What is the formula for future value of a lump sum?

The future value of a single lump sum with periodic compounding is FV = PV × (1 + r/m)^(m×t), where PV is present value, r is the annual interest rate, m is the number of compounding periods per year, and t is the number of years.

How do you calculate future value with monthly deposits?

For equal monthly deposits, the future value of an ordinary annuity is FV = Pmt × [((1 + i)^n − 1) / i], where Pmt is the monthly deposit, i is the periodic interest rate (annual rate divided by 12), and n is the total number of deposits.

What is the difference between nominal and effective annual rate?

The nominal annual rate is the stated rate before considering compounding. The effective annual rate (EAR) includes the impact of compounding and is calculated as EAR = (1 + r/m)^(m) − 1, where r is the nominal rate and m is the number of compounding periods per year.

Can this calculator handle growing contributions?

Yes. Use the "Growing annuity" mode to model contributions that increase by a fixed percentage each period, such as raising your savings by 3% per year. The calculator uses the growing annuity future value formula to compute the result.

Future Value Calculator

Q: What is future value?

Future value (FV) is the amount that an investment or cash flow will grow to at a specific date in the future, given an assumed interest rate and compounding frequency. It answers the question: "If I invest this money today, how much will it be worth later?"

Estimate how much your money will be worth in the future with lump sums, regular deposits, or growing contributions.

Initial amount (present value)

Regular contribution (each period)

Set to 0 if you only invest a lump sum.

Interest rate (nominal annual)

% per year

Time horizon

years

Compounding frequency

Contribution frequency

Contribution timing

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

Results

Future value

$0.00

Total contributions

$0.00

Total interest earned

$0.00

Show yearly breakdown

Year	Start balance	Contributions	Interest	End balance

How this future value calculator works

This tool lets you estimate how much your money will grow to in the future under different scenarios:

Lump sum – a single amount invested today.
Equal deposits (annuity) – the same contribution every period (e.g., monthly savings).
Growing deposits – contributions that increase by a fixed percentage each period.

1. Future value of a lump sum

Periodic compounding:

\[ FV = PV \times \left(1 + \frac{r}{m}\right)^{m \cdot t} \]

$FV$ = future value
$PV$ = present value (initial amount)
$r$ = nominal annual interest rate (decimal)
$m$ = compounding periods per year
$t$ = years

Continuous compounding:

\[ FV = PV \times e^{r \cdot t} \]

2. Future value of an annuity (equal deposits)

For regular contributions of the same amount each period, the future value of an ordinary annuity is:

Ordinary annuity (payments at end of period):

\[ FV_{\text{annuity}} = Pmt \times \frac{(1 + i)^n - 1}{i} \]

Annuity due (payments at beginning of period):

\[ FV_{\text{annuity due}} = Pmt \times \frac{(1 + i)^n - 1}{i} \times (1 + i) \]

$Pmt$ = contribution per period
$i$ = periodic interest rate (annual rate / payments per year)
$n$ = total number of payments

3. Future value of a growing annuity

For contributions that grow at a constant rate $g$ each period:

Growing annuity (payments at end of period):

\[ FV_{\text{growing}} = Pmt \times \frac{(1 + i)^n - (1 + g)^n}{i - g} \]

Growing annuity due (payments at beginning of period):

\[ FV_{\text{growing due}} = Pmt \times \frac{(1 + i)^n - (1 + g)^n}{i - g} \times (1 + i) \]

$g$ = growth rate of contributions per period (decimal)
Requires $i \neq g$. When $i \approx g$, the formula becomes numerically unstable; the calculator switches to a step-by-step approach.

4. Effective annual rate (EAR)

The calculator also reports the effective annual rate implied by your compounding choice:

Periodic compounding:

\[ EAR = \left(1 + \frac{r}{m}\right)^m - 1 \]

Continuous compounding:

\[ EAR = e^{r} - 1 \]

Practical tips for using the future value calculator

Match compounding and payment frequency when possible (e.g., monthly deposits with monthly compounding) for more realistic results.
Use annuity due if you contribute at the beginning of each period (e.g., paycheck contributions at the start of the month).
Use growing deposits to model increasing savings over time, such as raising your contributions by 2–3% annually.
Remember inflation: this calculator shows nominal future value. To estimate real purchasing power, subtract expected inflation from the interest rate.

Frequently asked questions

What is future value?

Future value is the value of a current amount of money at a specified date in the future, based on an assumed rate of return. It is a core concept in time value of money, investing, and retirement planning.

Is future value the same as compound interest?

Compound interest is the process of earning interest on both your original principal and previously earned interest. Future value is the result of that compounding process applied to a lump sum, a series of payments, or both.

What interest rate should I use?

Use a rate that reflects your expected long-term return after fees, and be conservative. For example, many long-term stock market projections use 5–7% per year in nominal terms, while high-yield savings accounts may be closer to 3–5%.

Can I get a negative future value?

With a negative interest rate or negative cash flows (e.g., withdrawals instead of deposits), the future value can be lower than your total contributions. This calculator assumes positive rates and contributions; for more complex cash-flow patterns, a full cash-flow or IRR calculator is more appropriate.