# Future Value (FV) Calculator

## What is a Future Value (FV)?

Future Value (FV) is the value of money (either a lump sum or a stream of payments) at a time in the future.

If you were to invest $10,000 for 5 years at 4% compounded annually, what would the value of that investment be at the end of those 5 years? Future value tells us$12,166.53.

If you were to invest $500 a month for 10 years at 6% compounded monthly (0.5% each month), what would the value of that investment be at the end of those 10 years? Future value tells us$81,939.67.

## Formula

A financial formula calculates the future value of a sum of money.

There are two separate calculations involved – the base sum and the payment schedule.

Base sum formula:
$latex \text{Future Value} = \text{Present Value} \times (1 + \text{Rate of Return})^\text{Number of Periods}$

Payment formula – payments at the end of each period (annuity):
$latex \text{Future Value} = \text{Payment} \times (\frac{(1 + \text{Rate of Return})^\text{Number of Periods} – 1}{\text{Rate of Return}})$

Payment formula – payments at the beginning of each period (annuity due):
$latex \text{Future Value} = \text{Payment} \times (\frac{(1 + \text{Rate of Return})^\text{Number of Periods} – 1}{\text{Rate of Return}}) \times (1 + \text{Rate of Return})$

## Example

We have $1000 to save now and then$100 per year after for the next 10 years. The account we save to yields 2.2% interest compounded annually. After 10 years, how much will we have saved?
Step 1: Calculate the future value of the fixed portion
$latex \text{Future Value} = 1,000 \times (1 + 0.022)^{10}$
$latex \text{Future Value} = 1,000 \times (1.022)^{10}$
$latex \text{Future Value} = 1,000 \times 1.24311$
$latex \text{Future Value} = 1,243.11$
Step 2: Calculate the present value of the payment annuity
$latex \text{Future Value} = 100 \times (\frac{(1 + 0.022)^{10} – 1}{0.022})$
$latex \text{Future Value} = 100 \times (\frac{(1.022)^{10} – 1}{0.022})$
$latex \text{Future Value} = 100 \times (\frac{1.24311 – 1}{0.022})$
$latex \text{Future Value} = 100 \times (frac{0.24311}{0.022})$
$latex \text{Future Value} = 100 \times 11.0505$

$latex \text{Future Value} = 1,105.05 Step 3: Add the two together$latex \text{Future Value} = 1,243.11 + 1,105.05$Therefore, the future value of the account in 10 years would be$2,348.16.