## What does it do?

This loan repayment period calculator works out the number of periods needed to repay a loan (PV) if interest is compounded at a periodic interest rate i and payments (Pmt) are made at the end of each period.

## Formula

The calculator uses the present value of an annuity formula and rearranges this to solve for the number of periods (n).

n= (LN(Pmt) - LN(Pmt - PV x i)) / LN(1 + i)

## Instructions

The Excel loan repayment period calculator, available for download below, is used to compute the number of periods required to repay the loan by entering details relating to the amount of the loan, interest rate and the periodic payment. The calculator is used as follows:

### Step 1

Enter the amount of the loan (PV). This is the amount taken as a loan today, at the start of period 1.

### Step 2

Enter the interest rate (i). The interest rate should be for a period, so for example, if the payments are to be made monthly, then the rate should be the monthly rate. A nominal annual rate can be converted to a periodic rate by dividing by the number of periods in a year.

### Step 3

Enter the periodic payment (Pmt). The amount is the payment made at the end of each period. The amount must be more than the interest on the loan or the calculator will produce an error as it will not be possible to clear the loan.

### Step 4

The loan repayment calculator works out the number of periods required to repay the loan amount (PV) at a periodic interest rate (i) assuming periodic payments (Pmt).

## Loan Repayment Period Calculator Download

The loan repayment period calculator spreadsheet is available for download in Excel format by following the link below.

**Notes and major health warnings**

Users use this free loan repayment period calculator at their own risk. We make no warranty or representation as to its accuracy and we are covered by the terms of our legal disclaimer, which you are deemed to have read. This is an example of a payments calculator that you might use when considering how to calculate the number of periods required to repay a loan. It is purely illustrative of a loan repayment calculator. This is not intended to reflect general standards or targets for any particular business, company or sector. If you do spot a mistake in this loan payment period calculator, please let us know and we will try to fix it.

## About the Author

Chartered accountant Michael Brown is the founder and CEO of Plan Projections. He has worked as an accountant and consultant for more than 25 years and has built financial models for all types of industries. He has been the CFO or controller of both small and medium sized companies and has run small businesses of his own. He has been a manager and an auditor with Deloitte, a big 4 accountancy firm, and holds a degree from Loughborough University.