SELINA Solutions for Class 9 Maths Chapter 3 - Compound Interest (Using Formula)

Learn more about interest and principal amount with the help of TopperLearning’s Selina Solutions for ICSE Class 9 Mathematics Chapter 3 Compound Interest using formula. In this chapter, learn how to apply a formula and calculate the compound interest or principal amount of a given problem.

Practise Selina textbook solutions to understand how to compute simple interest by using the available data on compound interest for a specific amount of money. As you revise the problems with reference solutions, your logical thinking skills for solving such problems will improve. This, in turn, will benefit you in applying Maths concepts for scoring higher marks in your final exam.

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Chapter 3 - Compound Interest (Using Formula) Exercise Ex. 3(A)

Question 1

Find the amount and the compound interest on Rs12,000 in 3years at 5% compounded annually.

Solution 1

Given : P= Rs12,000; n=3years and r=5%

Amount= Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula= Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

=Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

=Rs13,891.50 Ans.

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using FormulaC.I. =RS13,891.50 - Rs12,000

= Rs1,891.50 Ans.

Question 2

Calculate the amount of Rs15,000 is lent at compound interest for 2years and the rates for the successive years are 8% and 10% respectively.

Solution 2

Given : P= Rs15,000; n=2years; r1 =8% and r2 =10%

Amount=Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula=Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

=Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

=Rs17,820 Ans.

Question 3

Calculate the compound interest accrued on Rs6,000 in 3years, compounded yearly, if the rates for the successive years are 5%, 8% and 10% respectively.

Solution 3

Given : P=Rs6,000; n= 3years; r1= 5%; r2= 8% and r3 =10%

 

Amount=Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

=Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

=Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

=Rs7,484.40

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using FormulaC.I. = Rs7,484.40 - Rs6,000 = Rs1,484.40 Ans.

Question 4

What sum of money will amount to Rs5,445 in 2years at 10% per annum compound interest?

Solution 4

Given : Amount= Rs5,445; n= 2years and r = 10%

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula A= Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula 5,445= Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula 5,445= Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula P=Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula=Rs4,500 Ans.

Question 5

On what sum of money will the compound interest for 2years at 5% per annum amount to Rs768.75?

Solution 5

Given : C.I.= Rs768.75; n= 2years and r = 5%

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula A= Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula A= Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula A=Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula=Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula A - P =C.I

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula- P=Rs768.75

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula=Rs768.75

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula P=RsSelina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula Ans.

Question 6

Find the sum on which the compound interest for 3years at 10% per annum amounts to Rs1,655.

Solution 6

Given : C.I.= Rs1,655; n= 3years and r = 10%

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula A= Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula A= Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula A= Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula A - P =C.I

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula- P=Rs1,655

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula=Rs1,655

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula P=Rs Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula Ans.

Question 7

What principal will amount to Rs9,856 in two years, if the rates of interest for successive years are 10% and 12% respectively?

Solution 7

Given : Amount =Rs9,856; n=2years; r1 =10% and r2 =12%

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Ans.

Question 8

On a certain sum, the compound interest in 2 years amounts to Rs.4,240. If the rate of interest for the successive years is 10% and 15% respectively, find the sum.

Solution 8

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

 

 

The sum is Rs.16,000

Question 9

At what per cent per annum will Rs.6,000 amount to Rs.6,615 in 2 years when interest is compounded annually?

Solution 9

 

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

 

 

At 5% per annum the sum of Rs.6,000 amounts to Rs.6,615 in 2 years when the interest is compounded annually.

Question 10

At what rate per cent compound interest, does a sum of money become 1.44 times of itself in 2years?

Solution 10

Let Principal = Rs y

Then Amount= Rs 1.44y

n= 2years

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Question 11

At what rate per cent will a sum of Rs. 4,000 yield Rs. 1,324 as compound interest in 3 years?

Solution 11

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Question 12

A person invests Rs5,000 for three years at a certain rate of interest compounded annually. At the end of two years this sum amounts to Rs6,272. Calculate :

(i)the rate of interest per annum.

(ii)the amount at the end of the third year.

Solution 12

Given: P=Rs5,000; A=Rs6,272 and n= 2years

(i)

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

(ii) Amount at the third year

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Question 13

In how many years will Rs7,000 amount to Rs9,317 at 10% per annum compound interest?

Solution 13

Given : P=Rs7,000; A=Rs9,317 and r= 10%

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Question 14

Find the time, in years, in which Rs4,000 will produce Rs630.50 as compound interest at 5% compounded annually.

Solution 14

Given : P=Rs4,000; C.I.=Rs630.50 and r=5%

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Question 15

Divide Rs28,730 between A and B so that when their shares are lent out at 10% compound interest compounded per year, the amount that A receives in 3years is the same as what B receives in 5years.

Solution 15

Let share of A = Rs y

share of B = Rs (28,730 - y)

rate of interest= 10%

According to question

Amount of A in 3years= Amount of B in 5years

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Therefore share of A=Rs15,730

Share of B=Rs28,730 - Rs 15,730=Rs13,000

Question 16

A sum of Rs44,200 is divided between John and Smith, 12years and 14years old respectively, in such a way that if their portions be invested at 10% per annum compound interest, they will receive equal amounts on reaching 16 years of age.

(i)What is the share of each out of Rs44,200?

(ii)What will each receive, when 16years old?

Solution 16

(i)Let share of John = Rs y

share of Smith = Rs (44,200 - y)

rate of interest= 10%

According to question

Amount of John in 4years= Amount of Smith in 2years

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

 

Therefore share of John=Rs20,000

Share of Smith=Rs44,200- Rs 20,000=Rs24,200

(ii)Amount that each will receive

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Question 17

The simple interest on a certain sum of money and at 10% per annum is Rs. 6,000 in 2 years, Find:

  1. the sum.
  2. the amount due to the end of 3 years and at the same rate of interest compounded annually.
  3. the compound interest earned in 3 years. 
Solution 17

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Question 18

Find the difference between compound interest and simple interest on Rs. 8,000 in 2 years and at 5% per annum.

Solution 18

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Chapter 3 - Compound Interest (Using Formula) Exercise Ex. 3(B)

Question 1

The difference between simple interest and compound interest on a certain sum is Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula54.40 for 2 years at 8 per cent per annum. Find the sum.

Solution 1

Let principal (P) = x

R = 8%

T = 2 years

 

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

 Given, CI = SI = 54.40

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Thus, principal sum = Rs. 8500

 

Question 2

A sum of money, invested at compound interest, amounts to Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula19,360 in 2 years and to Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula23,425.60 in 4 years. Find the rate per cent and the original sum of money.

Solution 2

(for 2 years) A = Rs. 19360

T = 2 years

Let P = X

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula...(1)

A (for 4 years) = Rs. 23425.60

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula...(2)

(2) Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula(1)

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Form (1), we have

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

 Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Thus, sum = Rs. 16000

Question 3

A sum of money lent out at C.I. at a certain rate per annum becomes three times of itself in 8 years. Find in how many years will the money becomes twenty-seven times of itself at the same rate of interest p.a.

Solution 3

Let principal = x, A = 3x, T = 8 years, R = ?

Case I,

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Case II,

P = x, A = 27x, T = ?

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

From (1) and (2)

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Hence, time = 24 years.

Question 4

On what sum of money will compound interest (payable annually) for 2 years be the same as simple interest on Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula9,430 for 10 years, both at the rate of 5 per cent per annum?

Solution 4

P = Rs. 9430

R = 5%

R = 10 years

SI = Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Let sum = x

CI = 4715, T = 2 years, Rs= 5%

CI = A - P

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Thus principal from = Rs. 46,000

Question 5

Kamal and Anand each lent the same sum of money for 2 years at 5% at simple interest and compound interst respectively. Anand recived Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula15 more than Kamal. Find the amount of money lent by each and the interest received.

Solution 5

Let principal = Rs. 100, R = 5% T = 2 years

For Kamal, SI = Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

  

For Anand, Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula 

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

 CI = Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Difference of CI and SI = Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

 

When difference is Rs. Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula, then principal = Rs. 100

If difference is 1, principal = 100 Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula4

If difference is Rs, 15, principal = 100 Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula4 Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula15 = Rs. 6000


For kamal, interest = Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

 

For Anand, interest = Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Question 6

Simple interest on a sum of money for 2 years at 4% is Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula450. Find compound interest of the same sum and at the same rate for 2 years.

Solution 6

SI = Rs. 450

R = 4%

T = 2 years

P = ?

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula 

 

Now, P = 5625, R = 4%, T = 2 years

A = Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

CI = A - P = 6084 - 5625

= Rs. 459

Question 7

Simple interest on a certain sum of money for 4 years at 4% per annum exceeds the compound interest on the same sum for 3 years at 5 per cent per annum by Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula228. Find the sum.

Solution 7

Let principal (P), R = 4%, T = 4 years

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Given: SI - CI = Rs. 228

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Thus, Principal = Rs. 96000

Question 8

Compound interest on a certain sum of money at 5% per annum for two years is Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula246. Calculate simple interest on the same sum for 3 years at 6% per annum.

Solution 8

CI = Rs. 246, R = 5%, T = 2 years

CI = A - P

 

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula 

Now, P = Rs. 2400, R = 6%, T = 3 years

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Question 9

A certain sum of money amounts to Rs. 23,400 in 3 years at 10% per annum simple interest. Find the amount of the same sum in 2 years and at 10% p.a. compound interest.

 

Solution 9

Let the sum (principle) = x

Given Amount = 23400, R = 10% and T = 3 years

 

 Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Amount = Principle + Interest


23400 = x + Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula 

x = 18000


Principle = 18000


Now,


Principle = `18000, r = 10% and n = 2 years

 

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

 

The amount of the same sum in 2 years and at 10% p.a. compound interest is 21780.

Question 10

Mohit borrowed a certain sum at 5% per annum compound interest and cleared this loan by paying Rs. 12,600 at the end of the first year and Rs. 17,640 at the end of the second year. Find the sum borrowed.

Solution 10

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Chapter 3 - Compound Interest (Using Formula) Exercise Ex. 3(C)

Question 1

If the interest is compounded half-yearly, calculate the amount when principal is Rs7,400; the rate of interest is 5% per annum and the duration is one year.

Solution 1

Given: P=Rs7,400; r=5% p.a. and n= 1year

Since the interest is compounded half-yearly,

Then Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Question 2

Find the difference between the compound interest compounded yearly and half-yearly on Rs10,000 for 18 months at 10% per annum.

Solution 2

(i)When interest is compounded yearly

Given: P=Rs10,000; n=18months=Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formulayear and r=10%p.a.

For 1year

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using FormulaSelina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using FormulaSelina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using FormulaSelina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

 

For1/2 year

P=Rs11,000;n= 1/2 year and r=10%

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using FormulaSelina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using FormulaSelina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using FormulaC.I.= Rs11,550 - Rs10,000= Rs1,550

(ii)When interest is compounded half-yearly

P=Rs10,000; n= Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formulayear and r=10%p.a.

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using FormulaSelina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula C.I.= Rs11,576.25 - Rs10,000=Rs1,576.25

 

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using FormulaDifference between both C.I.= Rs1,576.25 - Rs1,550

= Rs26.25 Ans.

Question 3

A man borrowed Rs.16,000 for 3 years under the following terms:

20% simple interest for the first 2 years.

20% C.I. for the remaining one year on the amount due after 2 years, the interest being compounded half-yearly.

Find the total amount to be paid at the end of the three years.

Solution 3

 

 

For the first 2 years

 

 

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula 

 

 

Amount in the account at the end of the two years is Rs.22,400.

 

 

For the remaining one year

 

 

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula 

 

 

 

 

The total amount to be paid at the end of the three years is Rs.27,104.

 

 

Question 4

What sum of money will amount to Rs.27,783 in one and a half years at 10% per annum compounded half yearly?

Solution 4

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula 

 

 

The sum of Rs.24,000 amount Rs.27,783 in one and a half years at 10% per annum compounded half yearly.

Question 5

Ashok invests a certain sum of money at 20% per annum, compounded yearly. Geeta invests an equal amount of money at the same rate of interest per annum compounded half-yearly. If Geeta gets Rs33 more than Ashok in 18 months, calculate the money invested.

Solution 5

(i)For Ashok(interest is compounded yearly)

Let P=Rs y; n=18months=Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formulayear and r=20%p.a.

For 1year

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using FormulaSelina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using FormulaSelina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

For1/2 year

PSelina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula;n= ½ year and r=20%

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using FormulaSelina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using FormulaSelina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

(ii)For Geeta(interest is compounded half-yearly)

P=Rs y; n= Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formulayear and r=20%p.a.

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using FormulaSelina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using FormulaSelina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

According to question

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using FormulaSelina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using FormulaMoney invested by each person=Rs3,000 Ans.

Question 6

At what rate of interest per annum will a sum of Rs.62,500 earn a compound interest of Rs.5,100 in one year? The interest is to be compounded half yearly.

Solution 6

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula 

 

 

The rate of interest is 8%.

Question 7

In what time will Rs1,500 yield Rs496.50 as compound interest at 20% per year compounded half-yearly?

Solution 7

Given: P=Rs1,500; C.I.=Rs496.50 and r=20%

Since interest is compounded semi-annually

Then Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula Ans.

Question 8

Calculate the C.I. on Rs3,500 at 6% per annum for 3years, the interest being compounded half-yearly.

Do not use mathematical tables. Use the necessary information from the following:

(1.06)3 =1.191016; (1.03)3 = 1.092727

(1.06)6 =1.418519; (1.03)6 = 1.194052

Solution 8

Given: P=Rs 3,500; r=6% and n= 3years

Since interest is being compounded half-yearly

Then Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Ans.

Question 9

Find the difference between compound interest and simple interest on Rs12,000 and in Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula years at 10% compounded yearly.

Solution 9

Given: P=Rs12,000; n= Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula years and r= 10%

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

To calculate C.I.

For 1 year

P=Rs 12,000; n=1 year and r=10%

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

For next 1/2 year

P=Rs 13,200; n= 1/2 year and r=10%

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula C.I. = Rs 13,860 - Rs 12,000= Rs 1,860

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using FormulaDifference between C.I. and S.I

= Rs 1,860 - Rs 1,800=Rs 60 Ans.

Question 10

Find the difference between compound interest and simple interest on Rs12,000 and in Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula years at 10% compounded half-yearly.

Solution 10

Given: P=Rs12,000; n= Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula years and r= 10% Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

To calculate C.I.(compounded half-yearly)

P=Rs12,000;n=Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula and r=10%

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula C.I.Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula - Rs12,000= Rs1,891.50

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using FormulaDifference between C.I. and S.I

=Rs1,891.50 - Rs1,800=Rs91.50 Ans.

Chapter 3 - Compound Interest (Using Formula) Exercise Ex. 3(D)

Question 1

The cost of a machine is supposed to depreciate each year at 12% of its value at the beginning of the year. If the machine is valued at Rs44,000 at the beginning of 2008, find its value :

(i)at the end of 2009.

(ii)at the beginning of 2007.

Solution 1

Cost of machine in 2008 = Rs44,000

Depreciation rate=12%

(i) Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula Cost of machine at the end of 2009

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

(ii) Cost of machine at the beginning of 2007(P)

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Question 2

The value of an article decreases for two years at the rate of 10% per year and then in the third year it increases by 10%. Find the original value of the article, if its value at the end of 3 years is Rs.40,095.

Solution 2

Let x be the value of the article.

 

 

The value of an article decreases for two years at the rate of 10% per year.

 

 

The value of the article at the end of the 1st year is

X - 10% of x = 0.90x

 

 

The value of the article at the end of the 2nd year is

0.90x - 10% of (0.90x) = 0.81x

 

 

The value of the article increases in the 3rd year by 10%.

 

 

The value of the article at the end of 3rd  year is

0.81x + 10% of (0.81x) = 0.891x

 

 

The value of the article at the end of 3 years is Rs.40,095.

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

 

 

The original value of the article is Rs.45,000.

Question 3

According to a census taken towards the end of the year 2009, the population of a rural town was found to be 64,000. The census authority also found that the population of this particular town had a growth of 5% per annum. In how many years after 2009 did the population of this town reach 74,088 ?

Solution 3

Population in 2009 (P) = 64,000

Let after n years its population be 74,088(A)

Growth rate= 5% per annum

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Ans.

Question 4

The population of a town decreased by 12% during 1998 and then increased by 8% during 1999. Find the population of the town, at the beginning of 1998, if at the end of 1999 its population was 2,85,120.

Solution 4

Let the population in the beginning of 1998 = P

The population at the end of 1999 = 2,85,120(A)

r1 = - 12% and r2 = +8%

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula Ans.

Question 5

A sum of money, invested at compound interest, amounts to Rs 16,500 in 1 year and to Rs19,965 in 3 years. Find the rate per cent and the original sum of money invested.

Solution 5

Let sum of money be Rs P and rate of interest= r%

Money after 1year= Rs16,500

Money after 3years=Rs19,965

For 1year

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

For 3years

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Divide eqn (2) by eqn (1)

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

On comparing, we get

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula r= 10% Ans.

Put value of r in eqn (1)

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula Ans

Question 6

The difference between C.I. and S.I. on Rs7,500 for two years is Rs12 at the same rate of interest per annum. Find the rate of interest.

Solution 6

Given: P = Rs 7,500 and Time(n)= 2 years

Let rate of interest = y%

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Given: C.I. - S.I. = Rs 12

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula Ans.

Question 7

A sum of money lent out at C.I. at a certain rate per annum becomes three times of itself in 10years. Find in how many years will the money become twenty-seven times of itself at the same rate of interest p.a.

Solution 7

Let Principal be Rs y and rate= r%

According to 1st condition

Amount in 10 years = Rs 3y

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

According to 2nd condition

Let after n years amount will be Rs 27y

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Question 8

Mr. Sharma borrowed a certain sum of money at 10% per annum compounded annually. If by paying Rs.19,360 at the end of the second year and Rs.31,944 at the end of the third year he clears the debt; find the sum borrowed by him.

Solution 8

At the end of the two years the amount is

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

 

 

Mr. Sharma paid Rs.19,360 at the end of the second year.

So for the third year the principal is A1 - 19,360.

Also he cleared the debt by paying Rs.31,944 at the end of the third year.

 

 

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

 

 

Mr. Sharma borrowed Rs.40,000.

Question 9

The difference between compound interest for a year payable half-yearly and simple interest on a certain sum of money lent out at 10% for a year is Rs15. Find the sum of money lent out.

Solution 9

Let sum of money be RS y

To calculate S.I.

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

To calculate C.I.(compounded half-yearly)

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula


Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Question 10

The ages of Pramod and Rohit are 16 years and 18 years respectively. In what ratio must they invest money at 5% p.a. compounded yearly so that both get the same sum on attaining the age of 25 years?

Solution 10

Let Rs.x and Rs.y be the money invested by Pramod and Rohit respectively such that they will get the same sum on attaining the age of 25 years.

 

 

Pramod will attain the age of 25 years  after 25 - 16 = 9 years

 

 

Rohit will attain the age of 25 years  after 25 -18 = 7 years

 

 

 Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

 

 

Pramod and Rohit should invest in 400:441 ratio respectively such that they will get the same sum on attaining the age of 25 years.

Chapter 3 - Compound Interest (Using Formula) Exercise Ex. 3(E)

Question 1

Simple interest on a sum of money for 2 years at 4% is Rs.450. Find compound interest on the same sum and at the same rate for 1 year, if the interest is reckoned half yearly.

Solution 1

1st case

Given: S.I. = Rs 450;Time= 2 years and Rate = 4%

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

2nd case(compounded half-yearly)

 P = Rs.5,625;n= 1 year and r = 4%

  Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

  Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Question 2

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Solution 2

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

 For 2years

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

For ½ year

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using FormulaC.I. = A - P = Rs.13,721 - Rs.10,800 = Rs.2,921 

 

 

Question 3

The value of a machine, purchased two years ago, depreciates at the annual rate of 10%. If its present value is Rs.97,200, find:

  i.  Its value after 2 years.

  ii.  Its value when it was purchased.

Solution 3

(i) Present value of machine(P) =  Rs.97,200

 Depreciation rate = 10%

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

                                                                    =Rs.78732 

(ii) Present value of machine(A) = Rs.97,200

Depreciation rate = 10% and time = 2 years

 To calculate the cost 2 years ago

 Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

 

 

Question 4

Anuj and Rajesh each lent the same sum of money for 2 years at 8% simple interest and compound interest respectively. Rajesh received Rs.64 more than Anuj. Find the money lent by each and interest received.

Solution 4

Let the sum of money lent by both Rs.y

For Anuj

P = Rs.y ;rate = 8% and time = 2 years

  Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

 For Rajesh

 P = Rs.y ;rate = 8% and time = 2 years

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Given :  C.I. - S.I. = Rs.64

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula 

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula 

Question 5

Calculate the sum of money on which the compound interest (payable annually) for 2 years be four times the simple interest on Rs.4,715 for 5 years, both at the rate of 5% per annum.

Solution 5

Given: Principal = Rs.4,715;time = 5 years and rate= 5% p.a.

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Then C.I. = Rs.1,178.75 x 4 = Rs.4,715

Time = 2 years and rate = 5%

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Question 6

A sum of money was invested for 3 years, interest being compounded annually. The rates for successive years were 10%, 15% and 18% respectively. If the compound interest for the second year amounted to Rs.4,950, find the sum invested.

Solution 6

Given: C.I. for the 2nd year = Rs.4,950 and rate = 15%

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

  Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula 

 

 

Then amount at the end of 2nd year= Rs.33,000

 For first 2years

 A = Rs.33,000; r1 =10%

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

  Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

The sum invested is Rs.30,000.

Question 7

A sum of money is invested at 10% per annum compounded half yearly. If the difference of amounts at the end of 6 months and 12 months is Rs.189, find the sum of money invested.

Solution 7

Let the sum of money be Rs.y

and rate = 10% p.a. compounded half yearly

 For first 6months

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

 For first 12 months

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Given: The difference between the above amounts = Rs.189

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

y = 3600

Question 8

Rohit borrows Rs.86,000 from Arun for two years at 5% per annum simple interest. He immediately lends out this money to Akshay at 5% compound interest compounded annually for the same period. Calculate Rohit's profit in the transaction at the end of two years.

Solution 8

P = Rs.86,000;time = 2 years and rate = 5% p.a.

To calculate S.I.

  Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

 To calculate C.I.

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

 Profit = C.I. - S.I. = Rs.8,815 - Rs.8,600 = Rs.215

Question 9

The simple interest on a certain sum of money for 3 years at 5% per annum is Rs.1,200. Find the amount and the compound interest due on this sum of money at the same rate and after 2 years. Interest is reckoned annually.

Solution 9

Let Rs.x be the sum of money.

Rate = 5 % p.a. Simple interest = Rs.1,200, n = 3years.

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

The amount due and the compound interest on this sum of money at the same rate and after 2 years.

 P = Rs.8,000;rate = 5% p.a., n = 3 years

  Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

 

The amount due after 2 years is Rs.8,820 and the compound interest is Rs.820.

Question 10

Nikita invests Rs.6,000 for two years at a certain rate of interest compounded annually. At the end of first year it amounts to Rs.6,720. Calculate:

(a) The rate of interest.

(b) The amount at the end of the second year.

Solution 10

Let x% be the rate of interest.

 

 

P = Rs.6,000, n = 2 years, A = Rs.6,720

 

 

  1. For the first year

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

 

 

The rate of interest is x% = 12%.

  1. The amount at the end of the second year.

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Using Formula

 

 

The amount at the end of the second year = Rs.7,526.40