*The Business Professor*, updated February 24, 2019, last accessed August 12, 2020, https://thebusinessprofessor.com/lesson/amortized-loan-definition/.

Back to: BANKING, LENDING, & CREDIT INDUSTRY

### Amortized Loan Definition

Amortized loan debt requires monthly payments over a set period, in which a portion of the monthly payment goes toward the loan’s principal and the rest goes toward interest.

### A Little More on Amortized Loans

Amortized loan payments process periodically over a set period, paying the corresponding interest before regular payment and capital reduction. Typical amortized loans include car loans, mortgages, personal bank loans and debt consolidation.

### The relationship between capital and interest

The final loan balance determines interest, thus, as payments over the interest amount stack, the interest calculated for future payments lowers. Conversely, payments increase as the proportion of amortized loans decrease.

**Calculation**

To calculate depreciating loans, first calculate the monthly interest rate by dividing the annual interest rate by 12. Multiply the current loan balance by the monthly interest rate, and subtract the product from the monthly loan payment. The difference calculated is the dollar capital paid for that period. Subtract the capital paid from the current loan balance for a new outstanding balance, and use the new outstanding balance for the next period’s interest rate.

**Amortized Table**

A depreciation table displays the calculation of amortized loans, including balance and dollar amount. The rows of the table represent each period, while the columns represent current loan balance, total monthly payment, payment percentage, primary payment amount and final unpaid balance respectfully.

### References for Amortized Loan

- https://www.investopedia.com/terms/a/amortized_loan.asp
- http://www.businessdictionary.com/definition/amortized-loan.html
- https://www.bankrate.com/glossary/a/amortizing-loan/
- https://en.wikipedia.org/wiki/Amortizing_loan

### Academic Research on Amortized Loan

- The relative termination experience of adjustable to fixed‐rate mortgages, Cunningham, D. F., & Capone Jr, C. A. (1990). The Journal of Finance, 45(5), 1687-1703. This paper analyzes the termination experience of ARMs (adjustable rate mortgages) and FRMs (fixed rate mortgages) using a multinomial logit model. The study uses the FRM as a control to isolate the behaviors of ARMs, finding that expected rate adjustments and large lifetime caps are positively related to ARM termination probabilities, whilst caps and long adjustment frequencies are inversely related. Finally, the model shows FRM terminations to be more strongly affected by interest-rate expectations than ARMs.
- Re-examining an old question: Does the IRR method implicitly assume a reinvestment rate?, Rich, S. P., & Rose, J. T. (2014). Journal of Financial Education, 152-166. The article addresses a common debate among scholarly academics and practitioners. The internal rate of return does not explicitly calculate a rate for reinvestment of company funds; however, it begs the question of whether the reinvestment of company profits is implicitly calculated within the valuation.
- Point of View Revealing the True Meaning of the IRR via Profiling the IRR and Defining the ERR, Crean, M. (2005). Journal of Real Estate Portfolio Management, 11(3), 323-330. This article compares the expected rate of return against the internal rate of return. Relevant to this research is the amortized loan payment rate.
- The determinants of default on insured conventional residential mortgage loans, Campbell, T. S., & Dietrich, J. K. (1983). The determinants of default on insured conventional residential mortgage loans. The Journal of Finance, 38(5), 1569-1581. This paper employs empirical evidence on the determinants of default for insured residential mortgages, based on a multinomial logit model constructed from relevant data. The paper covers the significance of factors such as payment/income ratio, loan/value ratio, and other commonly studied determinants of default.
- What to do about Savings and Loan Associations?, Jaffee, D. M. (1974). This book examines the workings, function, and purpose of savings and loan associations.
- The equivalent loan principle and the value of corporate promised cash flows, Nachman, D. C. (2003). Journal of Applied Finance, 13(1), 5-18. This paper examines the “equivalent loan principle,” which asserts that before-tax cash flows is the present value of after-tax cash flows at the after-tax corporate borrowing rate, given equivalent financing. The principle has two validations: one when promised cash flows are of a coupon bond and another when of a fully amortized loan. To verify one must account for effective interest charges in calculating after-tax cash flows. The role of the equivalent loan principle in the valuation of tax shields is unclear, because the role of tax shields in expanding debt capacity must be found to resolve a contradiction in the typical valuation of interest tax shields and depreciation tax shields.
- Farm Mortgage Loan Repayment: A Survey of Existing Plans and Some Possible Alternatives, Galbraith, J. K., Macy, R. M., & Malenbaum, W. (1937). Journal of Farm Economics, 19(3), 764-782. This article addresses a specific type of amortized loan, the farm loan.
- Implementing discounted cash flow valuation models: what is the correct discount rate?, Ling, D. C. (1992). The Appraisal Journal, 60(2), 267. This article addresses the often uncertain question of what is the appropriate discount rate to use when calculating present value. This uses principles of amortized loan rates in this evaluation.
- Financing the American Dream: A History of the Fully-Amortized 30-Year Mortgage, Cooper, D., & Grinder, B. (2015). Financial History, (113), 10. This article addresses the common amortized loan, the 30-year mortgage.
- Real Estate Investment, Claassen, C. J. (1921). Law. & Banker & S. Bench & B. Rev., 14, 117. The concept of amortized loans is highly relevant to the real estate finance and investment industry.
- Effects on Credit Markets and Lending Practices, Saulnier, R. J., Halcrow, H. G., & Jacoby, N. H. (1957). In Federal Lending: Its Growth and Impact (pp. 44-48). NBER. This article addresses amortized loans and how credit markets affect lending practices.