# Simple Interest and Compound Interest

## Simple Interest

” *The interest as well as the principal remains ﬁ xed for every compounding period.”*

## Compound Interest

” *In case of compound interest, the interest will be added to the initial principal after every compounding period. Hence, compound interest keeps on increasing after every compoundin*g period.”

**In Case of SI**

** For example, if the rate of interest = 10% and the principal = `1000, then:**

**Interest for 1st year = 10% of `1000 = `100****Interest for 2nd year = 10% of `1000 = `100****Interest for 3rd year = 10% of `1000 = `100**

**It can be seen that interest generated every year = `100**

**In Case of CI**

**Principal of 1st year (initially) = P****Principal of 2nd year = P + interest of 1st year****Principal of 3rd year = P + interest of 1st year + interest of 2nd year For example, if the rate of interest = 10% and the principal = `1000,**

** then Interest for 1st year = 10% of `1000 = `100**

**In Case of CI**

**Principal of 1st year (initially) = P****Principal of 2nd year = P + interest of 1st year****Principal of 3rd year = P + interest of 1st year + interest of 2nd year**

**For example, if the rate of interest = 10% and the principal = `1000, then Interest for 1st year = 10% of `1000 = `100**

**Here is expression**

**[latex] Simple\, Interest= \frac{Principle*Time*Rate\, of\,Interest }{100} [/latex]**

**[latex] CI= Principal*\left [ 1+\frac{R}{100} \right ]^{N}-Principal [/latex]**

**In case of CI, **

**if the compounding is not done annually, then formula changes like the following,**

**Half Yearly compounding=**

**[latex] CI= Principal*\left [ 1+\frac{R/2}{100} \right ]^{2N}-Principal [/latex]**

**2.Quarterly compounding= **

**[latex] CI= Principal*\left [ 1+\frac{R/4}{100} \right ]^{4N}-Principal [/latex]**

**Important Shortcut**

1. If the rate of interest = R% per annum for both CI and SI, then the difference between CI and SI for 2 yr will be equal to (R% of R)% of principal [latex]= \frac{R^{2}}{100}% [/latex] of 2 principal.

In the above case, R = 10%, so the difference between CI and SI for 2 yr is 1%.

2. If a sum doubles itself in n years at SI, then rate of interest = [latex]= \frac{100}{n} [/latex]

3. At SI, if a sum of money amount to n times in t years, then rate of interest = [latex] = \frac{\left ( n-1 \right )}{100}% [/latex]