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Future Value (FV) Calculator

Future Value 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.

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