Rate Compounded Annually or Half Yearly

You may notice that, in the beginning, we used “rate compounded yearly”. What does it mean?

It means that interest was compounded once a year. We can also have our interest compounded half-yearly or quarterly. What happens in such cases?

Let’s compare the two cases through an example to see the difference between rates compounded yearly and half-yearly. 

Suppose P = 1000, R = 5% and n = 2 years,

Case 1: Interest compound annually.

[Tex]I = \frac{PR}{100} = \frac{1000 \times 5}{100} = 50[/Tex]

A = 50 + 1000 = 1050.

Case 2: Interest Compounded Half-Yearly.

[Tex]I = \frac{PRT}{100} = \frac{1000 \times 5 \times \frac{1}{2}}{100} = 25[/Tex]

P₂ = I + P = 1025

[Tex]I_{2} = \frac{P_{2} RT }{100} = \frac{1025 \times 5 \times \frac{1}{2}}{100} = 25.625[/Tex]

Final amount in this case A = P₂ + I₂ = 1025 + 25.625 = 1050.625  

We can that if interest is compounded half-yearly, compute the interest two times. So the time period becomes twice and the rate is taken half.

So the formula becomes, 

[Tex]A  = P(1 + \frac{\frac{R}{2}}{100})^{2n}[/Tex]

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.