## SIMPLE INTEREST FORMULA

**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:- *

- A) Principal (P):-The money borrowed by a borrower from a lender is known as the Principal or sum.
- B) Interest(I):-The additional money paid by the borrower to the lender for having used his money is called the interest.
- C) Simple interest (SI):-If interest is calculated uniformly on the original principal throughout the loan period, it is called simple interest.
- 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.**

*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 2^{1}/_{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= 2^{1}/_{2}years = 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 2 ^{1}/_{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 = 2^{1}/_{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 x^{2} )/100

x^{2}= (686X 100)/1400

x^{2 }= 49

√x^{2 }= √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 4 ^{1}/_{2} years.*

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

Time (T)= 4^{1} /_{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 4 ^{1}/_{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 8^{1}/_{3 }years sum will be doubled.

*19) Find S.I. in Rs. 7200 at 7 ^{1}/_{2} % for 10 months.*

* *

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

Rate of interest ( R) = 7^{1}/_{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, a**^{2} = (49X100)/81

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

a= (7X10)/9

Therefore, time = 7^{7}/_{9 }years and rate of interest = 7^{7}/_{9}%.

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