## ICSE Class 10 Compound Interest Solution New Pattern By Clarify Knowledge

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## 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 ↓ | Initialamount (Rs.) | Interest(Rs.) | Finalamount(Rs.) |

1 st | 16,000 | 800 | 16,800 |

2 nd | |||

3 rd | |||

4 th | |||

5 th |

Solution 1

Year ↓ | Initialamount (Rs.) | Interest(Rs.) | Finalamount(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)

Solution 2(i)

Question 2(ii)

Solution 2(ii)

Question 3

Calculate the amount and the compound interest on:

(i)4,600 in 2 years when the rates of interest of successive years are 10%and 12% respectively.

(ii) 16,000 in 3 years, when the rates of the interest for successive years are 10%, 14% and 15% respectively.Solution 3

(i)

For 1^{st} year

P = Rs. 4600

R = 10%

T = 1 year.

A = 4600 + 460 = Rs. 5060

For 2^{nd} year

P = Rs. 5060

R = 12%

T = 1 year.

A= 5060 + 607.20 = Rs. 5667.20

Compound interest = 5667.20 - 4600

= Rs. 1067.20

Amount after 2 years = Rs. 5667.20

(ii)

For 1^{st} year

P = Rs. 16000

R = 10%

T = 1 year

A = 16000 + 1600 = 17600

For 2^{nd} year,

P = Rs. 17600

R = 14%

T = 1 year

A = 17600 + 2464 = Rs. 20064

For 3^{rd} year,

P = Rs. 20064

R = 15%

T = 1 year

Amount after 3 years = 20064 + 3009.60

= Rs. 23073.60

Compound interest = 23073.60 - 16000

= Rs. 7073.60Question 4

Find the compound interest, correct to the nearest rupee, on 2,400 for years at 5 per cent per annum.Solution 4

For 1^{st} years

P = Rs. 2400

R = 5%

T = 1 year

A = 2400 + 120 = Rs. 2520

For 2^{nd} year

P = Rs. 2520

R = 5%

T = 1 year

A = 2520 + 126 = Rs. 2646

For final year,

P = Rs. 2646

R = 5%

T = year

Amount after years = 2646 + 66.15

= Rs. 2712.15

Compound interest = 2712.15 - 2400

= Rs. 312.15Question 5

Calculate the compound interest for the second year on 8,000/- invested for 3 years at 10% per annum.Solution 5

For 1^{st} year

P = Rs. 8000

R = 10%

T = 1 year

A = 8000 + 800 = Rs. 8800

For 2^{nd} year

P = Rs. 8800

R = 10%

T = 1 year

Compound interest for 2^{nd} years = Rs. 880Question 6

A borrowed 2,500 from B at 12% per annum compound interest. After 2 years, A gave 2,936 and a watch to B to clear the account. Find the cost of the watch.Solution 6

For 1^{st} year

P = Rs. 2500

R = 12%

T = 1 year

Amount = 2500 + 300 = Rs. 2800

For 2^{nd} year

P = Rs. 2800

R = 12%

T = 1 year

Amount = 2800 + 336 = Rs. 3136

Amount repaid by A to B = Rs. 2936

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

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

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 = Rs1,800

To calculate C.I.

For 1^{st} half- year

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

Interest= Rs = Rs900

Amount= Rs18,000+ Rs900= Rs18,900

For 2^{nd} year

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

Interest= Rs = Rs945

Amount= Rs18,900+ Rs945= Rs19,845

Compound interest= Rs19,845- Rs18,000= Rs1,845

His gain= Rs1,845 - Rs1,800= Rs45Question 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

## 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 4,000 in 2 years at 8% per annum compounded yearly.Solution 1

For 1^{st} year

P = Rs. 4000

R = 8

T = 1 year

A = 4000 + 320 = Rs. 4320

For 2^{nd} year

P = Rs. 4320

R=8%

T = 1 year

A = 4320 + 345.60 = 4665.60

Compound interest = Rs. 4665.60 - Rs. 4000

= Rs. 665.60

Simple interest for 2 years =

= Rs. 640

Difference of CI and SI = 665.60 - 640

= Rs 25.60Question 2

A man lends 12,500 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 1^{st} year

P = Rs. 12500

R = 12%

R = 1 year

A = 12500 + 1500 = Rs. 14000

For 2^{nd} year

P = Rs. 14000

R = 15%

T = 1 year

A = 1400 + 2100 = Rs. 16100

For 3^{rd} year

P = Rs. 16100

R = 18%

T = 1 year

A = 16100 + 2898 = Rs. 18998

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

= Rs. 2898 - Rs. 1500

= Rs. 1398Question 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 1^{st} year

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

Interest for the first year= Rs= Rs8

Amount= Rs100+ Rs8= Rs108

For 2^{nd} year

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

Interest for the second year= Rs= 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=Rs=Rs15,000Question 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

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 1^{st} six months:

P = Rs. 5,000, R = 12% and T = year

∴ Interest = = 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 2^{nd} six months:

P = Rs. 3,500, R = 12% and T = year

∴ Interest = = 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 3^{rd} six months:

P = Rs. 1,910, R = 12% and T = year

∴ Interest = = Rs. 114.60

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

Thus, the 3^{rd} 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 180/-. 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 =

Compound interest payable half yearly

R = 5% half yearly

T = year = 1 half year

For first year

I =

A = 100 + 5 = Rs. 105

For second year

P = Rs. 105

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 =

If the difference is Rs. = 180,sum =

= Rs. 72000Question 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

Question 8

A man invest 5,600 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 1^{st} years

P = Rs. 5600

R = 14%

T = 1 year

(ii) Amount at the end of the first year

= 5600 + 784

= Rs. 6384

(iii) For 2^{nd} year

P = 6384

R = 14%

R = 1 year

= Rs. 893.76

= Rs. 894 (nearly)Question 9

A man saves 3,000 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 2^{nd} year

P = Rs. 3000

R = 10%

T = 1 year

A = 3000 + 300 = Rs. 3300

For third year, savings = 3000

P = 3000 + 3300 = Rs. 6300

R = 10%

T = 1 year

A = 6300 + 630 = Rs. 6930

Amount at the end of 3^{rd} year

= 6930 + 3000

= Rs. 9930Question 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

## 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

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

Difference between the C.I. of two successive half-years

= Rs760.50 - Rs650= Rs110.50

Rs110.50 is the interest of one half-year on Rs650

Rate of interest= Rs%= %= 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

Difference between the amounts of two successive years

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

Rs264.60 is the interest of one year on Rs5,292

Rate of interest= Rs%= %= 5%

(ii) Let the sum of money= Rs100

Interest on it for 1^{st} year= 5% of Rs100= Rs5

Amount 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

When amount in two years is Rs5,292, sum = Rs

= Rs4,800Question 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

Difference between the C.I. of two successive years

= Rs1,197.90 - Rs1089= Rs108.90

Rs108.90 is the interest of one year on Rs1089

Rate of interest= Rs%= %= 10%

(ii) Let the sum of money= Rs100

Interest on it for 1^{st} year= 10% of Rs100= Rs10

Amount in one year= Rs100+ Rs10= Rs110

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

= Rs11

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

When C.I. for 2^{nd} year is Rs1089, sum = Rs = Rs9,900Question 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 1^{st} year

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

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

Rate=%=%=18%

For 2^{nd} year

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

Interest= Rs= Rs1,699.20

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

For 3^{rd} year

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

Interest= Rs= Rs2,005.06Question 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 1^{st} half-year

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

Interest= Rs15,600 - Rs15,000= Rs600

Rate= %=%= 8% Ans.

For 2^{nd} half-year

P= Rs15,600; R=8% and T= ½ year

Interest= Rs= Rs624

Amount= Rs15,600 + Rs624= Rs16,224

For 3^{rd} half-year

P= Rs16,224; R=8% and T= ½ year

Interest= Rs= 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 1^{st} year

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

Interest= Rs= Rs1,280

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

For 2^{nd} year

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

Interest= Rs= Rs1,408

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

For 3^{rd} year

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

Interest= Rs= Rs1,548.80

Amount= Rs15,488+ Rs1,548.80= Rs17,036.80Question 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 1^{st} year

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

Interest= Rs= Rs560

Amount= Rs8,000+ Rs560= Rs8,560

Money returned= Rs3,560

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

For 2^{nd} year

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

Interest paid for the second year= Rs= 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:

- The rate of depreciation.
- The original cost of the machine.
- 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

(ii)

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

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

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

⇒When the depreciation during 1^{st} year = Rs.4,000,

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

(iii)

Total depreciation during all the three years

= Depreciation in value during(1^{st} year + 2^{nd} year + 3^{rd} 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.29,160Question 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 1^{st} year= 10% of Rs100= Rs10

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

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

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

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

Difference between interest of 3^{rd} year and 1^{st} year

=Rs12.10- Rs10=Rs2.10

When difference is Rs2.10, principal is Rs100

When difference is Rs252, principal = =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 1^{st} year

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

Interest= Rs=Rs1,000

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

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

Principal for 2^{nd} year=Rs11,000- Rs3,000=Rs8,000

For 2^{nd} year

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

Interest= Rs = Rs800

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

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

Principal for 3^{rd} 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 1^{st} year

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

Interest= Rs=Rs1,000

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

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

Principal for 2^{nd} year=Rs11,000- Rs2,200=Rs8,800

For 2^{nd} year

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

Interest= Rs= Rs880

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

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

Principal for 3^{rd} 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 6,593.40 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 1^{st} year

P = Rs. 100

R = 10%

T = 1 year

A = 100 + 10 = Rs. 110

For 2^{nd} year

P = Rs. 110

R = 11%

T = 1 year

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 =

If amount is Rs. 6593.40, sum =

= Rs. 5400Question 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 1^{st} year depreciation = 10% of Rs. 100 = Rs. 100

Value of machine for second year = 100 - 10

= Rs. 90

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

Value of machine for third year = 90 - 9

= Rs. 81

For 3^{rd} 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 1^{st} half-year

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

Interest= Rs= Rs600

Amount= RS12,000 + Rs600= Rs12,600

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

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

For 2^{nd} half-year

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

Interest=Rs=Rs430

Amount= Rs8,600+ Rs430= Rs9,030

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

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

For 3^{rd} half-year

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

Interest = Rs= Rs251.50

Amount= Rs5,030 + Rs251.50= Rs5,281.50Question 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 1^{st} year

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

Interest= Rs= Rs10

Amount= Rs100 + Rs10= Rs110

For 2^{nd} year

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

Interest= Rs= Rs11

Amount= Rs110 + Rs11= Rs121

For 3^{rd} year

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

Interest= Rs= Rs12.10

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

When sum is Rs22.10, principal is Rs100

When sum is Rs2,652, principal =Rs=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 1^{st} year

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

Depreciation in 1^{st} year= Rs =Rs12

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

For 2^{nd} year

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

Depreciation in 2^{nd} year= Rs =Rs10.56

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

When depreciation in 2^{nd} year is Rs2,640, original cost=

=Rs25,000Question 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.

Compound interest

For 1^{st} year:

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

For 2^{nd} year:

P = Rs.*x *+ Rs. 0.08*x* = Rs. 1.08*x*

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. 0.1664*x* - Rs. 0.16*x* = Rs.64

⇒ Rs. 0.0064*x* = 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 1^{st} year

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

Interest= Rs= Rs2,160

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

For 2^{nd} year

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

Interest= Rs= Rs2,505.60

=Rs2,506Question 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 1^{st} year

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

Interest= Rs= Rs4,800

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

For 2^{nd} year

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

Interest= Rs= Rs5,280

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

For 3^{rd} year

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

Interest= Rs= Rs5,808Question 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:

- The rate of interest charged
- The amount of debt at the end of the second year

Solution 9

(i)

Let *x%* be the rate of interest charged.

For 1^{st} year:

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

For 2^{nd} year:

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

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

The compound interest for the second year is Rs.920

Rs. (80*x +* 1.20*x ^{2}) = *Rs.920

⇒1.20*x ^{2} +* 80

*x*- 920 = 0

⇒3*x ^{2} + 2*00

*x*- 2300 = 0

⇒3*x ^{2}* + 230

*x*- 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 1^{st} year:

Interest = Rs.120*x* = Rs.1200

For 2^{nd} year:

Interest = Rs.(80*x +* 1.20x* ^{2})* = 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.10,120Question 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