difference between Simple and compound interest- formula and problems

After reading this post you will have clear understanding of what is simple interest and what is compound interest. Difference between simple interest and compound interest is explained with the help of solved examples.

What is the simple interest

Interest paid is computed on the principal (the original sum of money). The simple interest remains the same in every time period provided that the rate of interest doesn't change.
Say, if the time period is one year

Interest of 1st year = Interest of 2nd year = Interest of 3rd year .................and so on.

Simple interest formula:

Simple interest formula

Amount = Principal + Interest 

What is compound interest

Interest earned on both the principal and accumulated interest of prior periods. 

Compound interest formula 

Compound interest formula 

Difference between simple interest and compound interest:

difference between SI and CI 

Let we take an example and find the simple interest and compound interest of different years.

A person takes a loan of Rs 100000  from the bank at an interest rate of 10 % per year. Find the simple interest and compound interest for the 1st and 2nd year separately.

Here, P = 100000

R = 10 % per year 

For the 1st year: 

Simple interest =	P * R * T
	100

=	100000 * 10 * 1
	100

= 10000

Compound Interest:

CI = A - P

So, First, we need to find the Amount                   

A= P * [ 1 + ( R / 100) ]T

= 100000 * [ 1 + ( 10 / 100) ]1 

= 100000 * [ 1 + 0.1 ] = 110000

CI = 110000 - 100000 = 10000

Readers should note that for the first year both simple interest and compound interest are the same.

For the 2nd year:

Simple interest doesn't count interest on interest so, the principal remains the same as of 1st year.

P = 100000
R = 10 %
T = 1 year

Simple interest =	P * R * T
	100

=	100000 * 10 * 1
	100

= 10000

Compound interest of 2nd year

It is the simple interest earned in 2nd year on the principal and interest of 1st year. So, Amount after 1st year will become the principal for the 2nd year.
P = 110000
R = 10 %
T = 1 year

Simple interest =	P * R * T
	100

=	110000 * 10 * 1
	100

= 11000

We can cross-check our answer using the compound interest formula:

CI = A - P

A = P * [ 1 + ( R / 100)]T

= 110000 * [ 1 + ( 10 / 100)]1
= 110000 * [ 1 + 0.1 ]

= 110000 * 1.1 
= 121000

CI = A - P
CI = 121000 - 110000 =
CI = 11000

The readers must note that the compound interest of 1st year was Rs 10000 and compound interest of 2nd year is 11000 rupees. the extra 1000 rupees in 2nd year are coming from the interest on the 10000 rupees ( Interest of 1st year ).
Compound interest of 2nd year:
10% of 100000 + 10 % of interest on 10000
= 10000 + 1000
= 11000

Now we know the simple interest and compound interest formula, let us solve some questions.

Question no. 1: 

Jyoti invested an amount of 10000 in a bank for 2 years at an interest rate of 5 % anually compounded annually. How much Jyoti will get at the end of two years.

Answer: 

CI = A - P

A = P * [ 1 + ( R / 100)]T
= P = 10000

Rate = 5 % annually compounded annually 
T ( no. of time periods) = 2/1 = 2

A = 10000 * [ 1 + (5 / 100)]2

A = 10000 * [ 1.05]2

A = 11025

CI = 11025 - 10000 = 1025

Note: This interest is combined interest of both 1st and 2nd year. 

Questions no. 2:

Jyoti invested an amount of 10000 in a bank for 2 years at an interest rate of 5 % annually compounded monthly. How much Jyoti will get at the end of two years.

Answer:

In the above question interest rate was compounded annually but in this question interest rate is compounded monthly.

P = 10000
Rate = 5 % annually compounded monthly 
= 5/12 % monthly compounded monthly
T ( Total no. of time periods) =  Total no. of months in 2 year = 24                           

A = 10000 * [ 1 + {5 / (12 * 100)}]24

A = 10000 * [ 1.00416]24

A = 11049 
CI = 11049 - 10000 = 1049

Question no. 3:

The difference in simple interest and compound interest on a certain sum of money in 2 years at 10% per year is Rs 100. find the sum.

Answer: 

CI = A - P                 

CI = P * [ 1 + ( R / 100) ]T- P

SI = P * R * T / 100

Let 'D' be the difference of CI and SI 

CI - SI = D

D = P * [ 1 + ( R / 100) ]T- P- (P * R * T )/100

D = P {  [ 1 + ( R / 100) ]T- 1-  (R * T) / 100 }

Given, D = 100

R = 10 %

T = 2 years

100 = P {  [ 1 + ( 10 / 100) ]2- 1-  (10 * 2) / 100 }

100 = P {  [ 1.1 ]2- 1-  0.2 }

100 = P * 0.01

P = 100 / 0.01 

P = 10000

Question no. 4:

A sum of Rs 25000 amounts to 31000 in 4 years at some rate of simple interest. find the rate percent.

Solution: 

Simple interest ( SI ) =	P * R * T
	100

P = 25000

T = 4 Years

Amount = 31000

SI = 31000 - 25000 = 6000

6000 =	25000 * R * 4
	100

R =	100 * 6000
	4 * 25000

R = 6 %

Tags: Simple interest problems, compound interest problems, SI and CI





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