# How to use the NPER function

The NPER function calculates the number of payment periods for a loan or an investment based on periodic constant payments and a fixed interest rate.

##### What is a payment period?

A payment period is the length of time between payments made on a loan or investment. For example, a loan with monthly payments the payment period would be one month. A loan with quarterly payments the payment period would be three months.

##### What is a loan?

A loan is an amount of money you borrow from an individual or entity. The lender is usually a corporation, financial institution, or government, however it can also be an individual. A lender is an entity or individual that makes funds available for a borrower that can be a person or a business. The borrower agrees to repay the loan amount plus interest over an agreed-upon period of time.

##### What is an investment?

An investment is an asset or business acquired with the goal of generating income or appreciation, the purpose is to grow the money over time.

##### What is periodic constant payments?

Periodic constant payments are payments that are made at regular intervals such as monthly, quarterly, or yearly and have the same amount each time.

##### What is fixed interest rate?

A fixed interest rate is an interest rate that remains the same throughout the term of a loan or an investment.

#### Table of Contents

## 1. NPER Function Syntax

NPER(*rate*, *pmt*, *pv*, [*fv*], [*type*])

## 2. NPER Function Arguments

rate |
Required. The interest rate per period. |

pmt |
Required. The payment per period; it must be constant. |

pv |
Required. Argument pv is an abbreviation for present value, in other words, the total value right now based onÂ future payments. |

[fv] |
Optional. The future value, or the value you want to achieve when the last payment is made. Default value is 0 (zero). |

[type] |
Optional.Â When payments are due. 0 (zero) - Default value. At the end of the period. 1 - At the beginning of the period. |

## 3. NPER Function Example

This example shown in the image above demonstrates the NPER function in cell C7. It calculates the number of periods needed to repay $1000 based on a constant payment of $100 and a fixed interest rate of 5%.

Formula in cell F3:

The table below the calculation in the image above shows interest, amortization, and the remaining loan amount after each periodic payment. Get the workbook to see how the calculations are made, link below.

Note, the specified interest is on a yearly payment period, this makes the function return how many years it takes to repay the loan. However, to make it return a monthly payment period divide 5% by 12 (there are 12 months in a year) and you get approx. 0.42% which is the interest rate per month.

The NPER function returns 10.23 months to repay the loan.

## 4. How is the NPER function calculated?

Use the following math formula to calculate the number of periods :

nper = log((pmt - rate * pv) / (pmt + rate * fv)) / log(1 + rate)

where:

- nper is the number of periods
- pmt is the payment made each period
- rate is the interest rate per period
- pv is the present value of the investment
- fv is the future value of the investment

For example, if you want to know how many months it will take to pay off a loan of $10,000 at 5% annual interest rate with monthly payments of $200, here is how to populate the formula above:

nper = log((200 - 0.05/12 * 10000) / (200 + 0.05/12 * 0)) / log(1 + 0.05/12)

becomes

log((200 - 0.00416666666666667 * 10000) / (200 + 0.00416666666666667 * 0)) / log(1 + 0.00416666666666667)

becomes

log((200 - 41.6666666666667) / (200 + 0)) / log(1.00416666666666667))

becomes

log(0.791666666666665) / log(1.00416666666666667))

becomes

-0.101457640758777/0.00180580086326235

and returns -56.1842907614321

The result is 56.18 months.

## 5. NPER function not working

The NPER function returns a #VALUE! error if an invalid argument is used, the example above shows a letter as an interest rate.

The #NAME! error is returned if the NPER function is misspelled, the image above shows this error.

The NPER function returns a #NUM! error if it can't calculate the number of payment periods, in other words no matter how many payment periods the loan grows larger month by month.

## 6. Fixed payments calculator and amortization schedule

The file below contains a fixed payment calculator, you need Excel 365 to use it. It calculates the amortization table dynamically meaning the data spills to cells below instantly when you change the interest rate, payment and loan value.

Formula in cell B24:

Formula in cell C24:

Formula in cell D24:

Formula in cell E24:

Formula in cell F24:

### Get Excel file

### Useful links

NPER function - Microsoft

Fixed payment calculator

Microsoft Excel Loan Calculator With Amortization Schedule

### Functions in 'Financial' category

The NPER function function is one of 29 functions in the 'Financial' category.

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