8.3 Loan Amortization

Loans come in two main flavors: amortizing and non-amortizing. Amortizing loans, like mortgages, have fixed payments that cover both principal and interest. Non-amortizing loans, such as balloon loans, only require interest payments until a big principal payment at the end.

Loan amortization spreads payments over time, with each installment covering principal and interest. Early on, more of each payment goes to interest. As the loan progresses, more goes to principal. Understanding amortization helps borrowers grasp their debt service and compare loan options.

Loan Types and Amortization

Types of loans: amortizing vs non-amortizing

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• Amortizing loans require periodic payments that include both principal and interest, with the payment amount remaining constant throughout the loan term (mortgages, auto loans, student loans)
  • Over time, the portion of each payment allocated to principal increases, while the interest portion decreases
• Non-amortizing loans involve principal being paid in a lump sum at the end of the loan term, with periodic payments consisting of interest only (interest-only loans, balloon loans, bullet loans)
• Amortizing loans typically have lower periodic payments but result in higher total interest paid over the life of the loan compared to non-amortizing loans
  • Non-amortizing loans have lower total interest paid but require a large principal payment at the end of the term

Process of loan amortization

• Loan amortization spreads out loan payments into fixed installments over a specified period, with each payment consisting of both principal (original amount borrowed) and interest (cost of borrowing)
• Early in the loan term, a larger portion of each payment is allocated to interest due to the remaining principal balance being highest at the beginning
  • As the loan progresses and the remaining principal balance decreases with each payment, a larger portion of each payment is allocated to principal, resulting in less interest charged
• The loan term (duration of the loan) affects the total amount of interest paid and the size of periodic payments

Construction of amortization schedules

• An amortization schedule shows the breakdown of each loan payment into principal and interest, as well as the remaining loan balance after each payment
• To create an amortization schedule using spreadsheet software:
  1. Input loan details such as principal amount, interest rate, and loan term
  2. Use the formula $Payment = \frac{P * i}{1 - (1 + i)^{-n}}$ to calculate the fixed periodic payment amount, where $P$ is the principal loan amount, $i$ is the periodic interest rate, and $n$ is the total number of payments
  3. For each payment period, calculate the interest portion (remaining balance from previous period * periodic interest rate), principal portion (fixed periodic payment - interest portion), and remaining balance (previous remaining balance - principal portion)
• The amortization schedule helps borrowers understand their debt service (total amount paid in principal and interest) over time

Analysis of total borrowing costs

• Total cost of borrowing includes interest expenses (sum of interest portion of each payment from amortization schedule) and fees (origination fees, closing costs, prepayment penalties) over the life of the loan
  • Higher interest rates and longer loan terms result in higher total interest expenses
• When comparing loan options, consider that shorter loan terms generally have higher periodic payments but lower total interest expenses
  • Fixed-rate loans provide predictable payments, while adjustable-rate loans may have lower initial payments but carry the risk of higher future payments if interest rates rise

Time Value of Money and Loan Calculations

• The time value of money concept is fundamental to understanding loan calculations and amortization
• Compound interest is used in loan calculations, where interest is earned on both the principal and previously accumulated interest
• Present value calculations are used to determine the current worth of future loan payments, helping in loan comparisons and decision-making