### Present Value Calculator

Your browser does not support iframes.

### 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:

For a payment annuity that occurs at the end of each period, the formula is:

For a payment annuity that occurs at the beginning of each period, the formula is:

### 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

Step 2: Calculate the present value of the payment annuity

Step 3: Add the two together

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A payment is an amount either deposited or withdrawn at each compounding period. A negative number designates an amount that is deposited, while a positive one withdrawn.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.### Sources and External Resources

- Wikipedia – Time Value of Money
- Wikipedia – Present Value
- Accounting Coach – Present Value of a Single Amount
- Math is Fun – Present Value