## Purpose

## Return value

## Arguments

*rate*- The interest rate per period.*nper*- The number of payment periods.*pmt*- The payment made each period.*fv*- [optional] Future value. If omitted, defaults to zero.*type*- [optional] Payment type, 0 = end of period, 1 = beginning of period. Default is 0.

## Syntax

## Usage notes

The PV function returns the value in today's dollars of a series of future payments, assuming periodic, constant payments and a constant interest rate. You can use the PV function to calculate the present value of a loan or investment when the interest rate and cash flows are constant. The PV function takes five separate arguments, three of which are required as explained below.

*rate* (required) - the interest rate per period. For example, if the annual interest rate is 6% and periods are one month, then the interest rate is =6%/12 = 0.5% (0.005). You can enter *rate* as 6%/12 as a reminder of how it is derived.

*nper* (required) - The total number of payment periods in the annuity. For example, a 5-year car loan with monthly payments has 60 periods. You can enter *nper* as 5*12 to note how the number was determined.

*pmt* (required) - The payment made each period. This number cannot change over the life of the annuity. In annuity functions, cash paid out is represented by a negative number. Note: If *pmt* is not provided, the optional *fv* argument must be supplied.

*fv* (optional) - The future value. This is the cash balance required after all payments have been made. When *fv* is omitted, it defaults to zero, and *pmt* must be supplied.

*type* (optional) - *type* is a boolean that controls when when payments are due. Supply 0 for payments due at the end of the period (regular annuities) and 1 for payments due at the end of the period (annuities due). *Type* defaults to 0 (end of period).

### Examples

The PV function can be used to calculate the present value of a loan, when the interest rate, payment, and number of periods are known. For example, the present value of a 5-year loan with an annual interest rate of 4.5% and monthly payments of $93.22 is approximately $5,000:

```
=PV(4.5%/12,5*12,-93.22) // returns 5000.26
```

In the worksheet shown above, the formula in C10 is:

```
=PV(C5/C8,C7,C6)
```

### Present value of annuity

To calculate the present value of an annuity that pays 10,000 per year for 25 years, with an annual interest rate of 7%:

```
=PV(7%,25,10000) // returns -116,535.832
```

To returns a positive present value, enter payment as a negative number:

```
=PV(7%,25,-10000) // returns 116,535.832
```

Also see: Present value of an annuity.

### Investment goal

To calculate the initial investment required to reach $15,000 in 10 years with an annual interest rate of 5%:

```
=PV(5%,10,0,15000) // returns -9,208.70
```

Enter future value as a negative number to get a positive result:

```
=PV(5%,10,0,-15000) // returns 9,208.70
```

### PV versus NPV

Both the PV function and the NPV function calculate present value, but there are differences in the way they operate:

- The PV function can only be used when cash flows are constant and don't change. The NPV function can be used to calculate the present value of
*uneven*cash flows spaced evenly in time. - The PV function has a
*type*argument to handle regular annuities and annuities due. The NPV function always assumes a regular annuity, where payments are due at the end of the period.

### Notes

- A stream of cash flows that includes the same amount of cash outflow (or inflow) each period is called an annuity. For example, a car loan or a mortgage is an annuity. When each period's interest rate is the same, an annuity can be valued using the PV function.
- In annuity functions, cash you pay out (such as a deposit to savings) is represented by a negative number; cash you receive, such as a dividend check, is represented by a positive number. For a $2,500 deposit to a bank,
*pmt*would be -2500 if you are the depositor, and 2500 if you are the bank.