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Simple Interest and Compound Interest Important Concepts

By GovJobAdda, Bengaluru 2 years ago 3602 Views

First you should have an understanding of the term Interest .

Interest is defined as the cost of borrowing money, and depending on how it is calculated, can be classified as Simple Interest or Compound Interest.

Principal - The money borrowed or given for certain period is called the principal or the Sum. It is also referred to the original sum of money borrowed in a loan, or put into an investment.

Basically Simple Interest is the interest calculated on the Principal, or original sum of money borrowed/deposited. 
It is fixed for the term of the loan/deposit. 
It is generally lower than compound interest, keeping other things same.



Let Principal = P, Rate = r % per annum (p.a.), and Time = t years then

Simple Interest(SI)= ((P×r×t))/100  
 
Using this formula we can also find out 
P=(100×SI)/(r×t);
 
r=(100×SI)/(P×t);
 
t=(100×SI)/(P×r).

Whereas, Compound Interest is the interest calculated on the outstanding amount, that is, the principal plus the unpaid interest.
It varies for the term of the deposit.
It is generally higher than simple interest, keeping other things same.

Amount = Principal + Interest 
 
A= P (1+r/100) ^n 
 
A= Amount, 
P= Principal, 
r= Rate %, 
n= no. of years.
So Compound Interest = [P (1+r/100) ^ n - P] 
= P [(1+r/100) ^ n – 1]



Let us consider a simple example:

Suppose you deposit Rs.1000 in bank in July,2017 at annual rate of 5%

a. How much will you have 5 years later using Simple Interest?

b. How much will you have 5 years later using Compound Interest?

Solution: 

a.Principal is Rs.1000

Simple interest is only earned on principal.

So for one year interest earned is (1000)*(0.05)= Rs.50

End of year 1= Rs.1000+50 

For the next year again SI will be calculated on the original principal i.e. on Rs.1000 and you will earn the same interest as the first year.

End of year 2 amount you have in bank =Rs. (1050+50)= Rs.1100 

So at the end of 5 years amount you have in bank is (Rs. 1000+250) = Rs.1250

 

b. Starting principal is Rs.1000

End of year 1= Rs. 1000 + (1000*0.05) = Rs.1050

Now at the end of year 1 your principal for next year will be Rs.1050

End of year 2= 1050 + (1050*0.05) = Rs. 1102.50

End of year 3 = 1102.5 +(1102.5*0.05) =Rs.1157.6

End of year 4 =  1157.5 +(1157.5*0.05) =Rs.1215.48

End of year 5 amount in bank will be= Rs.1276.254

So from the above example you observe that the interest earned is more on compound interest than Simple Interest as you calculate interest on a larger principal amount.

Compound interest works to your advantage when you're an investor but works against you when you're a borrower

Formulas and conditions to remember

1.When  interest is compounded annually, 

Amount = P(1+r/100)^n
 
2.When interest  is compounded half yearly,
Amount = P(1+(r/2)/100)^2n
 
3.When interest is compounded Quarterly,
Amount =P(1+(r/4)/100)^4n
 
4.When interest is compounded annually but time is in fraction, say 3 whole 2/5 year 
Amount = P(1+r/100)^3×(1+(2r/5)/100)
 
5.When Rates are different for different years, say r1%, r2%, and r3% for 1st, 2nd and 3rd year respectively.
 
Then,    
Amount = P(1+r1/100)×(1+r2/100)×(1+r3/100).
 
Present worth of Rs. x due n years hence is given by:
                                         
Present Worth = x/(1+r/100)
 
Difference between Compound Interest & Simple interest Concept For Two years
 
CI – SI =P(r/100)^2
 
For Two year 
CI/SI=(200+r)/200 
 
For Three Year
CI – SI =P(r^2/(100^2 ))×(300+r)/100)



Now, that you know how to calculate interest, it's going to be a cakewalk to solve questions that appear on how to calculate simple interest and compound interest. Also you will easily be able to solve questions on how to find the amount, principal, rate of interest or the time period that was taken to return the money by just substituting the values in these formulas.

Examples for practice:

1.Anil deposited some money in bank. The sum of money at simple interest amounted to Rs. 815 in 3 years and to Rs. 854 in 4 years. The sum is:

A) Rs. 720

B) Rs. 698

C) Rs. 678

D) Rs. 696

E) none of these

 

2.The sum of money Mira deposited fetched a total simple interest of Rs. 4016.25 at the rate of 9 % p.a. in 5 years. What is the sum she deposited?

A) Rs.  8045

B) Rs.  8925

C) Rs. 8900

D) Rs. 8032.45

E) none of these

 

3.Find the rate of interest when the sum of money amounts to Rs. 9800 after 5 years and Rs. 12005 after 8 years at the same rate of simple interest

A) 12 %

B) 13 %

C) 8 % 

D) 12.5 %

 

4.Ajit borrows Rs. 5000 for 2 years at 4% p.a. simple interest. He immediately lends it to another person at 6.25% p.a. for 2 years.What is his gain in transaction per year.

A) Rs. 112.50

B) Rs. 175

C) Rs.  150

D) Rs. 125.50 

 

5.Divya took loan from a bank at the rate of 12% p.a. simple interest. After 3 years she had to pay Rs. 5400 interest only for the period.The principal amount borrowed by her was:

A) Rs.  12000

B) Rs.15000 

C) Rs.  12500

 D) Rs. 22000

 

6.Find the time taken for an amount of Rs. 450 to yield Rs. 81 as interest at 4.5% per annum of simple interest?

A)3 year

B)4 year

C)5 year

D)6 year

 

7.Ramya took a loan of Rs. 1200 with simple interest for as many years as the rate of interest.If she paid Rs. 432 as interest at the end of the loan period, what was the rate of interest?

A)3.6

B) 5

C) 6

D)25

 

8.If you lent Rs. 5000 to A for 2 years and Rs. 3000 to B for 4 years on simple interest at the same rate of interest and received Rs. 2200 in all from both of them as interest. The rate of interest per annum is:

A) 5 %

B) 7% 

C)10 %

D) 12%

 

9.A bank offers 5% compound interest calculated on half-yearly basis. If you deposited  Rs. 1600 each on 1st January and 1st July of a year. 

At the end of the year, what amount you would have gained by way of interest is:

A)123 

B) 122

C)121  

D)120   

 

10.The compound interest on Rs. 30,000 at 7% per annum is Rs. 4347. What I :

A)2.5 

B) 2

C) 3

D)  4 

E) none of these

 

11.What is the rate of compound interest per annum will be if a sum of Rs. 1200 becomes Rs. 1348.32 in 2 years?

A)8 % 

B) 9%

C) 6 %

 D) 8.5 %

E) none of these

 

12.The difference between simple interest and compound on Rs. 1200 for one year at 10% per annum computed half-yearly is:

A)Rs. 3 

B) Rs. 4 

C) Rs. 3.5

D) Rs. 7.5

E) none of these

 

13.What is the minimm number of complete years in which a sum of money which is put out at 20% compound interest will be more than doubled is:

A) 4

B) 5

C) 6

 D) 2.5

E) none of these

 

14.Find compound interest on a sum of Rs. 25,000 after 3 years at the rate of 12 % per annum.?A) Rs.10123.20

B) Rs. 9000

C) Rs. 12000

D) Rs. 10163.34

E) none of these

 

15.The SI on a certain sum of money for 3 years at 8% per annum is half the compound interest on Rs. 4000 for 2 years at 10% per annum. What is the sum placed on simple interest?

A)Rs. 1650

B)Rs. 2000

C)Rs. 1750

D) Rs.1550

E) none of these


Anwers:

1.B

2.B

3.A

4.A

5.B

6.B

7.C

8.C

9.C

10.B

11.C

12.A

13.A

14.A

15.C



Explanation

1.S.I. for 1 year = Rs. (854 - 815) = Rs. 39.

S.I. for 3 years = Rs.(39 x 3) = Rs. 117.

Principal = Rs. (815 - 117) = Rs. 698.

 

2.Sum = (100× S.I.)/ r × t

= (100 × 4016.25)/ 9 × 5 = Rs. 8925 

 

3.S.I. for 3 years = Rs. (12005 - 9800) = Rs. 2205.

S.I. for 5 years= Rs. 3675

Principal = Rs. (9800 - 3675) = Rs. 6125 

Hence Rate = {(100 × 3675) / 6125 × 5} % = 12 %

 

4.Gain in 2 years = Rs. [{(5000×6.25×2)/100} – {(5000×4×2)/100}] 

 = Rs. (625- 400) = Rs. 225.

So gain in 1 year = Rs.225/ 2 = Rs. 112.50

 

5.Principal = Rs. {(100× 5400)/ (12×3)} = Rs.15000.

 

6.Time =(100×81)/ (450×4.5) years = 4 years

 

7.Let rate = r% and  time = r years

  Then (1200×r×r)/100= 432

  12 r^2= 432

  r=6 %

 

8.Let the rate be r% p.a.

Then,(5000 x r x 2)/100 +(3000 x r x 4)/100 = 2200.

100R + 120R = 2200

  R = 2200/220= 10.

 Rate = 10%.

9.Amount  = Rs. [1600×(1+ 5/200)^2 + 1600 × (1+5/200)]

  = Rs. 3321

So  CI = Amount- Principal 

 = Rs. 3321 – Rs. 3200 = Rs. 121

 

10.Amount = Rs. (30000 + 4347) = Rs. 34347,

Let the time be n years then 

30000(1+7/100) ^n = 34347

(107/100) ^n = 34347/30000

So n= 2 year.

 

11.Let rate r % per annum 

1200× (1+r/100) ^ 2 = 1348.32

(1+r/100) ^ 2 = 1348.32/1200

1+r/100 = 106 / 100

r= 6 %

 

12.SI =Rs. (1200 ×10×1)/100= Rs. 120 

CI = Rs.[ 1200×(1+5/100) ^2 - 1200] = Rs.123

So CI-SI = Rs. 3

 

13.P(1+20/100) ^n > 2P

(6/5)^ n >2 

(6/5×6/5×6/5×6/5)>2 

so n = 4 years

14.Amount=  Rs. 25000(1+12/100)^3= 35123.20

So CI= Rs. (35123.20 - 25000) = Rs. 10123.20

 

15.C.I.= Rs. 4000(1+10/100)^2 – 40

= Rs. 840

Sum= Rs. (420 × 100)/(3×8) = Rs. 1750

 

Let us know if this blog was helpful to understand the concept of SI and CI!

Happy learning!



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