# Loan Constant Tables

The purpose of the loan constant tables (sometimes referred to as debt constant tables or mortgage constant tables) is to make it possible to calculate loan payments and outstanding loan balances without the use of a financial calculator.

Full details of the use of the loan constant can be found in our How to Calculate a Debt Constant tutorial.

The loan constant formula is:

`Loan constant = i / (1 - 1 / (1 + i)n)`

Loan constant tables are used to provide a solution to the formula for any value of interest rate (i) and loan term (n).

The interest rate must be constant throughout the term of the loan and must be for the length of one period.

## Loan Constant – Table Payment Example

What is the constant periodic payment needed to clear a loan of 250,000, if payments are made at the end of each year for 20 years, and the interest rate is 6%.

```PV = loan = 250,000
n = 20 years
i = 6%
Payment = Loan x Loan constant
From the tables at 20 years and 6% the loan constant is 8.7185%
Payment = 250,000 x 8.7185%
Payment = 21,796 per year
```

The loan constant factor of 8.7185%, is found using the tables by looking along the row for n = 20, until reaching the column for i = 6%, as shown in the preview below.

## Loan Constant Table Outstanding Balance Example

For the loan above, what is the outstanding balance at the end of year 6?

The outstanding balance is given by the ratio of the loan constants for 20 years and 14 years, further details of this calculation can be seen in our how to calculate a debt constant tutorial.

```PV = loan = 250,000
n = 20 years loan term
m = 14 years to go until the end of the loan
i = 6%
Outstanding balance = Loan x Loan constant (20,6%) / Loan constant (14,6%)
From the tables for 20 years and 6% the loan constant is 8.7185%, and for 14 years and 6% is 10.7585%
Balance = 250,000 x 8.7185%/10.7585%
Balance = 250,000 x 81.038%
Balance = 202,595
```

The balance at the end of year 6, with 14 years left to run will be 81.038% of the original balance or 202,295.