# Compound and continuous interest in the context of debt

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.) • it is difficult to understand what have you not understood. Author has already presented the concept in most simplified way.Can you please point out particular line which is puzzling you ? Commented Feb 15, 2016 at 17:45 • @Neeraj: For starters, what does it mean to take a mortgage at an APR of$r\$, compounded monthly? The notion of a mortgage is not mentioned in the article at all until the end. Commented Feb 15, 2016 at 18:39
• A mortgage is a large loan to buy a house. 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. Commented Feb 15, 2016 at 19:09
• @AlexC could you make this an answer? It will help other users to know this one has an answer (and help our stats ;). Commented Feb 17, 2016 at 20:49