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Simple Interest and Compound Interest

Interest is defined as the “Time value of money.” As the time passes on, value of money keeps on changing. And while factors like inflation or depreciation in money decreases the value of money with the passage of time, interest the counters all these.

The basic difference between simple interest and compound interest lies in the fact that while in case of simple interest, the principal as well as the interest remain same for the entire period given, in case of compound interest, after a certain period, both the principal and the compound interest keep on changing.

Simple interest
In case of simple interest, interest is reckoned at a flat rate for the entire period of time for the amount borrowed.
Simple interest can be calculated by finding the percentage of principal for that period of time.
If the principal is P, rate of interest per annum = R% and time = T years, then Simple Interest will be equal to RT % of P.
So, Simple Interest (SI) = Description: 3036.png 
A sum of money becomes 3 times in 5 years. In how many years will the same sum become 6 times at the same rate of SI?
The sum of money gets 3 times means that 200% is being added to the original sum (principal) in 5 years.
So, 500% will be added up in Description: 3045.pngyears.

Compound interest
In case of compound interest, interest is reckoned on the interest of previous years also apart from reckoning it on the current year.
So, compound interest can be seen as the extension of simple interest in such a way that previous year interest also becomes principal for the next year.
If principal is P, rate of interest per annum = R% and time = n years, then
Compound Interest = Description: 3054.pngn - P
Amount = Description: 3063.png
It can be seen thatDescription: 3072.pngis nothing but Description: 3077.pngDescription: 10013.pngn times, which is simply the application of successive percentage change.
The difference between two years of compound interest and simple interest at 10% over Rs X is Rs 10. What is the value of x?
Description: 6543.png
So, 1% = Rs 10
⇒ 100% = Rs 1000
It is pertinent to understand here that if the rate of Interest = R% per annum for both CI and SI, then the difference between CI and SI for 2 years will be equal to R% of R% = R2/100%
In the above case, R = 10%, so the difference between CI and SI for 2 years = 1%

Comparison between SI and CI
Assume that two different sums are getting doubled at their respective rates of SI and CI in 5 years. The following table gives us the mechanism of getting money n times in the above situation.
Description: 6573.png

Simple Annual Growth Rate (SAGR) and Compounded Annual Growth Rate (CAGR)

Consider the following table pertaining to the sales value of Due North Inc. in different years:
Description: 6578.png 

If we find out the growth over the given period, then it is equal to 31%.
However, there are two more growth models, namely, Simple Annual Growth Rate (SAGR) and Compounded Annual Growth Rate (CAGR).
Description: 3086.png 

To find out CAGR, we are needed to use the approach of CI and we will consider 131 as the amount and 100 as the principal.
So, 131 = 100 Description: 3095.png
To find out the value of R, we will apply the method of hit and trial, or otherwise find out the value of Description: 3104.png.
Since we know, (1.1)3 = 1.331, so value of R will be less than 10% and very close to 10%.
So, it will be around 9.7%  9.8%.

Compound interest reckoned half-yearly or quarterly
 If the rate of interest is R% annually and CI is compounded half yearly for n years, then the expression for Compound
Interest = Description: 3113.png

If the rate of interest is R% annually and CI is compounded quarterly, then the expression for Compound
Interest = Description: 3122.png


Percentage is mostly helpful in multiplication and division. Let us learn this with the help of examples.

To use this percentage method effectively for multiplying two values, we should be thorough with the equivalent ratio of the percentage figures. Besides, having a good addition speed will be an added advantage.
63 × 72.
The moment we see any number, we should start mental scanning of the percentage–ratio equivalence.
Here, 63 × 72 = (62.5 + 0.5) × 72
= 5/8 × 100 × 72 + 0.5 × 72 (5% of 72)
= 4500 + 36
= 4536

76 × 24
= (75 + 1) × 24 = ¾ × 100 × 24 + 1 × 24 = 1800 + 24 = 1824

Dividing 243 by 50.
Description: 3131.png
To divide any number by 25, we will divide it by 100 and multiply by 4.
Similarly, while dividing any number by any such number for which we can find out a comparable value in terms of 100 Description: 3149.png should be used.

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