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

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

Solution 1(a)

Correct option: (i)

When the interest is compounded yearly, the formula for finding the amount is  . 

Solution 1(b)

Correct option: (ii)   

When the rates for successive years are different then,

 . 

Solution 1(d)

Correct option: (iii) Rs. 5000 

Solution 1(e)

Correct option: (iv) Rs. 5500 

  

Solution 1(f)

Correct option: (i) 15% 

  

Solution 1(g)

Correct option: (ii) 15%

A = Rs. 5017.60, P = Rs. 4000. T = 2 months =   

  

Solution 2

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

Amount= =

=

=Rs13,891.50 Ans.

C.I. =RS13,891.50 - Rs12,000

= Rs1,891.50 Ans.

Solution 3

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

Amount==

=

=Rs17,820 Ans.

Solution 4

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

 

Amount=

=

=

=Rs7,484.40

C.I. = Rs7,484.40 - Rs6,000 = Rs1,484.40 Ans.

Solution 5

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

A=

5,445=

5,445=

P==Rs4,500 Ans.

Solution 6

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

A=

A=

A==

A - P =C.I

- P=Rs768.75

=Rs768.75

P=Rs Ans.

Solution 7

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

A=

A=

A=

A - P =C.I

- P=Rs1,655

=Rs1,655

P=Rs Ans.

Solution 8

 

 

 

 

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

Solution 9

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

Ans.

Solution 10

 

 

The sum is Rs.16,000

Solution 11

Let Principal = Rs y

Then Amount= Rs 1.44y

n= 2years

Solution 12

Solution 13

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

(i)

(ii) Amount at the third year

Solution 14

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

Solution 15

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

Solution 16

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

Therefore share of A=Rs15,730

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

Solution 17

(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

 

Therefore share of John=Rs20,000

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

(ii)Amount that each will receive

Solution 18

Solution 19

Solution 1(c)

Correct option: (i) Rs. 615

P = Rs. 6000, n = 2 years, r = 5%

C.I. = A – P = Rs. 6615 – Rs. 6000 = Rs. 615

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

Solution 1(a)

Correct option: (iii) Rs. 60

Difference between C.I. and S.I. = Rs. 1260 - Rs. 1200 = Rs. 60

Solution 1(b)

Correct option: (iv) 25%

Solution 1(c)

Correct option: (ii) Rs. 7,040

Solution 1(d)

Correct option: (ii) Rs. 6,400

Solution 1(e)

Correct option: (i) Rs. 640

Difference between C.I. and S.I. in 2 years = Rs. 7040 - Rs. 6400 = Rs. 640

Solution 2

Let principal (P) = x

R = 8%

T = 2 years

 Given, CI - SI = 54.40

Thus, principal sum = Rs. 8500

Solution 3

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

For Kamal, SI =

  

For Anand, straight A equals straight P open parentheses 1 plus straight R over 100 close parentheses to the power of straight T 

 CI = 441 over 4 minus 100 equals 41 over 4

Difference of CI and SI =

 

When difference is Rs. , then principal = Rs. 100

If difference is 1, principal = 100 4

If difference is Rs, 15, principal = 100 4 15 = Rs. 6000


For kamal, interest =

 

For Anand, interest =

Solution 4

SI = Rs. 450

R = 4%

T = 2 years

P = ?

 

 

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

A =

CI = A - P = 6084 - 5625

= Rs. 459

Solution 5

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

CI = A - P

 

 

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

Solution 6

For 2 years, A = Rs. 19360

T = 2 years

Let P = X

...(1)

A (for 4 years) = Rs. 23425.60

...(2)

(2) (1)

Form (1), we have

 

Thus, sum = Rs. 16000

Solution 7

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

Case I,

Case II,

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

From (1) and (2)

3 to the power of 1 divided by 8 end exponent equals open parentheses 3 cubed close parentheses to the power of 1 divided by straight T end exponent
3 to the power of 1 divided by 8 end exponent equals 3 to the power of 3 divided by straight T end exponent
1 over 8 equals 3 over straight T
straight T equals 24

Hence, time = 24 years.

Solution 8

P = Rs. 9430

R = 5%

R = 10 years

SI =

Let sum = x

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

CI = A - P

Thus principal from = Rs. 46,000

Solution 9

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

Given: SI - CI = Rs. 228

Thus, Principal = Rs. 96000

Solution 10

Let the sum (principal) = x

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

 

 

Amount = Principal + Interest


23400 = x + fraction numerator 3 x over denominator 10 end fraction 

x = 18000


Principle = Rs. 18000


Now,


Principal = Rs. 18000, r = 10% and n = 2 years

 

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

Solution 11

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

Solution 1(a)(i)

Correct option: (2)

For n =  , when interest is compounded yearly

  

Solution 1(a)(ii)

Correct option: (1)

For n = 1 year, when interest is compounded yearly

Solution 1(a)(iii)

Correct option: (4)   

For n =  , when interest is compounded yearly

  

Solution 1(b)(i)

Correct option: (1)   

For n = 1 year, when interest is compounded half-yearly

  

Solution 1(b)(ii)

Correct option: (2)   

For n =  , when interest is compounded half-yearly

  

Solution 1(b)(iii)

Correct option: (3)   

For n = 2 years, when interest is compounded half-yearly

  

Solution 1(c)

Correct option: (i) 42%

P = Rs. 6000, C.I. = Rs. 1260, n = 6 months

A = P + C.I. = Rs. 6000 + Rs. 1260 = Rs. 7260

Solution 1(d)(i)

Correct option: (i) Rs. 1,200

 

 

Now, C.I. for 1st year,

Solution 1(d)(ii)

Correct option: (i) Rs. 1,320

 

 

C.I. for 1st year,

 

C.I. for 2 years,

Therefore, C,.I. for 2nd year = Rs. 2520 - Rs. 1200 = Rs. 1320

Solution 1(d)(iii)

Correct option: (i) Rs. 12,000

 

Solution 1(d)(iv)

Correct option: (i) Rs. 14,520

 

 

The amount in 2 years, at compound interest,

Solution 2

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

Since the interest is compounded half-yearly,

Then

Solution 3

When interest is compounded yearly

Given: P = Rs. 10,000; n = 18 months = year and r = 10% p.a.

For 1 year

 

For 1/2 year

P = Rs. 11,000; n = 1/2 year and r = 10%

C.I. = Rs. 11,550 - Rs. 10,000 = Rs. 1,550

When interest is compounded half-yearly

P = Rs. 10,000; n =  year and r = 10% p.a.

C.I. = Rs. 11,576.25 - Rs. 10,000 = Rs. 1,576.25

 Difference between both C.I. = Rs. 1,576.25 - Rs.1,550

= Rs. 26.25

Solution 4

For the first 2 years,

 

  

 

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

 

For the remaining one year,

  

  

  

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

Solution 5

  

 

 

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

Solution 6

(i) For Ashok (interest is compounded yearly)

Let P = Rs. y; n = 18 months = year and r = 20% p.a.

For 1 year

For 1/2 year

P; n = ½ year and r = 20% p.a.

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

P = Rs. y; n =  year and r = 20% p.a.

According to question

Money invested by each person = Rs. 3,000

Solution 7

  

 

 

The rate of interest is 8%.

Solution 8

Given: P = Rs. 1,500; C.I. = Rs. 496.50 and r = 20%

Since interest is compounded semi-annually

Then

 

Solution 9

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

Since interest is being compounded half-yearly

Then

Solution 10

Given: P = Rs. 12,000; n= years and r = 10%

To calculate C.I.

For 1 year

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

For next 1/2 year

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

C.I. = Rs. 13,860 - Rs. 12,000 = Rs. 1,860

Difference between C.I. and S.I

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

Solution 11

Given: P = Rs. 12,000; n = years and r = 10%

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

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

C.I. = Rs. 13,891.50 - Rs. 12,000 = Rs. 1,891.50

Difference between C.I. and S.I

= Rs. 1,891.50 - Rs. 1,800 = Rs. 91.50

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

Solution 1(a)

Correct option: (iii)

When the present population (P) of a certain locality increases by r% per year, the population in n years will be Initial population ×

Solution 1(b)

Correct option: (ii)

In first year, the population is decreased by 10% and in the next year, the population is increased by 15%.

Therefore, the population at the end of two years =   

Solution 1(c)

Correct option: (ii)

When the cost of a machine decreases by r% per year, the cost of machine in 3 years =   

Solution 1(d)

Correct option: (iii)

For first 2 years, r = x%

For next 3 years, r = y%

Therefore, amount after 5 years =   

Solution 1(e)

Correct option: (iii)   

Initial cost of machine = Rs. x

For first 2 years, cost increases by 20% and then decreases by 25% in the next 2 years.

Therefore, the cost of machine

  

Solution 2

Cost of machine in 2008 = Rs. 44,000

Depreciation rate = 12%

(i) Cost of machine at the end of 2009

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



Solution 3

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.

 

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

Solution 4

Population in 2009 (P) = 64,000

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

Growth rate= 5% per annum

Solution 5

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%

 

Solution 6

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

Money after 1 year = Rs. 16,500

Money after 3 years = Rs. 19,965

For 1 year

For 3 years

Divide eqn (2) by eqn (1)

On comparing, we get

r= 10% 

Put value of r in eqn (1)

 

Solution 7

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

Let rate of interest = y%

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

Solution 8

Let Principal be Rs. y and rate = r%

According to 1st condition

Amount in 10 years = Rs. 3y

According to 2nd condition

Let after n years amount will be Rs. 27y


Solution 9

At the end of the two years the amount is

 

 

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.

 

 

 

 

Mr. Sharma borrowed Rs.40,000.

Solution 10

Let sum of money be Rs. y

To calculate S.I.

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




Solution 11

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

  

 

  

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.

Compound Interest (Using Formula) Exercise Test Yourself

Solution 1

1st case

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

2nd case(compounded half-yearly)

 P = Rs.5,625;n= 1 year and r = 4%

 

 

Solution 2

 For 2years

For ½ year

 C.I. = A - P = Rs.13,721 - Rs.10,800 = Rs.2,921 

 

 

Solution 3

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

 Depreciation rate = 10%

                                                                    =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

 

 

 

Solution 4

Let the sum of money lent by both Rs.y

For Anuj

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

 

 For Rajesh

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

Given :  C.I. - S.I. = Rs.64

  

  

Solution 5

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

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

Time = 2 years and rate = 5%

Solution 6

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

 

  

 

 

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

 For first 2years

 A = Rs.33,000; r1 =10%

 

The sum invested is Rs.30,000.

Solution 7

Let the sum of money be Rs. y

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

 For first 6 months

 For first 12 months

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

y = Rs. 3600

Solution 8

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

To calculate S.I.

 

 To calculate C.I.

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

Solution 9

Let Rs.x be the sum of money.

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

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

 

 

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

Solution 10

Let x% be the rate of interest.

 

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

 (a) For the first year,

 

 The rate of interest is x% = 12%.

 

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

 

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

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