# Installment loan formulas

When you take out a installment loan, you will be told by the provider the nominal interest and the annual percentage rate of charge. The nominal interest rate is the interest rate that is added to the loan amount, the APR also includes the fees and changes with the term. You sometimes want to know what happens if you repay the loan early or what the actual cost of the loan is. For this there are installment loan formulas.

## Pay attention to annuity

If the nominal interest rate were added to the sum using a simple interest rate formula, the result would be incorrect because the loan is repaid on a monthly basis. Here, the installment loan formulas take into account the so-called annuity, which is almost always applied to installment loans, unless you have agreed on flexible interest rates (very rarely common). Each month, they repay an increasing share of the loan, the interest portion of the rate decreases, the overall rate remains the same. The installment loan formulas must now take into account that through the monthly repayments an ever decreasing sum will pay interest. The bank calculates that too, and to the exact day. The installment loan formulas are based on monthly rhythms and offer a sufficient approximation.

## Employing installment loan formulas

If you repay a loan of 15,000 USD in 36 months at the interest rate of 5.2 percent, the respective residual debt is calculated as follows:

Capital times interest factor minus rate = residual debt 1

Remaining debt 1 time interest minus rate = residual debt 2

Remaining debt 2 times interest factor minus installment = residual debt 3

and continuously.

You can also solve the equations according to an unknown rate by calculating the capital times the interest factor high m by the interest factor high m-1 times the interest factor minus 1, where m represents the remaining term. You can calculate the interest factor as the root of the annual residual debt.

## Use of the calculations

The bank calculates on a daily basis, there are no known cases where these calculations were contested. It can be assumed that the rate calculation is correct. However, if you plan to repay a loan ahead of time, it is worthwhile to use the formulas as an approximation.