# 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 compounding 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

$Simple\, Interest= \frac{Principle*Time*Rate\, of\,Interest }{100}$

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

In case of CI,

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

1. Half Yearly compounding=

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

2.Quarterly compounding=

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

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 $= \frac{R^{2}}{100}%$ 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 = $= \frac{100}{n}$

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

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