# 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.

So, Simple Interest (SI) =

Example-1

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?

Solution

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 years.

Compound interestCompound 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 =

Amount =

^{}*- P*^{n}Amount =

^{}^{}is nothing but …

*n*times, which is simply the application of successive percentage change.

Example-2

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*?Solution

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

^{2}/100%

**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.

# 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:If we find out the growth over the given period, then it is equal to 31%.

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.

^{}

^{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

If the rate of interest is R% annually and CI is compounded quarterly, then the expression for Compound

# Calculation

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

Example-3

63 × 72.

Solution

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

Here, 63 × 72 = (62.5 + 0.5) × 72

= 5/8 × 100 × 72 + 0.5 × 72 (5% of 72)

= 4500 + 36

= 4536

Example-4

76 × 24

Solution

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

Division

Division

Example-5

Dividing 243 by 50.

Solution

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 should be used.