows more rapidly because each deposit starts earning interest from its own deposit date onward.

Future Value Formula Explained (lump sum, annuity, growing annuity, continuous compounding)

A. Future Value of a Lump Sum

If you invest a single amount today (PV) and it compounds at a rate rrr for nnn periods, the future value is:

FV=PV×(1+r)n\boxed{FV = PV \times (1+r)^n}FV=PV×(1+r)n

PV = present amount invested today
r = rate per period (decimal; 6% → 0.06)
n = number of periods

Intuition: (1+r)n(1+r)^n(1+r)n is the accumulation factor; it multiplies your principal by the compounded growth over nnn periods.

B. Future Value of an Ordinary Annuity (payments at period end)

For equal payments (PMT) made at the end of each period:

FV=PMT×(1+r)n−1r\boxed{FV = PMT \times \frac{(1+r)^n – 1}{r}}FV=PMT×r(1+r)n−1

This formula gives the accumulated value at the end of period nnn of all payments. Each payment is compounded for the number of periods remaining after it’s deposited.

If you also have a starting PV:

FV=PV×(1+r)n+PMT×(1+r)n−1rFV = PV \times (1+r)^n + PMT \times \frac{(1+r)^n – 1}{r}FV=PV×(1+r)n+PMT×r(1+r)n−1

(First term grows the initial principal; second term accumulates the series of payments.)

C. Future Value of an Annuity Due (payments at period beginning)

When payments occur at the beginning of each period (annuity due), each payment compounds one extra period:

FVdue=FVordinary×(1+r)\boxed{FV_{\text{due}} = FV_{\text{ordinary}} \times (1+r)}FVdue=FVordinary×(1+r)

So compute the ordinary annuity FV and then multiply by (1+r)(1+r)(1+r).

D. Future Value of a Growing Annuity (payments increase by g each period)

If payments grow at rate ggg each period (first payment = PMT, next = PMT(1+g), …), and r≠gr \ne gr=g, the FV at the end of nnn periods is:

FV=PMT×(1+r)n−(1+g)nr−g\boxed{FV = PMT \times \frac{(1+r)^n – (1+g)^n}{r – g}}FV=PMT×r−g(1+r)n−(1+g)n

Notes:

Use this when payments rise by a steady percentage (cost-of-living escalator, planned contribution increases).
If r=gr = gr=g, the formula simplifies to FV=PMT×n×(1+r)n−1FV = PMT \times n \times (1+r)^{n-1}FV=PMT×n×(1+r)n−1.

E. Continuous Compounding

Under continuous compounding, the accumulation factor is e^ {rn}. For a lump sum:

FV=PV×ern\boxed{FV = PV \times e^{r n}}FV=PV×ern

Continuous compounding assumes interest is applied an infinite number of times per period, used in some theoretical finance settings and for high-precision work.

How to Use PrimeCalculator’s FV Calculator

PrimeCalculator’s Future Value Calculator is designed for clarity and flexibility. Two main workflows are supported: single lump sum and series of periodic deposits. Follow the steps below depending on your scenario.

A. Lump-sum accumulation

Enter Present Value (PV): the amount you’ll invest today.
Set the interest/return rate (r): enter as an annual % (e.g., 6).
Choose the compounding frequency: annual, semiannual, quarterly, monthly, daily, or continuous. The calculator converts rates to the chosen per-period rate automatically.
Enter the number of periods (n): if frequency is monthly and you want 10 years, enter n = 120.
Click Calculate: to see the Future Value. The calculator also shows the accumulation factor (1+rperiod)n(1+r_{period})^{n}(1+rperiod)n or erne^{rn} e for continuous compounding.

B. Periodic deposits (annuities)

Enter PMT (payment per period) and whether PMT occurs at the beginning or end of each period.
Enter PV (optional): if you’re starting with a lump balance as well.
Set the rate and frequency consistent with PMT timing (monthly payments → monthly rate).
Enter the number of periods and click calculate: Outputs include: FV, total principal contributed (PV + sum of PMTs), total interest earned, and a period-by-period schedule that shows how principal and interest accumulate over time.

Advanced options

Growing contributions: specify an annual or per-period growth rate for PMT to model raises or escalating contributions.
Inflation adjustment: compute real FV by using a real rate (nominal minus inflation via the Fisher relation) if you prefer purchasing-power projections.
Export & schedule: download the period schedule (CSV/print) for reporting or planning.

Worked Examples

All numeric steps were computed precisely, presented here, and rounded to cents for clarity.

Example 1: Lump sum accumulation (basic)

Problem: If you invest $1,000 today at 6% annual interest, how much will you have in 10 years with annual compounding?

Formula: FV=PV(1+r)nFV = PV (1+r)^nFV=PV(1+r)n

Plug in:

PV=1,000PV = 1{,}000PV=1,000
r=0.06r = 0.06r=0.06
n=10n = 10n=10

Step-by-step:

Compute accumulation factor: (1+0.06)10=1.0610≈1.7908476965(1+0.06)^{10} = 1.06^{10} \approx 1.7908476965(1+0.06)10=1.0610≈1.7908476965.
FV=1,000×1.7908476965≈$1,790.85.FV = 1{,}000 \times 1.7908476965 \approx \$1{,}790.85.FV=1,000×1.7908476965≈$1,790.85.

Interpretation: Your $1,000 will grow to ≈ $1,790.85 in 10 years at 6% annually

Example 2: Future value with monthly deposits (ordinary annuity)

Problem: Start with $1,000 and deposit $100 at the end of every month for 10 years. Annual nominal rate = 6%, compounded monthly. What is the FV?

Parameters:

PV=$1,000PV = \$1{,}000PV=$1,000
PMT=$100PMT = \$100PMT=$100 (monthly, end of period)
annual rate = 6% → monthly rate r=0.06/12=0.005r = 0.06/12 = 0.005r=0.06/12=0.005
n=10×12=120n = 10 \times 12 = 120n=10×12=120

Formula:

FV=PV(1+r)n+PMT⋅(1+r)n−1rFV = PV(1+r)^n + PMT\cdot\frac{(1+r)^n – 1}{r}FV=PV(1+r)n+PMT⋅r(1+r)n−1

Step-by-step (rounded intermediate values shown):

Compute (1+r)n=(1.005)120≈1.788024(1+r)^n = (1.005)^{120} \approx 1.788024(1+r)n=(1.005)120≈1.788024.
PV growth: 1,000×1.788024≈$1,788.021{,}000\times1.788024\approx \$1{,}788.021,000×1.788024≈$1,788.02.
Annuity accumulation factor: 1.788024−10.005=0.7880240.005≈157.6048\dfrac{1.788024 – 1}{0.005} = \dfrac{0.788024}{0.005} \approx 157.60480.0051.788024−1=0.0050.788024≈157.6048.
PMT contribution: 100×157.6048≈$15,760.48100 \times 157.6048 \approx \$15{,}760.48100×157.6048≈$15,760.48.
Total FV ≈ 1,788.02+15,760.48=$17,548.50.1{,}788.02 + 15{,}760.48 = \$17{,}548.50.1,788.02+15,760.48=$17,548.50.

Interpretation: After 10 years of monthly $100 deposits plus the starting $1,000, you’d accumulate ≈ $17,548.50 at a 6% nominal annual rate compounded monthly. (Note: if you see slightly different rounding in other calculators, differences come from rounding intermediate digits.)

Example 3: Annuity due (payments at beginning)

Problem: Same as Example 2, but deposits are made at the beginning of each month (annuity due).

Adjustment: Multiply the ordinary-annuity PMT term by (1+r)(1+r)(1+r) (i.e., shift each payment one period earlier).

Using prior result:

Ordinary PMT contribution ≈ $15,760.48
Multiply by (1+r)=1.005(1+r) = 1.005(1+r)=1.005: 15,760.48×1.005≈$15,838.28.15{,}760.48 \times 1.005 \approx \$15{,}838.28.15,760.48×1.005≈$15,838.28.
PV growth term unchanged ≈ $1,788.02.
Total FV ≈ 1,788.02+15,838.28=$17,626.30.1{,}788.02 + 15{,}838.28 = \$17{,}626.30.1,788.02+15,838.28=$17,626.30.

Interpretation: Because each deposit is invested one month earlier, you gain extra interest; the FV increases from ≈ $17,548.50 (end-of-period) to ≈ $17,626.30 (beginning-of-period).

Example 4: Growing annuity (payments that increase)

Problem: You plan to deposit $100 at the end of each year for 10 years, but you will increase each deposit by 2% annually (so payments are $100, $102, $104.04, …). The annual return is 6%. What’s the FV at year 10?

Formula (when r≠gr \ne gr=g):

FV=PMT×(1+r)n−(1+g)nr−gFV = PMT \times \frac{(1+r)^n – (1+g)^n}{r – g}FV=PMT×r−g(1+r)n−(1+g)n

PMT=100PMT = 100PMT=100, r=0.06r = 0.06r=0.06, g=0.02g = 0.02g=0.02, n=10n=10n=10.

Step-by-step:

(1+r)10=1.0610≈1.7908476965.(1+r)^{10} = 1.06^{10} \approx 1.7908476965.(1+r)10=1.0610≈1.7908476965.
(1+g)10=1.0210≈1.2189944190.(1+g)^{10} = 1.02^{10} \approx 1.2189944190.(1+g)10=1.0210≈1.2189944190.
Numerator: 1.7908476965−1.2189944190≈0.5718532775.1.7908476965 – 1.2189944190 \approx 0.5718532775.1.7908476965−1.2189944190≈0.5718532775.
Denominator: r−g=0.06−0.02=0.04.r – g = 0.06 – 0.02 = 0.04.r−g=0.06−0.02=0.04.
Ratio: 0.5718532775/0.04≈14.2963319370.5718532775 / 0.04 \approx 14.2963319370.5718532775/0.04≈14.296331937.
FV = 100×14.296331937≈$1,429.63.100 \times 14.296331937 \approx \$1{,}429.63.100×14.296331937≈$1,429.63.

Interpretation: A growing series of annual deposits, starting at $100 with a 2% growth rate, accumulates to ≈ approximately $1,429.63 in 10 years at a 6% annual return.

Example 5: Continuous compounding (theoretical)

Problem: Invest $1,000 today at a continuously compounded annual rate of 6% for 10 years. What is FV?

Formula: FV=PV×ernFV = PV \times e^{r n}FV=PV×ern

Step-by-step:

e0.06×10=e0.6≈1.8221188004.e^{0.06 \times 10} = e^{0.6} \approx 1.8221188004.e0.06×10=e0.6≈1.8221188004.
FV = 1,000×1.8221188004≈$1,822.12.1{,}000 \times 1.8221188004 \approx \$1{,}822.12.1,000×1.8221188004≈$1,822.12.

Interpretation: Continuous compounding yields a slightly larger FV ($1,822.12) than discrete annual compounding ($1,790.85) because interest is effectively applied continuously.