Selina Chapter 3 Compound Interest (using formula) ICSE Solutions Class 9 Maths

ICSE Solutions for Selina Concise Chapter 2 Compound Interest (using formula) Class 9 Maths

Exercise 3(A)

1. Find the amount and the compound interest on Rs. 12,000 in 3 years at 5% compounded annually.

Answer

Given : P= Rs. 12,000; n = 3 years and r = 5%

= Rs. 13,891.50

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

2. Calculate the amount of Rs. 15,000 is lent at compound interest for 2 years and the rates for the successive years are 8% and 10% respectively.

Answer

Given : P = Rs. 15,000; n = 2 years; r₁ = 8 % and r₂ = 10%

= Rs. 17,820.

3. Calculate the compound interest accrued on Rs. 6,000 in 3 years, compounded yearly, if the rates for the successive years are 5%, 8% and 10% respectively.

Answer 

Given : P = Rs. 6,000; n = 3 years; r₁ = 5%; r₂ = 8% and r₃ = 10%

= Rs. 7,484.40
∴ C.I. = Rs. 7,484.40 – Rs. 6,000 = Rs. 1,484.40.

4. What sum of money will amount to Rs. 5,445 in 2 years at 10% per annum compound interest ?

Answer 

Given: P= Rs. 5,445 ; n = 2 years and r = 10%

= Rs. 4,500

5. On what sum of money will the compound interest for 2 years at 5% per annum amount to Rs. 768.75?

Answer 

Given : C.I.= Rs. 768.75; n= 2 years and r = 5%

= Rs. 7,500

6. Find the sum on which the compound interest for 3 years at 10% per annum amounts to Rs. 1,655.

Answer 

Given : C.I. = Rs. 1,655; n = 3 years and r = 10%

= Rs. 5,000

7. What principal will amount to Rs. 9,856 in two years, if the rates of interest for successive years are 10% and 12% respectively ?

Answer 

Given : A = Rs. 9,856 ; n = 2 years ; r₁ = 10 % and r₂ = 12%

= Rs. 8,000

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.

Answer 

⇒ (P + 4240) = P(1.265)

⇒ P = Rs. 16000

The sum is Rs.16,000.

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

Answer 

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

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

Answer 

Let Principal = Rs. y
Then Amount= Rs 1.44y
n= 2 years

On solving, we get r = 20 %

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

Answer 

Given : P = Rs. 4,000, C.I. = Rs. 1,324 and n = 3 years
Now, A = P + I
⇒ A = Rs. (4,000 + 1,324) = Rs. 5,324

Thus, the rate of interest is 10%.

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.

Answer 

Given: P = Rs. 5,000; A = Rs. 6,272 and n = 2 years.

= Rs. 7,024.64

13. In how many years will Rs. 7,000 amount to Rs. 9,317 at 10% per annum compound interest ?

Answer 

Given : P = Rs. 7,000; A = Rs. 9,317 and r = 10%.

On comparing, n = 3 years

14. Find the time, in years, in which Rs. 4,000 will produce Rs. 630.50 as compound interest at 5% compounded annually.

Answer 

Given : P= Rs. 4,000; C.I.= Rs. 630.50 and r = 5%

On comparing, n = 3 years

15. Divide Rs. 28,730 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 3 years is the same as what B receives in 5 years.

Answer

Let share of A = Rs. y
share of B = Rs (28,730 – y)
rate of interest= 10%

According to question,
Amount of A in 3 years= Amount of B in 5 years

Therefore, share of A = Rs. 15,730

Share of B = Rs. 28,730 – Rs.15,730 = Rs. 13,000

16. A sum of Rs 44,200 is divided between John and Smith, 12 years and 14 years 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 ?

Answer 

(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 4 years = Amount of Smith in 2 years

= Rs. 29,282

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.

Answer 

(i) I = Rs. 6,000, T = 2 years and R = 10%

= Rs. 39,930

(iii) C.I. earned in 3 years = A – P = Rs. (39,930 – 30,000) = Rs. 930.

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

Answer

Given: P = Rs. 8,000, R = 5%, T = 2 years
For simple interest,

C.I. = A - P
= Rs. (8,820 – 8,000)
= Rs. 820

Now, C.I. – S.I. = Rs. (820 – 800) = Rs. 20.
Thus, the difference between the compound interest and the simple interest is Rs. 20.

Exercise 3(B)

1. The difference between simple interest and compound interest on a certain sum is Rs. 54.40 for 2 years at 8 per cent per annum. Find the sum.

Answer 

Let principal (P) = x
R = 8%
T = 2 years

X = Rs. 8500
Thus, principal sum = Rs. 8500

2. A sum of money, invested at compound interest, amounts to Rs. 19,360 in 2 years and to Rs. 23,425.60 in 4 years. Find the rate per cent and the original sum of money.

Answer 

(for 2 years) A = Rs. 19360
T = 2 years
Let P = X

X = Rs. 16,000

Thus, sum = Rs. 16000

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.

Answer 

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

Case I,

T = 24

Time = 24 years.

4. On what sum of money will compound interest (payable annually) for 2 years be the same as simple interest on Rs. 9,430 for 10 years, both at the rate of 5 per cent per annum ?

Answer 

P = Rs. 9430
R = 5%
T = 10 years

Thus, principal from = Rs. 46,000

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 Rs. 15 more than Kamal. Find the amount of money lent by each and the interest received.

Answer 

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

= Rs. 615

6. Simple interest on a sum of money for 2 years at 4% is Rs. 450. Find compound interest of the same sum and at the same rate for 2 years.

Answer 

SI = Rs. 450
R = 4%
T = 2 years
P = ?

CI = A - P = 6084 - 5625 = Rs. 459

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 Rs. 228. Find the sum.

Answer 

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

P = Rs. 96000

Thus, Principal = Rs. 96000

 8. Compound interest on a certain sum of money at 5% per annum for two years is Rs. 246. Calculate simple interest on the same sum for 3 years at 6% per annum.

Answer 

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

CI = A – P

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.

Answer 

Let the sum (principle) = X
Given Amount = 23400, R = 10% and T = 3 years

A = 21780

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

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.

Answer 

For the payment of Rs. 12,600 at the end of first year :
A = Rs. 12,600; n = 1 year and r = 5%

∴ Sum borrowed = Rs. (12,000 + 16,000 ) = Rs. 28,000.

Exercise 3(C)

1. If the interest is compounded half-yearly, calculate the amount when principal is Rs. 7,400; the rate of interest is 5% per annum and the duration is one year.

Answer 

Given: P = Rs. 7,400; r = 5% p.a. and n = 1 year

Since the interest is compounded half-yearly,

= Rs. 7,774.63

 

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

Answer 

(i) When interest is compounded yearly :
Given : P = Rs. 10,000 ; n = 18 months = 1.5 year and r = 10% p.a.
For 1 year

= Rs. 11,576.25

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

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.

Answer 

For the first 2 years

⇒ A = 27,104

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

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

Answer 

⇒ P = 24,000

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

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 Rs. 33 more than Ashok in 18 months, calculate the money invested.

Answer 

(i) For Ashok (interest is compounded yearly) : 

Let P = Rs. y; n = 18 months = 1.5 year and r = 20% p.a.

For 1 year

Money invested by each person=Rs. 3,000.

 

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.

Answer 

⇒ r = 8

The rate of interest is 8%.

7. In what time will Rs. 1,500 yield Rs. 496.50 as compound interest at 20% per year compounded half-yearly ?

Answer 

Given: P=Rs. 1,500; C.I.= Rs. 496.50 and r = 20%
Since interest is compounded semi-annually

8. Calculate the C.I. on Rs. 3,500 at 6% per annum for 3 years, 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

Answer 

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

Since interest is being compounded half-yearly

= 3,500[(1.03)⁶ – 1]

= 3,500[1.194052 – 1]

= 3,500 × 0.194052

= Rs. 679.18

9. Find the difference between compound interest and simple interest on Rs.12,000 and in 1.5 years at 10% compounded yearly.

Answer 

= Rs. 13,860

∴ 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.

10. Find the difference between compound interest and simple interest on Rs. 12,000 and in 1.5 years at 10% compounded half-yearly.

Answer 

A = Rs. 13,891.50

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.

Exercise 3(D)

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 Rs. 44,000 at the beginning of 2008, find its value :
(i) at the end of 2009.
(ii) at the beginning of 2007.

Answer

Cost of machine in 2008 = Rs. 44,000
Depreciation rate = 12%

(i) ∴ Cost of machine at the end of 2009

= Rs. 50,000

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.

Answer

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.
0.891X = 40,095

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

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 ?

Answer

Population in 2009 (P) = 64,000
Let after n years its population be 74,088(A)
Growth rate= 5% per annum

On comparing, we get,
n = 3 years

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.

Answer

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%

5. A sum of money, invested at compound interest, amounts to Rs. 16,500 in 1 year and to Rs. 19,965 in 3 years. Find the rate per cent and the original sum of money invested.

Answer

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

6. The difference between C.I. and S.I. on Rs. 7,500 for two years is Rs. 12 at the same rate of interest per annum. Find the rate of interest.

Answer

Given : P = Rs. 7,500 and Time(n) = 2 years
Let rate of interest = y%

⇒ y² = 16
⇒ y = 4 %

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

Answer

Let Principal be Rs y and rate= r%
According to 1^st condition
Amount in 10 years = Rs 3

On comparing, we get
n = 10×3 = 30 years

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.

Answer

At the end of the two years the amount is

⇒ P = Rs. 40,000

Mr. Sharma borrowed Rs. 40,000.

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 Rs. 15. Find the sum of money lent out.

Answer

Let sum of money be Rs. y
To calculate S.I.

⇒ y/400 = 15 ⇒ y = Rs. 6,000.

 

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?

Answer

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.

Exercise 3(E)

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.

Answer

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

= Rs. 5852.25

∴ C.I. = 5,852.25 – 5,625 = Rs. 227.25

2. Find the compound interest to the nearest rupee on Rs. 10,800 for 2.5 years at 10% per annum.

Answer

Given : P = Rs. 10,800 ; Time = 2.5 years and Rate = 10% p.a.

For 2 years

∴ Rs.13,721 – Rs.10,800 = Rs.2,921

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:

1. Its value after 2 years.
2. Its value when it was purchased.

Answer

(i) Present value of machine(P) = Rs.97,200
Depreciation rate = 10%

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.

Answer

Let the sum of money lent by both Rs. y
For Anuj
P = Rs. y ; rate = 8% and time = 2 years

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.

Answer

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

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.

Answer

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

The sum invested is Rs.30,000.

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.

Answer

Let the sum of money be Rs. y
and rate = 10% p.a. compounded half yearly

y = 3600.

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.

Answer

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

To calculate S.I

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

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.

Answer

Let Rs.X be the sum of money.
Rate = 5 % p.a. Simple interest = Rs.1,200, n = 3 years.

⇒ A = 8,000( 1.1025 )

⇒ A = 8,820

C.I. = A – P

⇒ C.I. = 8,820 – 8,000

⇒ C.I. = 820.

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

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.

Answer

Let X % be the rate of interest.
P = Rs. 6,000, n = 2 years, A = Rs.6,720
For the first year

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