# NPER function

Returns the number of periods for an investment based on periodic, constant payments and a constant interest rate.

## Syntax

NPER(rate,pmt,pv,fv,type)

Argument

Description

Remarks

rate

The interest rate per period. For example, if you obtain an automobile loan at a 10 percent annual interest rate and make monthly payments, your interest rate per month is 10 percent divided by 12, or 0.83 percent. You would enter 10%/12, or 0.83%, or 0.0083, into the formula as the rate.

• None.

pmt

The payment made each period. It cannot change over the life of the annuity. Typically, pmt contains principal and interest but no other fees or taxes. For example, the monthly payments on a \$10,000, four-year car loan at 12 percent are \$263.33. You would enter -263.33 into the formula as the pmt.

• None.

pv

The present value, or the lump-sum amount that a series of future payments is worth now.

• None.

fv

The future value, or a cash balance that you want to have after the last payment is made. For example, if you want to save \$50,000 to pay for a special project in 18 years, then \$50,000 is the future value. You could then make a conservative guess at an interest rate and determine how much you must save each month.

• If fv is omitted, it is assumed to be 0 (the future value of a loan, for example, is 0).

type

The number 0 or 1, which indicates when payments are due.

• 0 (zero) = at the end of the period

1 = at the beginning of the period

## General remarks

An annuity is a series of constant cash payments made over a continuous period. For example, a car loan or a mortgage is an annuity. In annuity functions, the 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 example, a \$1,000 deposit to the bank would be represented by the argument -1000 if you are the depositor and by the argument 1000 if you are the bank.

## Example

To make the following example easier to understand, you can copy the data to a blank sheet and then enter the function underneath the data. Do not select the row or column headings (1, 2, 3... A, B, C...) when you copy the sample data to a blank sheet.

 Note  The interest rate is divided by 12 to obtain a monthly rate.
 1 2 3 4 5 6
 A B Data Description 12% Annual interest rate -100 Payment made each period -1000 Present value 10000 Future value 1 Payment is due at the beginning of the period Formula Description (Result) =NPER(A2/12,A3,A4,A5,A6) Periods for the investment with the terms in the table (60) =NPER(A2/12,A3,A4,A5) Periods for the investment with the terms in the table, except payments are made at the beginning of the period (60) =NPER(A2/12,A3,A4) Periods for the investment with the terms in the table, except with a future value of 0 (-9.5786)
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