# Future Value (FV) Calculator

### What is a Future Value (FV)?

Future Value (FV) is a financial calculation used when determining the time value of money to determine the “present day value” of a series of financial inputs.
It takes into consideration a value at a time in the present as well as the interest rate and payments occurring each compounding period.
As this calculator is structured to parallel the results of a financial calculator, inputs and outputs will be similar – for example, a negative means an outflow as opposed to a directly negative number.

### How is the Future Value calculated?

Future value is calculated through a financial formula used to determine the time value of money.
There are two separate calculations involved: The base sum as well as the payment schedule.
For the base sum, the formula is:
$text{Future Value} = text{Present Value} times (1 + text{Rate of Return})^text{Periods}$
For a payment annuity that occurs at the end of each period, the formula is:
$text{Future Value} = text{Payment} times (frac{(1 + text{Rate of Return})^text{Periods} - 1}{text{Rate of Return}})$
For a payment annuity that occurs at the beginning of each period, the formula is:
$text{Future Value} = text{Payment} times (frac{(1 + text{Rate of Return})^text{Periods} - 1}{text{Rate of Return}}) times (1 + text{Rate of Return})$

### Example

We have \$1000 to save now and then \$100 per year after for the next 45 years. The account we save to yields 4.3% interest compounded annually. After 45 years, how much will we have saved?
Step 1: Calculate the future value of the fixed portion
$text{Future Value} = -1000 times (1 + 0.043)^45$
$text{Future Value} = -1000 times (1.043)^45$
$text{Future Value} = -1000 times 6.64957485$
$text{Future Value} = -6649.57$
Step 2: Calculate the present value of the payment annuity
$text{Future Value} = -100 times (frac{(1 + 0.043)^45 - 1}{0.043})$
$text{Future Value} = -100 times (frac{(1.043)^45 - 1}{0.043})$
$text{Future Value} = -100 times (frac{6.64957485 - 1}{0.043})$
$text{Future Value} = -100 times (frac{5.64957485}{0.043})$
$text{Future Value} = -13138.55$
Step 3: Add the two together
$text{Future Value} = -6649.57 + (-13138.55)$
$text{Present Value} = -19788.12$
The future value of the account would be 19788.12. The result would be converted from negative (-19788.12) as this would be the amount that would need to be paid out of (cash flow in) the account to reach the balance of 19788.12.

### What is Present Value?

Present Value (PV) is the total value at the beginning of the time period.

### What are periods?

Periods are the number of times that compounding (and payments) take place.

### What is the rate?

The rate is the amount of interest earned per compounding period.

### What is Payment (PMT)?

A payment is an amount either deposited or withdrawn at each compounding period. A negative number designates an amount that is deposited, while a positive one withdrawn. For example, if \$100 is deposited each compounding period, it would be entered as '-100', while if \$75 was payed out each compounding period, it would be entered as '75'.

### What is Payments at start or end of period?

A payment at the beginning of a period would mean that the payment (or deposit) occurs at the beginning of each period. A payment at the end of a period would mean that the payment (or deposit) occurs at the end of each period.