INTRODUCTION: When a borrower borrows some money ( principal) from a lender or bank he or she also makes a promise to return it after a specified period of time. At the end of the specified period (time), the borrower has not only to pay the money which he had borrowed but also to pay some additional money (interest) for using lender’s money.

SOME DEFINITIONS:-

1. A) Principal (P):-The money borrowed by a borrower from a lender is known as the Principal or sum.
2. B) Interest(I):-The additional money paid by the borrower to the lender for having used his money is called the interest.
3. C) Simple interest (SI):-If interest is calculated uniformly on the original principal throughout the loan period, it is called simple interest.
4. D) Amount (A):- The total money which the borrower pays back to the lender at the end of the specified period is called the amount.

From the above definition we can say

AMOUNT = PRINCIPAL + INTEREST

OR A=P+I

So, if ₹P is the principal and the interest rate is R% per annum, then

Interest on ₹100 for 1 year = ₹R

Interest on Re 1 for 1 year = ₹( R/100)XT

Hence, interest on ₹P for T years = (₹ R/100)XTXP

=₹ (PXRXT)/100

Here are some examples to illustrate the calculations of interest and amount.

1. A sum of ₹800 is lent for one year at the rate of 18% per annum. Find the interest.

 

Solution: Here we have,

P= principal = ₹800

R= rate of interest = 18% per annum.

T= time = 1 year

Let SI be the interest, then

SI = (PXRXT)/100

=(800X18X1)/100

=8X18 = ₹144

Therefore, simple interest of ₹800 for one year is ₹144.

2.Anita borrowed ₹400 from her friend at the rate of 12% per annum for 2¹/₂ Find the interest and amount paid by her.

 

Solution: Here we have,

P= principal = ₹400

R= rate of interest= 12% per annum.

T= time= 2¹/₂years = 5/2 years.

Let SI = (PXRXT)/100

=₹ (400X12X5) / ( 2X100)

= 2X12X5

=₹120.

Hence, Amount = Principal + Interest

=₹400+ ₹120

=₹520

Therefore, interest is ₹120 ;amount paid is ₹520 by Anita.

3.A farmer borrowed ₹2400 at 12% interest per annum. After 2¹/₂  years, he had paid Rs.1200 and offered a cow to clear his account. Find the cost of the cow.

 

Solution: Here we have,

P= principal = ₹2400

R=rate of interest = 12% per annum

T= time = 2¹/₂ years= 5/2 years.

Let SI be the interest, then

SI= (PXRXT)/100

= ₹( 2400X12X5)/ (2X100)

=₹( 24X6X5)

= ₹720.

Amount = P+I = ₹( 2400 + 720)

=₹3120

Also Amount = ₹1200 + cost of the cow

₹3120 = ₹1200+ cost of cow

So, cost of  the cow = ₹( 3120 – 1200)

=₹1920.

Therefore, the cost of cow is ₹1920.

4.Find the interest on ₹1200 at 6% per annum for 146 days.

Solution: here we have,

P= principal = ₹1200

R= rate of interest= 6% per annum

T= time = 146 days = 146/365 years= 2/5 years.

Let SI  be the interest , then

SI = PXRXT/100

= ₹( 1200X6X2)/ (100X5)

= 144/5

= ₹28.80

Therefore, simple interest of ₹1200 for 146 days is ₹28.80.

5.Fatima donates ₹2000 to a school, the interest on which is to be used for awarding  5 scholarships of equal value every year. If the Fatimar  gets an interest of 10% per year, find the value of each  and every scholarship.

 

Solution: here we have,

P= principal = ₹2000

R=rate of interest = 10% per annum

T = time= 1 year

Let SI be the interest, then

SI= PXRXT/100

= ₹ ( 2000X10X1)/100

=₹200

This interest is to be ivided into 5 equal parts,

=₹( 200/5)

= ₹40

Therefore, value of each scholarship is ₹40.

6.In how many years will ₹750 amount to ₹900 at 4% per annum?

 

 

Solution: here we have,

P=principal = ₹750

R= rate of interest = 4% per annum

A= amount = ₹900

Let time be T years in which ₹750 will be amount to ₹900 at 4% per annum.

Now: Interest = Amount – Principal

= ₹( 900 – 750)

= ₹150

So SI = PXRXT/100

Or 150 = (750x4XT)/100

Or T = ( 150X100)/ ( 750X 4)

= (2X10)/4

= 5 Yars.

Therefore, ₹750 amounts to ₹900 at 4% per annum in 5 years.

7.A sum of money doubles itself in 8 years. What is the rate of interest?

 

Solutions, here we have,

Let the Principal be ₹P

Also the rate of interest be R% per annum

Since the money doubles itself in 8 years

So it becomes ₹2P in 8 years

 

SI= Amount – Principal

=₹( 2P-P)

=₹P

Now

SI = PXRXT/100

P= PXRX8/100

8PR = 100P

R= 100P/8P

=25/2

12.5

Therefore, the rate of interest is 12.5% per annum.

8.Sharma deposited ₹20,000 as a fixed depositin a bank at 10% per annum. If 30%of earned interest is decreased as deduction for  Income tax , find his annual income.

 Solution: here we have

Let SI  be the simple interest

P=principal = ₹20,000

R= rate of interest= 10%

T= time= 1 year

 

SI = PXRXT/100

= (20000X10X1) / 100

= ₹2000

According to the question, 30% of interest will be deducted,

So 2000 of 30%

= (2000X 30)/100

= ₹600

He will get ₹( 2000-600)

= ₹1400

Therefore, annual income of Mr. Sharma ‘s annual income is ₹1400.

 

9.How much time will it take for an amount of ₹900 to yield ₹81 as interest at 4.5% per annum of simple interest?

A)2 years B)3 Years C) 1 years D) 4 Years

 

Solution: T= (SI X 100)/PXR

= (81X 100)/ (900X 4.5)

=2

Ans: A) 2 years.

10.Arun took a loan of ₹1400 with simple interest for as many years as the rate of interest.  At the end of the loan period, if he paid  ₹686 as an  interest , what was the rate of interest?

A)8%  B) 6% C)4%  D) 7%

 

 

Solution: let R = P = x

₹686 = (1400X x² )/100

x²= (686X 100)/1400

x² = 49

√x² = √49

x= 7

Ans: D) 7%

11) Find the interest on Rs.500 for a period of 4 years at the rate of 8% perannum, also find the amount to be paid at the end of the period.

Ans:- We have principal (p) = Rs.500

Time (T)= 4   years

Rate of interest (R)= 8%p.a.

So

S.I.= PXRXT/100

=500X8X4/100

=Rs.160

Amount= P+S.I.

A= 500+160

=Rs.660

Therefore, the interest Rs. 160, and amount will be Rs. 660.

12)  A sum of Rs.400 is lent at the rate of 5% per annum.  After 2 years what will be the simple interest?

Ans:-  We have principal (P) = Rs. 400

Time (T)= 2 years

Rate of interest  (R)= 5%

So

S.I.= PXRXT/100

=400X2X5/100

=Rs.40

Therefore, the interest after 2 years will be Rs.40.

13) A person deposits Rs.30,000 in a firm who pays interest at the rate of 15%  per annum.calculate the income he gets from it annually.

Ans:-  We have principal (P)= Rs. 30000

Time (T)= 1 year

 

So

S.I. = PXRXT/100

= 30000X1X15/100

=Rs.450

Therefore, he gets annually Rs. 4500

14) A man borrowed Rs. 10,000 from a bank at 10% per annum. Find the amount hy will pay after 4¹/₂ years.

Ans:- We have principal (P)= Rs. 10,000

Time (T)= 4¹ /₂ years =  9/2 yea

So

S.I. = PXRXT/100

10000X(9/2)X10/100

Rs. 4500

Total amount = 4500+ 10,000 = Rs. 14,5000

After the 4¹/₂  years, he will pay 14,500

15) Rashida took a loan of Rs. 12,000 from a money lender, who charged interest at the rate of 12% per annum. After  3 years, Rashida paid him  Rs15000 and her pet goat to clear her debt. What is the price of the goat?

Ans:- We have  principal (P) =  Rs.12,000

Time = 3 years

Rate of interest  (R)= 12%

S.I.= PXRXT/100

= 12000X3X12/100

=Rs.4320

After 3 years she paid Rs.15,000 ; but  she had to pay (12,000 + 4320)=  Rs.16,320

So balance amount is ( 16320- 15000)= Rs.1320 which she paid as goat instead.

Therefore , the   price of goat is  Rs.1320.

 

16) Find simple interest on Rs.15000 at 12% p.a. for 73 days.

Ans:- We have principal (P) = Rs.15000

Time (T) = 73 days = 73/365 years = 1/5 years

Rate of interest = (R )= 12%

S.I. = PXRXT/100

= 15000X12X1/100X5 = Rs. 360

Therefore, simple interest of 73 days will be Rs. 360.

 

17) A sum when reckoned at 15% S.I. amounts to Rs.2800 in 5 years. Find the sum.

Ans:- We have Rate of interest ( R) = 15%

Time = 5 years

And let the principal be Rs. P

So

S.I.= PX15X5/100 = 3P/4

Total amount = P+ 3P/4 =7P/4

According to the question ; 7P/4= 2800

Or P= 1600

Therefore, the sum is Rs.1600

 

18) At  what rate of simple interest  a certain sum will be doubled in 12 years?

 

Ans:- Let the principal be P

 

Time (T)= 12 years ; after this sum will be 2P

After 12 years the S.I. = PXRX12/100 = 3PR/25

So the amount will be P+ 3PR/25 = (25P+ 3PR)/25

Acording to the question; (25P + 3PR)/25 = 2P as the sum will be doubled.

25P+ 3PR = 50P

Or 3PR= 50P- 25P

Or 3PR = 25P

Or 3R= 25

Or  R = 25/3= 8 ¹/₃ Years.

Therefore , after 8¹/₃ years sum will be doubled.

 

19)  Find S.I. in Rs. 7200 at 7¹/₂ % for 10 months.

 

Ans :-  We have Principal (P) =Rs.7200

Rate of interest  ( R) = 7¹/₂% = 15/2 %

Time ( T) = 10 months = 10/12= 5/6 years.

So S.I. = PXRXT/100

 

Therefore, after 10 months the S.I. will be Rs. 950.

 

20) Simple interest on a certain sum is 49/81 of the sum.  If the rate of interest and time is same then find both rate and time period.

Ans:-   Let the rate of interest and time  (as both are same) =a

And principal be Rs.P.

S.I. = 49P/81

S.I.= PXRXT/100 = PXaXa/100 = 49P/81

So, a² = (49X100)/81

a= {(49X100)/81}^1/2

a= (7X10)/9

Therefore, time = 7⁷/₉ years and rate of interest  = 7⁷/₉%.