# Loan Repayment Calculator

## What does it do?

This loan repayment calculator works out the regular payment (Pmt) needed to repay a loan (PV) over n periods if interest is compounded at a periodic interest rate i. The repayments are assumed to be 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 payment (Pmt).

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

## Instructions

The Excel loan repayment calculator, available for download below, is used to compute the periodic loan repayment by entering details relating to the amount of the loan, interest rate and the number of periods. 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 number of periods (n). A period can be any term (month, year etc), but must be consistent with the interest rate provided (see step 2). For example, if the loan is to be repaid monthly for the next 10 years, then the number of periods is 120 months.

### Step 4

The loan repayment calculator works out the periodic payment (Pmt) required at the end of each of n periods to repay a loan amount (PV) at a periodic interest rate of i.