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Present Value (PV) Calculator

Present Value Calculator


What is a Present Value (PV)?

Present value (PV) 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 future 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 present value (or payment) means an outflow as opposed to a directly negative number.

How is the Present Value calculated?

Present 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{Present Value} = frac{text{Future Value}}{(1 + text{Rate of Return})^text{Periods}}
For a payment annuity that occurs at the end of each period, the formula is:
text{Present Value} = text{Payment} times (frac{1 - (1 + text{Rate of Return})^(-text{Periods)}}{text{Rate of Return}})
For a payment annuity that occurs at the beginning of each period, the formula is:
text{Present 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 are looking to save $2,000 over 12 years in an account that earns 2.2% interest per year. At the end of each year, we will pay $100 into the account. How much would we have to put into the account at the start of the saving period to reach the $2,000 goal?
Step 1: Calculate the present value of the fixed portion
text{Present Value} = frac{2000}{(1 + 0.022)^12}
text{Present Value} = frac{2000}{(1.022)^12}
text{Present Value} = frac{2000}{1.29840670}
text{Present Value} = 1540.35
Step 2: Calculate the present value of the payment annuity
text{Present Value} = -100 times (frac{1 - (1 + 0.022)^-12}{0.022})
text{Present Value} = -100 times (frac{1 - (1.022)^-12}{0.022})
text{Present Value} = -100 times (frac{1 - 0.77017470}{0.022})
text{Present Value} = -100 times (frac{0.2298253}{0.022})
text{Present Value} = -100 times 10.44660455
text{Present Value} = -100 times 10.44660455
text{Present Value} = -1044.66
Step 3: Add the two together
text{Present Value} = 1540.35 + (-1044.66)
text{Present Value} = 495.69
The present value of the account would be 495.69. The result would be converted to negative (-495.69) as this would be the amount that would need to be paid into (cash flow out) the account to reach the balance of 495.69.

What is Future Value?

Future Value (FV) is the total value at the end 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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