Compounding interest is a very important concept to understand in adult life. In compounding, interest earns interest, which helps savings but hurts debt. So, while credit cards and loans CHARGE interest on existing interest each month, increasing your debt, on the other hand, savings accounts, CD’s, and retirement funds EARN interest on interest, making the money grow over time. This is why compounding interest is often considered “magical”: “the magic of compounding interest”. However, this magic can both help you and also hurt you, depending whose earnings or debt is increasing.

Compounding interest is a very important concept to understand in adult life. In compounding, interest earns interest, which helps savings but hurts debt. So, while credit cards and loans CHARGE interest on existing interest each month, increasing your debt, on the other hand, savings accounts, CD’s, and retirement funds EARN interest on interest, making the money grow over time. This is why compounding interest is often considered “magical”: “the magic of compounding interest”. However, this magic can both help you and also hurt you, depending whose earnings or debt is increasing.

To do it, you take the starting amount (Principal), multiply it by a number that gets bigger over time (the Rate), and you do this multiplication for every year it sits in the bank (the Times). 
So for example, 
Interest Earned = Principal x (1 + Rate)^Times – Principal

The Principal x (1+Rate) repeats for as many times there are in “Times”. 
So $100 @ 5% interest:
1st year might be: $100 × 1.05 = $105. 
Interest earned: $5.
2nd year might be: $105 × 1.05 = $110.25.
Interest earned total: $10.25 so far., $5.25 of it this year. 
So year one earns $5. Year two earns $5.25

Once you fully grasp how this works, you will be ready to understand how it works when you break the year into periods. But having this as a solid foundation is most important.

This same way of thinking applies to amortization while your principal decreases and your interest payments decrease but your payment towards principal increases monthly, despite the monthly payment given them being the same, What is sneaky or painful with amortization is that while you you pay less towards the interest each month, the fact is you are paying most of the interest FIRST in the life of the loan and the least towards the principal. So the principal goes down VERY SLOWLY at first and the result is: the more months you have to pay towards the mortage, the more interest you end up paying, which is why people who teach you to save money encourage you to pay down your mortgage faster, because:

Lower principal means lower interest to be paid and fewer payments means less interest adding on as it stays there.

In short for the amortization: Less compounding = less you have to pay in the end. Same with credit cards. Get a sense for the mechanism working like a machine, and the calculations will begin to make sense. 

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