Compound Interest

Compound interest (or compounding interest) is the interest on a loan or deposit calculated based on both the initial principal and the accumulated interest from previous periods. Thought to have originated in 17th-century Italy, compound interest can be thought of as “interest on interest,” and will make a sum grow at a faster rate than simple interest, which is calculated only on the principal amount. Let’s see an example before working out the formula, 

Question: Hema borrowed a sum of Rs. 2,00,000 for 2 years at an interest of 8% compounded annually from a bank. Find the Compound Interest and the amount she had to pay at the end of 2 years.

Answer: 

To do it, we need to find interest year by year.

Step 1. First let’s find Simple Interest for the first year,

          Here, principal P₁ = 2,00,000, R = 8% and T = 1.

          SI₁ = SI at 8% on P₁ for one year = [Tex]\frac{P_{1} \times R \times T}{100} = \frac{200000 \times 8 \times 1}{100} = 16000[/Tex]

Step 2. So, now the amount received at the end of the first year = SI₁ + P₁ = 16000 + 2,00,000 = 2,16,000. Now, this will become principal.

            Thus, P₂ = 2,16,000, R = 8 and T = 1

Step 3. Now we will find simple interest for the second year by taking the total amount at the end of 1st year as principal P₂.

           SI₂ = SI at 8% on P₂ for one year =[Tex] \frac{P_{2} \times R \times T}{100} = \frac{216000 \times 8 \times 1}{100} = 17280[/Tex]

           This amount now at the end of 2nd year = SI₂ + P₂ = 17280 + 2,16,000 = 2,33,280

           Total interest given = 17280 + 16000 = 33280.,

We need to notice that Principal remains the same in Simple Interest(SI), but in Compound Interest(CI) it recalculated and changes every year. 

Compound Interest: Compounding is a process of re-investing the earnings in your principal to get an exponential return as the next growth is on a bigger principal, following this process of adding earnings to the principal. In this passage of time, the principal will grow exponentially and produce unusual returns.

Sometimes we come across some statements like “one year interest for FD in the bank @ 11 % per annum.” or “Savings account with interest @ 8% per annum”.  When it comes to investment, there are usually two types of interests :

• Simple Interest
• Compound Interest

We already know about Simple Interest(S.I), we will look at Compound Interest(C.I) in detail in this article. First, let’s understand what is compounding through a story. 

A Prisoner was once awaiting his death sentence when the king asked for his last wish.

The Prisoner demanded grain of rice (foolish demand right?) but added that the number of grain should be doubled after moving to every square till the last square of the Chess Board ( that is 1 on first, 2 on second, 4 on third, 8 on fourth, 16 on fifth and so on, till the 64th square).

The king thought that it is a very small demand and ordered his ministers to have that much amount of rice calculated and provided to the prisoner. The amount calculated was so big that the king lost his entire kingdom and was indebted to prisoner all of his life.

What the prisoner used was the idea of “Compounding“. Now, let’s define Compound Interest.