# The 7th Grade Concept - Power of Compounding

Author
Anmol Gupta

Much cliched topic, but very important when it comes to financial planning. In this post we will really break down the concept of compounding. So that, the next time you take a loan, you are well aware of the "effective" interest which you will end up paying.\

#### You actually pay more than 12% when bank gives you a loan at 12% interest rate

Our banks offer us a lot of lucrative loans, so that we can spend more and more. However, the quoted interest rates are not really which we end up paying. We pay more than that! With the quoted interest rates, there is always another term mentioned called as "Compounding Frequency".

Assume you take a loan of Rs. 100,000 for 5 years from a bank. For simplicity, assume that you will be paying back the loan in one shot after 5 years (no monthly installments). Suppose, bank is charging you 12% per annum "compounded monthly" as the interest rate. How much will you end up paying at the end of 5 years? Following are 3 ways in which different people will calculate this amount.

#### Type 1) People who screwed their 7th grade, and didn't care to understand the difference between simple interest and compound interest

These innocent people simply calculate interest as 12% of Rs. 100,000 which is Rs. 12000, and then multiply it by 5 to get the total interest for 5 years. So, as per them the interest will be Rs. 12000x5 = Rs. 60,000. They think that they will end up paying Rs. 100,000 + Rs. 60,000 = Rs. 160,000 at the end of 5 years (These innocents are usually most surprised by bankers).

#### Type 2) People who took 7th grade seriously

These people understand the difference between simple interest and compound interest, but they just couldn't dig deeper into conventions of banking industry. These people may feel superior to the innocent people described in first case. They apply their knowledge of mathematics and geometric progression, and calculate the interest amount as:

Rs. 100,000 + 12% of Rs. 100,000 = Rs. 100,000 + Rs. 12,000 as the amount payable after 1st year

Rs. 112,000 + 12% of Rs. 112,000 = Rs. 112,000 + Rs. 13,440 = Rs. 125,440 as the amount payable after 2nd year

The intelligent people here understand that after one year, you owe Rs. 112,000 to bank, and why would bank leave interest on that? Bank will charge you interest on every penny you owe to them!

And similarly they go ahead and calculate the final amount as

Rs. 125,440 + 12% of Rs. 125,440 = Rs. 125,440 + Rs. 15,052.8 = Rs. 140,492.8 payable after 3rd year

Rs. 140,492.8 + 12% of Rs. 140,492.8 = Rs. 140,492.8 + Rs. 16,859.14 = Rs. 157,351.94 payable after 4th year

Rs. 157,351.94 + 12% of Rs. 157,351.94 = Rs. 157,351.94 + Rs. 18,882.23 = Rs. 176,234.17 payable after 5th year.

So, as per these intelligent people, you will end up paying about Rs. 76,000 as interest to bank after 5 years. Well, they are close to reality. But being too logical, they just ignored the bureaucratic conventions of banks which really drives the interest calculations! After understanding the convention, these people feel jealous of banker's hidden ways of making money.

#### Type 3) The people who dared to take the unconventional path and opted for Commerce stream

These are the people who really understand what actually happens. They often advise us with the peculiar ways to save tax!

So, when bank tells you 12% per annum compounded "monthly", bank means that it will charge you interest each month and that interest will be 12% divided by 12 = 1% per month. If bank tells you 12% per annum compounded per quarter, then bank intends to charge 12% divided by 4 = 3% per quarter. Well, how does it make a difference? We'll see that in a while. But, this is just the standard "convention". This is how banks quote interest rates.

The calculation:

The method is same as used by the "intelligent" people, just that, here 1% interest is charged each month rather than 12% per year.

Rs. 100,000 + 1% of Rs. 100,000 = Rs. 100,000 + Rs. 1,000 = Rs. 101,000 payable after 1st month

Rs.101,000 + 1% of Rs. 101,000 = Rs. 101,000 + Rs. 1,010 = Rs. 102,010 payable after 2nd month and so on...

It comes out as Rs. 112,682.50 payable after one year..and

Rs. 181,669.67 payable after 60 months or 5 years! This is what your bank will actually want from you.

So, after one year, you are actually liable to pay back Rs. 112,682.50. That is 12.68% interest rate charged on Rs. 100,000. The quoted interest rate was 12% per annum, but the compounding frequency made it to an "effective" rate of 12.68%. This is how our geniuses calculate the actual interest and secretly feel superior to everyone out there.

#### It's not cheating, just a convention.. and you also get the benefits when you invest :)

Well, banks are not trying to hide anything from you here. It's just the well adopted convention in this industry. Whenever you invest your money as Fixed Deposit or Recurring Deposit in banks, the interest rate on them is also quoted the same way. The interest rate on such deposits in India is usually compounded quarterly. So, just like your end up paying more interest than the quoted due to frequent compounding in case of a loan, you earn more interest than the quoted on your deposit due to compounding. Try calculating it :)