Compound and continuous interest in the context of debt

Question

I'm trying to figure out the concepts "compound and continuous interest". This article explains the material very well in the context of a savings account. However, I find it difficult to transfer my understanding to the realm of debt. For instance, in the end of said article the following applications are presented.

• Should I pay my mortgage at the end of the month, or the beginning? The beginning, for sure. This way you knock out a chunk of debt early, preventing that “debt factory” from earning interest for 30 days. Suppose your loan APY is 6% and your monthly payment is \$2000. By paying at the start of the month, you’d save \$2000 * 6% = \$120/year, or \$3600 throughout a 30-year mortgage. And a few grand is nothing to sneeze at.

• Should I use several small payments, or one large payment?. You want to pay debt off as early as possible. \$500/week for 4 weeks is better than \$2000 at the end of the month. Each payment stops a few weeks’ worth of interest. The math is a bit tricker, but think of it as 4 \$500 investments, each getting different return. In a month, the first payment saves 3 week’s worth of interest: 500 · (1 + daily rate)21. The next saves 2 weeks: 500 · (1 + daily rate)14. The third saves a week 500 · (1 + daily rate)7 and the last payment doesn’t save any interest. Regardless of the details, prepayment will save you money.

I don't understand the answers. Help would be appreciated. (Again, you may assume that I understand the concepts of compound and continuous interest in the context of savings accounts.)

Answer 1

As a saver you are happy to receive interest but as a borrower the tables are turned and you have to pay interest on the outstanding balance. It is a different perspective that you may not thought about before. Basically you should try to reduce the interest you are paying to the minimum necessary.

For example to buy a house you may need to get a mortgage, i.e. a large loan from a bank. You repay the bank by making equal monthly payments. These payments include both a loan repayment and a certain amount of interest calculated based on the remaining outstanding balance. You also (in the USA) have an option to repay early, which will decrease the outstanding debt and thus future interest payments. Vice versa, in those cases were the bank allows you to postpone a payment, you will literally pay the price by having a larger loan balance and having to make greater payments in the future. The bank loves it (as long as real estate prices hold steady), but during the financial crisis of 2008 many borrowers hurt themselves by making use if this kind of "feature" that they perhaps didn't fully understand.

The passage you quoted is giving some numerical examples to illustrate this rather simple idea. A borrower gains by making more or quicker payments on a loan.