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

Correct option: (i)

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

Correct option: (ii)  

When the rates for successive years are different then,

. 

Correct option: (i) Rs. 3690 

P = Rs. 36000, n = 2 years, r = 5%

C.I. = A - P = Rs. 39690 - Rs. 36000 = Rs. 3690 

Correct option: (iii) Rs. 5000 

Correct option: (iv) Rs. 5500 

Correct option: (i) 15% 

Correct option: (ii) 15%

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

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.

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

Amount==

=

=Rs17,820 Ans.

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.

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

A=

5,445=

5,445=

P==Rs4,500 Ans.

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.

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.

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

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

Ans.

The sum is Rs.16,000

Let Principal = Rs y

Then Amount= Rs 1.44y

n= 2years

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

(i)

(ii) Amount at the third year

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

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

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

(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

Correct option: (iii) Rs. 60

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

Correct option: (iv) 25%

Correct option: (ii) Rs. 7,040

Correct option: (ii) Rs. 6,400

Correct option: (i) Rs. 640

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

Let principal (P) = x

R = 8%

T = 2 years

 Given, CI - SI = 54.40

Thus, principal sum = Rs. 8500

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

For Kamal, SI =

For Anand,  

 CI = 

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 =

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

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

CI = A - P

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

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

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

Case I,

Case II,

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

From (1) and (2)

Hence, time = 24 years.

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

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

Given: SI - CI = Rs. 228

Thus, Principal = Rs. 96000

Let the sum (principal) = x

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

Amount = Principal + Interest

23400 = x +  

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.

Correct option: (2)

For n = , when interest is compounded yearly

Correct option: (1)

For n = 1 year, when interest is compounded yearly

Correct option: (4)  

For n = , when interest is compounded yearly

Correct option: (1)  

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

Correct option: (2)  

For n = , when interest is compounded half-yearly

Correct option: (3)  

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

Correct option: (i) 42%

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

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

Correct option: (i) Rs. 1,200

Now, C.I. for 1^st year,

Correct option: (i) Rs. 1,320

C.I. for 1^st year,

C.I. for 2 years,

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

Correct option: (i) Rs. 12,000

Correct option: (i) Rs. 14,520

The amount in 2 years, at compound interest,

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

Since the interest is compounded half-yearly,

Then

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

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.

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

(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

The rate of interest is 8%.

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

Since interest is compounded semi-annually

Then

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

Since interest is being compounded half-yearly

Then

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

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

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 ×

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 =  

Correct option: (ii)

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

Correct option: (iii)

For first 2 years, r = x%

For next 3 years, r = y%

Therefore, amount after 5 years =  

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

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)

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 1^st year is

x - 10% of x = 0.90x

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

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

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

The value of the article at the end of 3^rd  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.

Population in 2009 (P) = 64,000

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

Growth rate= 5% per annum

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%

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)

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

Let rate of interest = y%

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

Let Principal be Rs. y and rate = r%

According to 1^st condition

Amount in 10 years = Rs. 3y

According to 2^nd condition

Let after n years amount will be Rs. 27y

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.

Let sum of money be Rs. y

To calculate S.I.

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

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.

1^st case

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

2^nd case(compounded half-yearly)

 P = Rs.5,625;n= 1 year and r = 4%

 For 2years

For ½ year

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

(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

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

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%

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

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

 For first 2years

 A = Rs.33,000; r₁ =10%

The sum invested is Rs.30,000.

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

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

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.

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