Loan Amortization: Definition, Examples, and Calculations

Loan amortization refers to the process of scheduling out a fixed rate loan into equal payments. This allows a borrower to pay loans for equal amounts or installments every month or every year. A portion of the amortized loan or installment goes towards the payment of interest while the other portion pays the principal loan amount. Lenders use loan amortization schedules to determine the amount of monthly payments that borrowers are required to pay. The loan amortization schedule also provides repayment details for customers. Borrowers can also use the amortization schedule to establish the amount of debt that they can afford, and how much they can save.

An amortization schedule is a table that has the periodic payments. It shows the amount of the loan that goes towards the principal and the amount that covers interest. In the early stages of the schedule, majority of the installment amounts go towards interest. However, towards the end of the loan amortization schedule a large amount of the money paid each period goes to the remaining loan principal. In this regard, the percentage of each instalment that goes towards interest diminishes with time, while the percentage that goes toward the principal increases.

For example, a loan amortization schedule for fixed-rate mortgage loan of $165,000 lasting for 30 years at an interest rate of 4.5% can be amortized using the amortization schedule below:

Loan Amortization Schedule

Apart from mortgage loans, car loans and personal loans can also be amortized over a set period of time with monthly payments.

Calculation of Loan Amortization

Borrowers and lenders use amortization schedules for installment loans that have payoff dates that are known at the time the loan is taken out, such as a mortgage or a car loan. Most formulas used to calculate loan amortization schedule is built into a software and customized for each borrower. Loan amortization can be calculated if the term of the loan and total periodic payments are known. The formula to calculate the monthly principal due on an amortized loan is as follows:

Principal Payment = Total Monthly Payment – [Outstanding Loan Balance x (Interest Rate / 12 Months)].

For example, a home owner took a mortgage of $250,000 that has 30-year term, an interest rate of 4.5% and monthly installments of $1,266.71. For the first month, the loan is amortized as follows:

Principal Payment = 1,266.71 – [250,000 x (0.045/12)] = $329.21

The interest and principal payment for the second month is calculated by first subtracting the principal payment from the loan balance ($250,000-$329.21). This gives a new loan balance of $249,670.79. Using the new loan balance, you repeat the calculation you did for the first month, and then do the same for all the subsequent months.

The total monthly payment is calculated using the formula below:

Total Monthly Payment = Loan Amount [ i (1+i) ^ n / ((1+i) ^ n) – 1) ]

Where; i = monthly interest rate, n = number of periods over the loan’s lifetime, e.g. 15 years

Monthly interest is given by the annual interest rate divided by 12 months; while the number of payments is calculated by multiplying the number of years of the loan term by 12 months. Therefore, for a 30-year loan of $250,000 with an interest rate of 4.5% as shown in the example above, the monthly payments are calculated as follows:

Total Monthly Payment = $250,000 [(0.00375 (1.00375) ^ 360) / ((1.00375) ^ 360) – 1)] = $1,266.71.

This is the total monthly payment due on the loan, including the sum of principal and interest amounts.

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