# Loan Repayment Period Calculator

## 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).