Impact of Changes in Interest Rates

By Cenen Herrera

Writing from San Francisco City, USA

A lower interest rate on loans generally leads to a lower periodic amortization, e.g., in an annuity type of payment. The exception of course is when there is a loan default scenario or even a protracted arrears situation, in which case, the amortization schedule could differ. The question that arises is whether there is a simple methodology that could be used to explain the impact of such changes. The discussion below provides an example of periodic amortizations used in an annuity type of loan repayments.

Spreadsheet programs easily construct an annuity table to derive the periodic amortization. However, a manual approach is offered to help understand this amortization process. I would use the following assumptions:
Assume a $1,000 loan principal with an interest rate of 5% per year. Assume further that the loan has a maturity of 5 years.

Step 1: Calculate for the year equal payments applicable for principal and interest for every $1
Get the discount factor of $1 after 5 years, i.e., manual way is to divide $1 by 1.05 in year 1 and then divide the result by another 1.05 yearly until year 5. Thus, for example, in year 1, you will get $0.95238, i.e., 1/1.05. In year 2 you will get $0.90703, i.e., 0.95238/1.05, and so on until you reach year 5 where you will get $0.78353, i.e., 0.822702/1.05 for that year. You then get the sum of all the discount factors from year 1 to year 5 which would amount to $4.3295.

Step 2: Divide 1 by $4.3295, i.e. the sum you get in step 1. This will give you $0.23097, which means the yearly amortization, i.e., total of principal and interest, for every $1 amount of original principal, i.e., with an interest rate of 5% per year. Since our original principal amount in the example is $1,000, multiply 1,000 by $0.23097 which results into $230.97 yearly amortization, i.e. principal and interest.

Step 3: Since we now know that the yearly amortization is $230.97, we now would want to get the composition of year 1 amortization, i.e., principal and interest. This is done by simply multiplying .05, i.e. the interest rate for year 1 by $1,000, i.e., loan principal amount to get $50 for interest and the remainder of $180.97, i.e., $230.97 minus $50, would therefore be applicable to the principal amortization.

Step 4: The remaining principal amount of loan for year 2 would be $819.03, i.e., $1,000 minus $180.97. Applying the same procedure in Step 3, you would then get an interest payment of $40.95, i.e., $810.03 multiplied by .05. Thus, $190.02, i.e., $230.97 minus $40.95, would be the principal repayment applicable for year 2. Repeat this procedure until you reach year 5.

Step 5: Now that you know the composition of the principal and interest payments for a given year amortization, you could then calculate total principal and interest payments for all the years. The results would lead to the following: Total Amortization for year 1 to year 5 equals $1,154.87 which is broken down as follows – principal $1,000 and interest $154.87.