SELINA Solutions for Class 9 Maths Chapter 2 - Compound Interest (Without using formula)

Chapter 2 - Compound Interest (Without using formula) Exercise Ex. 2(A)

Question 1

Rs.16,000 is invested at 5% compound interest compounded per annum. 

Use the table, given below, to find the amount in 4 years.

 

Year  

Initial

amount (Rs.)

Interest

(Rs.)

Final

amount

(Rs.)

1 st

16,000

800

16,800

2 nd

 

 

 

3 rd

 

 

 

4 th

 

 

 

5 th

 

 

 

 

 

Solution 1

 

Year  

Initial

amount (Rs.)

Interest

(Rs.)

Final

amount

(Rs.)

1 st

16,000

800

16,800

2 nd

16,800

840

17,640

3 rd

17,640

882

18,522

4 th

18,522

926.10

19448.10

5 th

19448.10

972.405

20420.505

 

Thus, the amount in 4 years is Rs. 19448.10.

 

Question 2(i)

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula

Solution 2(i)

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula

Question 2(ii)

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula 

Solution 2(ii)

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula

Question 3

Calculate the amount and the compound interest on:

(i)Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula4,600 in 2 years when the rates of interest of successive years are 10%and 12% respectively.

(ii) Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula16,000 in 3 years, when the rates of the interest for successive years are 10%, 14% and 15% respectively.

 

Solution 3

(i)

For 1st year

P = Rs. 4600

R = 10%

T = 1 year.

 

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula

 

A = 4600 + 460 = Rs. 5060

For 2nd year

P = Rs. 5060

R = 12%

T = 1 year.

 

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula

 

A= 5060 + 607.20 = Rs. 5667.20

Compound interest = 5667.20 - 4600

= Rs. 1067.20

Amount after 2 years = Rs. 5667.20

(ii)

For 1st year

P = Rs. 16000

R = 10%

T = 1 year

 

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula

 

A = 16000 + 1600 = 17600

For 2nd year,

P = Rs. 17600

R = 14%

T = 1 year

 

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula

 

A = 17600 + 2464 = Rs. 20064

For 3rd year,

P = Rs. 20064

R = 15%

T = 1 year

 

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula

 

Amount after 3 years = 20064 + 3009.60

= Rs. 23073.60

Compound interest = 23073.60 - 16000

= Rs. 7073.60

 

Question 4

Find the compound interest, correct to the nearest rupee, on Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula2,400 for Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formulayears at 5 per cent per annum.

Solution 4

For 1st years

P = Rs. 2400

R = 5%

T = 1 year

 

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula

 

A = 2400 + 120 = Rs. 2520

For 2nd year

P = Rs. 2520

R = 5%

T = 1 year

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula

 

A = 2520 + 126 = Rs. 2646

For final Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formulayear,

P = Rs. 2646

R = 5%

T = Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formulayear

 

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula

 

Amount after Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formulayears = 2646 + 66.15

= Rs. 2712.15

Compound interest = 2712.15 - 2400

= Rs. 312.15

 

Question 5

Calculate the compound interest for the second year on Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula8,000/- invested for 3 years at 10% per annum.

Solution 5

For 1st year

P = Rs. 8000

R = 10%

T = 1 year

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula

 

A = 8000 + 800 = Rs. 8800

For 2nd year

P = Rs. 8800

R = 10%

T = 1 year

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula

 

 

Compound interest for 2nd years = Rs. 880

 

Question 6

A borrowed Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula2,500 from B at 12% per annum compound interest. After 2 years, A gave Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula2,936 and a watch to B to clear the account. Find the cost of the watch.

Solution 6

For 1st year

P = Rs. 2500

R = 12%

T = 1 year

 

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula

 

Amount = 2500 + 300 = Rs. 2800

For 2nd year

P = Rs. 2800

R = 12%

T = 1 year

 

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula

 

Amount = 2800 + 336 = Rs. 3136

Amount repaid by A to B = Rs. 2936

The amount of watch =Rs. 3136 - Rs. 2936 = Rs. 200

 

 

Question 7

How much will Rs. 50,000 amount to in 3 years, compounded yearly, if the rates for the successive years are 6%, 8% and 10% respectively?

Solution 7

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula

Question 8

Meenal lends Rs. 75,000 at C.I. for 3 years. If the rate of interest for the first two years is 15% per year and for the third year it is 16%, calculate the sum Meenal will get at the end of the third year.

Solution 8

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula

Question 9

Govind borrows Rs18,000 at 10% simple interest. He immediately invests the money borrowed at 10% compound interest compounded half-yearly. How much money does Govind gain in one year ?

Solution 9

To calculate S.I.

P=Rs18,000; R=10% and T=1year

S.I.= Rs Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula= Rs1,800

To calculate C.I.

For 1st half- year

P= Rs18,000; R=10% and T= 1/2year

Interest= Rs Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula= Rs900

Amount= Rs18,000+ Rs900= Rs18,900

For 2nd year

P= Rs18,900; R= 10% and T= 1/2year

Interest= Rs Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula= Rs945

Amount= Rs18,900+ Rs945= Rs19,845

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using FormulaCompound interest= Rs19,845- Rs18,000= Rs1,845

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using FormulaHis gain= Rs1,845 - Rs1,800= Rs45

Question 10

Find the compound interest on Rs. 4,000 accrued in three years, when the rate of interest is 8% for the first year and 10% per year for the second and the third years.

Solution 10

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula

Chapter 2 - Compound Interest (Without using formula) Exercise Ex. 2(B)

Question 1

Calculate the difference between the simple interest and the compound interest on Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula4,000 in 2 years at 8% per annum compounded yearly.

 

Solution 1

For 1st year

P = Rs. 4000

R = 8

T = 1 year

 

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula

 

A = 4000 + 320 = Rs. 4320

For 2nd year

P = Rs. 4320

R=8%

T = 1 year

 

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula

 

A = 4320 + 345.60 = 4665.60

Compound interest = Rs. 4665.60 - Rs. 4000

= Rs. 665.60

 

Simple interest for 2 years = Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula

 

= Rs. 640

Difference of CI and SI = 665.60 - 640

= Rs 25.60

 

Question 2

A man lends Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula12,500 at 12% for the first year, at 15% for the second year and at 18% for the third year. If the rates of interest are compounded yearly ; find the difference between the C.I. fo the first year and the compound interest for the third year.

Solution 2

For 1st year

P = Rs. 12500

R = 12%

R = 1 year

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula

 

A = 12500 + 1500 = Rs. 14000

For 2nd year

P = Rs. 14000

R = 15%

T = 1 year

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula

A = 1400 + 2100 = Rs. 16100

For 3rd year

P = Rs. 16100

R = 18%

T = 1 year

 

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula

 

A = 16100 + 2898 = Rs. 18998

Difference between the compound interest of the third year and first year

= Rs. 2898 - Rs. 1500

= Rs. 1398

Question 3

A sum of money is lent at 8% per annum compound interest. If the interest for the second year exceeds that for the first year by Rs.96, find the sum of money.

Solution 3

Let money be Rs100

For 1st year

P=Rs100; R=8% and T= 1year

Interest for the first year= RsSelina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula= Rs8

Amount= Rs100+ Rs8= Rs108

For 2nd year

P=Rs108; R=8% and T= 1year

Interest for the second year= RsSelina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula= Rs8.64

Difference between the interests for the second and first year = Rs8.64 - Rs8 = Rs0.64

Given that interest for the second year exceeds the first year by Rs.96

When the difference between the interests is Rs0.64, principal is Rs100

When the difference between the interests is Rs96, principal=RsSelina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula=Rs15,000

Question 4

A man borrows Rs. 6,000 at 5% C.I. per annum. If he repays Rs. 1,200 at the end of each year, find the amount of the loan outstanding at the beginning of the third year.

Solution 4

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula

Question 5

A man borrows Rs. 5,000 at 12 percent compound interest payable every six months. He repays Rs. 1,800 at the end of every six months. Calculate the third payment he has to make at the end of 18 months in order to clear the entire loan.

Solution 5

For 1st six months:

P = Rs. 5,000, R = 12% and T = Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula year

Interest = Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula = Rs. 300

And, Amount = Rs. 5,000 + Rs. 300 = Rs. 5,300

Since money repaid = Rs. 1,800

Balance = Rs. 5,300 - Rs. 1,800 = Rs. 3,500

 

For 2nd six months:

P = Rs. 3,500, R = 12% and T = Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula year

Interest = Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula = Rs. 210

And, Amount = Rs. 3,500 + Rs. 210 = Rs. 3,710

Again money repaid = Rs. 1,800

Balance = Rs. 3,710 - Rs. 1,800 = Rs. 1,910

 

For 3rd six months:

P = Rs. 1,910, R = 12% and T = Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula year

Interest = Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula = Rs. 114.60

And, Amount = Rs. 1,910 + Rs. 114.60 = Rs. 2,024.60

 

Thus, the 3rd payment to be made to clear the entire loan is 2,024.60.

Question 6

On a certain sum of money, the difference between the compound interest for a year, payable half-yearly, and the simple interest for a year is Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula180/-. Find the sum lent out, if the rate of interest in both the cases is 10% per annum.

 

Solution 6

Let principal (p = Rs. 100

R = 10%

T = 1 year

 

SI = Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula

 

Compound interest payable half yearly

R = 5% half yearly

T = Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formulayear = 1 half year

For first Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formulayear

 

I = Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula

A = 100 + 5 = Rs. 105

For second Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formulayear

P = Rs. 105  

 

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula 

Total compound interest = 5 + 5.25

= Rs. 10.25

Difference of CI and SI = 10.25- 10

= Rs. 0.25

When difference in interest is Rs. 10.25, sum = Rs. 100

 

If the difference is Rs. 1 ,sum = Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula

 

If the difference is Rs. = 180,sum = Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula

= Rs. 72000

Question 7

A manufacturer estimates that his machine depreciates by 15% of its value at the beginning of the year. Find the original value (cost) of the machine, if it depreciates by Rs. 5,355 during the second year.

Solution 7

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula

Question 8

A man invest Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula5,600 at 14% per annum compound interest for 2 years. Calculate:

(i) The interest for the first year.

(ii) The amount at the end of the first year.

(iii) The interest for the second year, correct to the nearest rupee.

 

Solution 8

(i) For 1st years

P = Rs. 5600

R = 14%

T = 1 year

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula

 

(ii) Amount at the end of the first year

= 5600 + 784

= Rs. 6384

(iii) For 2nd year

P = 6384

R = 14%

R = 1 year

 

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula

 

 

= Rs. 893.76

= Rs. 894 (nearly)

 

Question 9

A man saves Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula3,000 every year and invests it at the end of the year at 10% compound interest. Calculate the total amount of his savings at the end of the third year.

Solution 9

Savings at the end of every year = Rs. 3000

For 2nd year

P = Rs. 3000

R = 10%

T = 1 year

 

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula

 

A = 3000 + 300 = Rs. 3300

For third year, savings = 3000

P = 3000 + 3300 = Rs. 6300

R = 10%

T = 1 year

 

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula

 

A = 6300 + 630 = Rs. 6930

Amount at the end of 3rd year

= 6930 + 3000

= Rs. 9930

 

Question 10

A man borrows Rs. 10,000 at 5% per annum compound interest. He repays 35% of the sum borrowed at the end of the first year and 42% of the sum borrowed at the end of the second year. How much must he pay at the end of the third year in order to clear the debt?

Solution 10

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula

Chapter 2 - Compound Interest (Without using formula) Exercise Ex. 2(C)

Question 1

A sum is invested at compound interest, compounded yearly. If the interest for two successive years is Rs.5,700 and Rs.7,410, calculate the rate of interest.

Solution 1

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula

Question 2

A certain sum of money is put at compound interest, compounded half-yearly. If the interest for two successive half-years are Rs650 and Rs760.50; find the rate of interest.

Solution 2

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using FormulaDifference between the C.I. of two successive half-years

= Rs760.50 - Rs650= Rs110.50

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using FormulaRs110.50 is the interest of one half-year on Rs650

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using FormulaRate of interest= RsSelina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula%= Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula%= 34%

Question 3

A certain sum amounts to Rs5,292 in two years and Rs5,556.60 in three years, interest being compounded annually. Find;

(i)the rate of interest.

(ii)the original sum.

Solution 3

(i)Amount in two years= Rs5,292

Amount in three years= Rs5,556.60

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using FormulaDifference between the amounts of two successive years

= Rs5,556.60 - Rs5,292= Rs264.60

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using FormulaRs264.60 is the interest of one year on Rs5,292

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using FormulaRate of interest= RsSelina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula%= Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula%= 5%

(ii) Let the sum of money= Rs100

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using FormulaInterest on it for 1st year= 5% of Rs100= Rs5

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using FormulaAmount in one year= Rs100+ Rs5= Rs105

Similarly, amount in two years= Rs105+ 5% of Rs105

= Rs105+ Rs5.25

= Rs110.25

When amount in two years is Rs110.25, sum = Rs100

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using FormulaWhen amount in two years is Rs5,292, sum = RsSelina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula

= Rs4,800

Question 4

The compound interest, calculated yearly, on a certain sum of money for the second year is Rs1,089 and for the third year it is Rs1,197.90. Calculate the rate of interest and the sum of money.

Solution 4

(i)C.I. for second year = Rs1,089

C.I. for third year = Rs 1,197.90

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using FormulaDifference between the C.I. of two successive years

= Rs1,197.90 - Rs1089= Rs108.90

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using FormulaRs108.90 is the interest of one year on Rs1089

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using FormulaRate of interest= RsSelina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula%= Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula%= 10%

(ii) Let the sum of money= Rs100

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using FormulaInterest on it for 1st year= 10% of Rs100= Rs10

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using FormulaAmount in one year= Rs100+ Rs10= Rs110

Similarly, C.I. for 2nd year= 10% of Rs110

= Rs11

When C.I. for 2nd year is Rs11, sum = Rs100

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using FormulaWhen C.I. for 2nd year is Rs1089, sum = RsSelina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula = Rs9,900

Question 5

Mohit invests Rs8,000 for 3years at a certain rate of interest, compounded annually. At the end of one year it amounts to Rs9,440. Calculate:

(i)the rate of interest per annum.

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

(iii)the interest accrued in the third year.

Solution 5

For 1st year

P=Rs8,000; A=9,440 and T= 1year

Interest= Rs9,440 - Rs8,000= Rs1,440

Rate=Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula%=Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula%=18%

For 2nd year

P= Rs9,440; R=18% and T= 1year

Interest= RsSelina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula= Rs1,699.20

Amount= Rs9,440 + Rs1,699.20= Rs11,139.20

For 3rd year

P= Rs11,139.20; R=18% and T= 1year

Interest= RsSelina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula= Rs2,005.06

Question 6

Geeta borrowed Rs15,000 for 18 months at a certain rate of interest compounded semi-annually. If at the end of six months it amounted to Rs15,600; calculate :

(i)the rate of interest per annum.

(ii)the total amount of money that Geeta must pay at the end of 18 months in order to clear the account.

Solution 6

For 1st half-year

P= Rs15,000; A= Rs15,600 and T= ½ year

Interest= Rs15,600 - Rs15,000= Rs600

Rate= Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula%=Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula%= 8% Ans.

For 2nd half-year

P= Rs15,600; R=8% and T= ½ year

Interest= RsSelina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula= Rs624

Amount= Rs15,600 + Rs624= Rs16,224

For 3rd half-year

P= Rs16,224; R=8% and T= ½ year

Interest= RsSelina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula= Rs648.96

Amount= Rs16,224+ Rs648.96= Rs16,872.96 Ans.

Question 7

Ramesh invests Rs12,800 for three years at the rate of 10% per annum compound interest. Find:

(i)the sum due to Ramesh at the end of the first year.

(ii)the interest he earns for the second year.

(iii)the total amount due to him at the end of the third year.

Solution 7

For 1st year

P=Rs12,800; R=10% and T= 1year

Interest= RsSelina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula= Rs1,280

Amount= Rs12,800+ Rs1,280= Rs14,080

For 2nd year

P=Rs14,080; R=10% and T= 1 year

Interest= RsSelina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula= Rs1,408

Amount= Rs14,080+ Rs1,408= Rs15,488

For 3rd year

P=Rs15,488; R=10% and T= 1year

Interest= RsSelina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula= Rs1,548.80

Amount= Rs15,488+ Rs1,548.80= Rs17,036.80

Question 8

Rs8,000 is lent out at 7% compound interest for 2years. At the end of the first year Rs3,560 are returned. Calculate :

(i)the interest paid for the second year.

(ii)the total interest paid in two years.

(iii)the total amount of money paid in two years to clear the debt.

Solution 8

(i) For 1st year

P= Rs8,000; R=7% and T=1year

Interest= RsSelina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula= Rs560

Amount= Rs8,000+ Rs560= Rs8,560

Money returned= Rs3,560

Balance money for 2nd year= Rs8,560- Rs3,560= Rs5,000

For 2nd year

P= Rs5,000; R=7% and T=1year

Interest paid for the second year= RsSelina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula= Rs350 Ans.

(ii)The total interest paid in two years= Rs350 + Rs560

= Rs910 Ans.

(iii) The total amount of money paid in two years to clear the debt

= Rs8,000+ Rs910

= Rs8,910 Ans.

Question 9

The cost of a machine depreciated by Rs.4,000 during the first year and by Rs.3,600 during the second year. Calculate:

  1. The rate of depreciation.
  2. The original cost of the machine.
  3. Its cost at the end of the third year.
Solution 9

(i)

 

Difference between depreciation in value between the first and second years

Rs.4,000 - Rs.3,600 = Rs.400

Depreciation of one year on Rs.4,000 = Rs.400

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula

 

(ii)

 

Let Rs.100 be the original cost of the machine.

 

Depreciation during the 1st year = 10% of Rs.100 = Rs.10

 

When the values depreciates by Rs.10 during the 1st year, Original cost = Rs.100

 

When the depreciation during 1st year = Rs.4,000,

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula

 

The original cost of the machine is Rs.40,000.

 

(iii)

 

Total depreciation during all the three years

= Depreciation  in value during(1st year + 2nd year + 3rd year)

= Rs.4,000 + Rs.3,600 + 10% of (Rs.40,000 - Rs.7,600)

= Rs.4,000 + Rs.3,600 + Rs.3,240

= Rs.10,840

 

The cost of the machine at the end of the third year

= Rs.40,000 - Rs.10,840 = Rs.29,160

Question 10

Find the sum, invested at 10% compounded annually, on which the interest for the third year exceeds the interest of the first year by Rs252.

Solution 10

Let the sum of money be Rs 100

Rate of interest= 10%p.a.

Interest at the end of 1st year= 10% of Rs100= Rs10

Amount at the end of 1st year= Rs100 + Rs10= Rs110

Interest at the end of 2nd year=10% of Rs110 = Rs11

Amount at the end of 2nd year= Rs110 + Rs11= Rs121

Interest at the end of 3rd year=10% of Rs121= Rs12.10

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using FormulaDifference between interest of 3rd year and 1st year

=Rs12.10- Rs10=Rs2.10

When difference is Rs2.10, principal is Rs100

When difference is Rs252, principal = Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula=Rs12,000 Ans.

Question 11

A man borrows Rs10,000 at 10% compound interest compounded yearly. At the end of each year, he pays back 30% of the sum borrowed. How much money is left unpaid just after the second year?

Solution 11

For 1st year

P= Rs10,000; R=10% and T= 1year

Interest= RsSelina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula=Rs1,000

Amount at the end of 1st year=Rs10,000+Rs1,000=Rs11,000

Money paid at the end of 1st year=30% of Rs10,000=Rs3,000

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using FormulaPrincipal for 2nd year=Rs11,000- Rs3,000=Rs8,000

For 2nd year

P=Rs8,000; R=10% and T= 1year

Interest= Rs Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula= Rs800

Amount at the end of 2nd year=Rs8,000+Rs800= Rs8,800

Money paid at the end of 2nd year=30% of Rs10,000= Rs3,000

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using FormulaPrincipal for 3rd year=Rs8,800- Rs3,000=Rs5,800 Ans.

Question 12

A man borrows Rs10,000 at 10% compound interest compounded yearly. At the end of each year, he pays back 20% of the amount for that year. How much money is left unpaid just after the second year?

Solution 12

For 1st year

P= Rs10,000; R=10% and T= 1year

Interest= RsSelina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula=Rs1,000

Amount at the end of 1st year=Rs10,000+Rs1,000=Rs11,000

Money paid at the end of 1st year=20% of Rs11,000=Rs2,200

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using FormulaPrincipal for 2nd year=Rs11,000- Rs2,200=Rs8,800

For 2nd year

P=Rs8,800; R=10% and T= 1year

Interest= RsSelina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula= Rs880

Amount at the end of 2nd year=Rs8,800+Rs880= Rs9,680

Money paid at the end of 2nd year=20% of Rs9,680= Rs1,936

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using FormulaPrincipal for 3rd year=Rs9,680- Rs1,936=Rs7,744 Ans.

Chapter 2 - Compound Interest (Without using formula) Exercise Ex. 2(D)

Question 1

What sum will amount of Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula6,593.40 in 2 years at C.I., if the rates are 10 per cent and 11 per cent for the two successive years?

Solution 1

Let principal (p) = Rs. 100

For 1st year

P = Rs. 100

R = 10%

T = 1 year

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula

A = 100 + 10 = Rs. 110

For 2nd year

P = Rs. 110

R = 11%

T = 1 year

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula

 

A = 110 + 12.10 = Rs. 122.10

If Amount is Rs. 122.10 on a sum of Rs. = 100

If amount is Rs. 1, sum = Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula

 

If amount is Rs. 6593.40, sum = Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula

 

= Rs. 5400

Question 2

The value of a machine depreciated by 10% per year during the first two years and 15% per year during the third year. Express the total depreciation of the machine, as per cent, during the three years.

Solution 2

Let the value of machine in the beginning= Rs. 100

For 1st year depreciation = 10% of Rs. 100 = Rs. 100

Value of machine for second year = 100 - 10

= Rs. 90

For 2nd year depreciation = 10% of 90 = Rs. 9

Value of machine for third year = 90 - 9

= Rs. 81

For 3rd year depreciation = 15% of 81

= Rs. 12.15

Value of machine at the end of third year = 81 - 12.15

= Rs. 68.85

Net depreciation = Rs. 100 - Rs. 68.85

= Rs. 31.15

Or 31.15%

 

Question 3

Rachna borrows Rs12,000 at 10 percent per annum interest compounded half-yearly. She repays Rs4,000 at the end of every six months. Calculate the third payment she has to make at end of 18 months in order to clear the entire loan.

Solution 3

For 1st half-year

P=Rs12,000; R=10% and T=1/2 year

Interest= RsSelina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula= Rs600

Amount= RS12,000 + Rs600= Rs12,600

Money paid at the end of 1st half year=Rs4,000

Balance money for 2nd half-year= Rs12,600- Rs4,000=Rs8,600

 

For 2nd half-year

P=Rs8,600; R=10% and T=1/2 year

Interest=RsSelina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula=Rs430

Amount= Rs8,600+ Rs430= Rs9,030

Money paid at the end of 2nd half-year=Rs4,000

Balance money for 3rd half-year= Rs9,030- Rs4,000=Rs5,030

 

For 3rd half-year

P=Rs5,030; R=10% and T=1/2 year

Interest = RsSelina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula= Rs251.50

Amount= Rs5,030 + Rs251.50= Rs5,281.50

Question 4

On a certain sum of money, invested at the rate of 10 percent per annum compounded annually, the interest for the first year plus the interest for the third year is Rs2,652. Find the sum.

Solution 4

Let Principal= Rs 100

For 1st year

P=Rs100; R=10% and T=1year

Interest= RsSelina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula= Rs10

Amount= Rs100 + Rs10= Rs110

For 2nd year

P=Rs110; R=10% and T= 1year

Interest= RsSelina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula= Rs11

Amount= Rs110 + Rs11= Rs121

For 3rd year

P=Rs121; R=10% and T= 1year

Interest= RsSelina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula= Rs12.10

Sum of C.I. for 1st year and 3rd year=Rs10+Rs12.10=Rs22.10

When sum is Rs22.10, principal is Rs100

When sum is Rs2,652, principal =RsSelina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula=Rs12,000 Ans.

Question 5

During every financial year, the value of a machine depreciates by 12%. Find the original cost of a machine which depreciates by Rs2,640 during the second financial year of its purchase.

Solution 5

Let original value of machine=Rs100

For 1st year

P=Rs100; R=12% and T= 1year

Depreciation in 1st year= Rs Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula=Rs12

Value at the end of 1st year=Rs100 - Rs12=Rs88

For 2nd year

P= Rs88; R=12% and T= 1year

Depreciation in 2nd year= Rs Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula=Rs10.56

When depreciation in 2nd year is Rs10.56, original cost is Rs100

When depreciation in 2nd year is Rs2,640, original cost=Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula

 

=Rs25,000

Question 6

Find the sum on which the difference between the simple interest and compound interest at the rate of 8% per annum compounded annually would be Rs.64 in 2years.

Solution 6

Let Rs. x be the sum. 

 

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula

 

Compound interest

For 1st year:

P = Rs.x, R = 8% and T=1

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula


For 2nd year:

P = Rs.Rs. 0.08x = Rs. 1.08x

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula

Amount = 1.08x + 0.0864x = Rs. 1.1664x

CI = Amount - P = 1.1664x - x = Rs. 0.1664x

The difference between the simple interest and compound interest at the rate of 8% per annum compounded annually should be Rs. 64 in 2 years.

⇒ Rs. 0.1664x - Rs. 0.16x = Rs.64

⇒ Rs. 0.0064x = Rs.64

⇒ x = 10000

 

Hence the sum is Rs. 10000.

Question 7

A sum of Rs13,500 is invested at 16% per annum compound interest for 5years.Calculate:

(i)the interest for the first year.

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

(iii)the interest for the second year, correct to the nearest rupee.

Solution 7

For 1st year

P=Rs13,500; R=16% and T= 1year

Interest= RsSelina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula= Rs2,160

Amount= Rs13,500 + Rs2,160= Rs15,660

For 2nd year

P=Rs15,660; R=16% and T= 1year

Interest= RsSelina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula= Rs2,505.60

=Rs2,506

Question 8

Saurabh invests Rs48,000 for 7 years at 10% per annum compound interest.

Calculate:

(i)the interest for the first year.

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

(iii)the interest for the third year.

Solution 8

For 1st year

P=Rs48,000; R=10% and T= 1year

Interest= RsSelina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula= Rs4,800

Amount= Rs48,000+ Rs4,800= Rs52,800

For 2nd year

P=Rs52,800; R=10% and T= 1year

Interest= RsSelina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula= Rs5,280

Amount= Rs52,800+ Rs5,280= Rs58,080

For 3rd year

P=Rs58,080; R=10% and T= 1year

Interest= RsSelina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula= Rs5,808

Question 9

Ashok borrowed Rs.12,000 at some rate on compound interest. After a year, he paid back Rs.4,000. If the compound interest for the second year is Rs.920, find:

  1. The rate of interest charged
  2. The amount of debt at the end of the second year
Solution 9

(i)

Let x% be the rate of interest charged.

 

For 1st year:

P = Rs.12,000, R = x% and T = 1

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula

 

For 2nd year:

After a year, Ashok paid back Rs.4,000.

P = Rs.12,000 + Rs.120x - Rs.4,000 = Rs.8,000 + Rs.120x

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula

The compound interest for the second year is Rs.920

Rs. (80x + 1.20x2) =  Rs.920

1.20x2 + 80x - 920 = 0

3x2 + 200x - 2300 = 0

3x2 + 230x - 30x - 2300 = 0

x(3x + 230) -10(3x + 230) = 0

(3x + 230)(x - 10) = 0

x = -230/3 or x = 10

 

As rate of interest cannot be negative so x = 10.

Therefore the rate of interest charged is 10%.

 


(ii)

 

For 1st year:

Interest = Rs.120x = Rs.1200

 

For 2nd year:

Interest = Rs.(80x + 1.20x2) = Rs.920

 

The amount of debt at the end of the second year is equal to the addition of principal of the second year and interest for the two years.

 

Debt = Rs.8,000 + Rs.1200 + Rs.920 = Rs.10,120

Question 10

On a certain sum of money, lent out at C.I., interests for first, second and third years are Rs. 1,500; Rs. 1,725 and Rs. 2,070 respectively. Find the rate of interest for the (i) second year (ii) third year.

Solution 10

Selina Solutions Icse Class 9 Mathematics Chapter - Compound Interest Without Using Formula