# Loan Amortization

Loan amortization is the process through which principal balance of amortized loans is paid off through periodic payments over the life of the loan. Amortized loans are loans whose periodic repayments include both a principal repayment and interest component.

There are several types of loans, some require periodic payment of interest and a bullet payment of principal at the end of the loan; others do not require a bullet repayment of principal instead their principal balance is paid together with interest through periodic payments. Bonds are a typical example of the bullet-payment loans while capital leases, mortgages, auto loans are amortized loans.

Loan amortization schedule is a table that lists each periodic payment that will accrue on a loan bifurcating it into the amount that is on account of interest and the amount that represents the repayment of principal. The principal balance of an amortized loan reduces over time and so does the associated interest expense.

## Formula

The periodic payments required on an amortized loan to write it off completely over its term can be worked out using the formula for present value of an ordinary annuity:

$$\text{PMT}=\frac{\text{PV}}{\frac{\text{1}-{(\text{1}+\frac{\text{i}}{\text{m}})}^{-\text{n}\times \text{m}}}{\frac{\text{i}}{\text{m}}}}$$

Where PV stands for the outstanding principal balance, i is the annual percentage return, n stands for the number of years in the loan and m is the number of compounding periods per year.

The interest expense each period is worked out by applying the periodic interest rate to the opening loan principal balance:

$$\text{Interest Expense}\\=\text{Outstanding Loan Principal}\times\frac{\text{i}}{\text{m}}$$

The principal repayment amount each period equals the difference between the total periodic payment on the loan in the given period minus the interest accrued on the loan:

$$\text{Principal Repayment}\\=\ \text{PMT}-\text{Interest Expense}$$

Excel PMT, IPMT and PPMT functions can be used to calculate the total periodic payment, interest component and principal repayment component respectively