This is “Loan Amortization”, section 7.4 from the book Finance for Managers (v. 0.1).

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- Explain loan amortization.
- Create an amortization schedule.

*Fred owes $1,500 on his credit card! When his monthly bill arrives, Fred is relieved to see that the minimum payment is only $30. If the advertised rate is 20% APR (assume monthly compounding), how many months will it take Fred to pay off his debt?*

If Fred makes his payments every month, the debt will finally be fully paid after 109 months, or over 9 years! We can verify this quickly using a financial calculator or spreadsheet.

=NPER(20%/12,30,−1500) =108.4During this time, the total amount of money paid by Fred will be about 109 * $30 = $3,270, or over twice the original amount owed. This means that Fred paid more in interest ($3,270−$1,500 = $1,770 in interest) than he originally borrowed ($1,500). On the plus side, Fred was able to slowly pay down the balance owed, so that he never had to pay more than $30 in any month, but the total principal was paid by the end of the loan. This process of spreading out principal payments of a loan over time is called amortizationThe process of spreading out the principal payments of a loan over time. (from the Latin root “mort-”, meaning death, as the loan balance slowly “dies” as the principal is paid down). Mortgages are a common example of this type of loan (also coming from the same Latin root), as the principal is paid down over 15, 30 or more years. A loan that pays only the interest payments, with no principal payments, is called an interest only loan. If the periodic payments are so low they don’t even cover the interest on the initial principal, then the loan will be a negative amortization loan, and the extra interest will be added to the principal due over time.

Figure 7.9 Amortization Schedule for Credit Card Payments

As each month passes, the outstanding principal balance decreases, so the interest due also decreases. Thus, over time, the amount paid toward principal grows from a small portion of the monthly payment to a larger portion. This is particularly important when evaluating mortgages, as often the interest portion is tax deductible, but the principal portion is not. If we were to continue the chart for the full 109 months, we would see that the last month would only require a partial payment (that is, less than $30) to pay off the remaining principal.

Figure 7.10 Principal and Interest Portion of Payments Over Time

Of course, not all loans have constant payment schedules. Some loans have “teaser” periods, with low interest rates for a certain period of time. These might seem like fantastic deals, until we realize that the loan is actually negatively amortizing over the period, causing higher rates (or a longer payoff time) once the period is over.

- Payments can be broken into principal and interest components.
- As principal is paid down, interest decreases. Future payments will, over time, accelerate in their rate of paying down principal.
- Negative amortization can actually increase principal balances over time.

- If Fred could afford to pay $5 more than the minimum payment, how many months would it take to pay off the balance?
- A 30 year fixed rate mortgage has monthly payments (and no payment due at the end). If the interest rate is 6% APR and the amount borrowed is $200,000, what is the monthly payment due? Create an amortization schedule for this mortgage.