Future value calculator

What is a future value calculator?

A future value calculator tells you how much money you will have at some point in the future, given what you hold today and what you keep adding along the way. It rests on a simple idea from the time value of money: a sum available now is worth more than the same sum later, because money that sits in an interest-bearing account earns more money. The tool projects that growth forward so you can compare savings goals, retirement plans, or one-off investments on equal footing.

How does the calculator work?

You provide a present value (the amount you start with), an optional periodic payment you add every period, an annual interest rate, how often the interest compounds, and the number of years. The calculator converts the annual rate into a periodic rate, counts the total number of compounding periods, grows the starting sum, and grows each payment by the number of periods it stays invested. It then reports the future value together with your total contributions and the interest those contributions earned.

Formula

The future value of a present sum combined with a series of equal periodic payments is:

$FV = PV \cdot (1 + r)^{n} + PMT \cdot \frac{(1 + r)^{n} - 1}{r}$

Where:

• $FV$ is the future value.
• $PV$ is the present value (the starting amount).
• $PMT$ is the payment added each period.
• $r$ is the interest rate per period.
• $n$ is the total number of periods.

The periodic rate and the period count come from the annual figures:

$r = \frac{\text{annual rate}}{k}, \qquad n = k \cdot t$

where $k$ is the number of compounding periods per year and $t$ is the number of years.

Annuity due variant

If each payment lands at the beginning of the period rather than the end, every payment compounds for one extra period. The payment term is multiplied by $(1 + r)$:

$FV = PV \cdot (1 + r)^{n} + PMT \cdot \frac{(1 + r)^{n} - 1}{r} \cdot (1 + r)$

Zero interest rate

When the rate is zero the payment formula would divide by zero, so it collapses to a plain sum of the payments:

$FV = PV + PMT \cdot n$

Examples of use

1. A one-off deposit of $1,000 left to grow at 4% compounded annually for 3 years, with no extra payments:

   • Present value $PV$ = 1000
   • Rate per period $r$ = 0.04
   • Periods $n$ = 3

   Calculation: $FV = 1000 \cdot (1.04)^{3} \approx 1124.86$

2. A starting balance of $1,000 with $100 added at the end of every month, at 6% compounded monthly for 10 years (an ordinary annuity):

   • Present value $PV$ = 1000
   • Payment $PMT$ = 100
   • Rate per period $r$ = 0.005
   • Periods $n$ = 120

   Calculation: $FV = 1000 \cdot (1.005)^{120} + 100 \cdot \frac{(1.005)^{120} - 1}{0.005} \approx 18207.33$

   The total contributed is $13,000 and the interest earned is about $5,207.33.

3. The same plan with payments made at the beginning of each month (an annuity due): $FV = 1000 \cdot (1.005)^{120} + 100 \cdot \frac{(1.005)^{120} - 1}{0.005} \cdot (1.005) \approx 18289.27$

Practical notes

• Match the payment frequency to the compounding frequency for the cleanest projection; mixing them changes how many periods each payment compounds.
• The future value grows fastest when contributions start early, because each early payment compounds for more periods.
• A rate of zero is a useful sanity check: the future value should equal everything you put in, with no interest.

FAQs

What is the difference between present value and future value?

Present value is what an amount is worth today, while future value is what it will grow into after earning interest over a set period. The future value calculator moves a present value forward in time.

Does the payment timing really matter?

Yes. Payments made at the beginning of each period (an annuity due) each compound for one extra period, so they always produce a slightly larger future value than the same payments made at the end of the period.

What happens if I only enter payments and no starting amount?

The calculator simply treats the present value as zero and returns the future value of the payment series alone, which is the classic future value of an annuity.