MATHEMATICS IN EVERYDAY LIFE–8

嚜燐ATHEMATICS IN EVERYDAY LIFE每8

Chapter 10 : Compound Interest

EXERCISE 10.1

1. Principal for 1st year = `7600

Rate of interest = 5% per annum

? 7600 ? 5 ? 1 ?

Interest for 1st year = ` ?

?

100

?

?

= `380

Amount at the end of 1st year = `7600 + `380

= `7980

Principal for 2nd year = ` 7980

? 7980 ? 5 ? 1 ?

Interest for 2nd year = ` ?

?

100

?

?

= `399

Amount at the end of 2nd year = `7980 + `399

= `8379

Compound interest = Amount 每 Principal

= `8379 每 `7600

= `779

Hence, compound interest = `779.

2. Principal for 1st year = `5000

Rate of interest = 15% per annum

? 5000 ? 15 ? 1?

Interest for 1st year = ` ?

??

100

?

= `750

Amount at the end of 1st year = `5000 + `750

= `5750

Principal for 2nd year = `5750

? 5750 ? 15 ? 1?

Interest for 2nd year = ` ?

??

?

100

= `862.50

Amount at the end of 2nd year = `5750 + `862.50

= `6612.50

Compound interest = Amount 每 Principal

= `6612.50 每 `5000

= `1612.50

Hence, compound interest = `1612.50.

Mathematics In Everyday Life-8

ANSWER KEYS

3. Principal for 1st year = `16000

Rate of interest = 5% per annum

? 16000 ℅ 5 ℅ 1?

Interest for 1st year = ` ?

??

100

?

= `800

Amount at the end of 1st year = `16000 + `800

= `16800

Principal for 2nd year = `16800

? 16800 ? 5 ? 1 ?

Interest for 2nd year = ` ?

?

100

?

?

= `840

Amount at the end of 2nd year = `(16800 + 840)

= `17640

Compound interest = Amount 每 Principal

= `(17640 每 16000)

= `1640

Hence, she will pay `17640 at the end of 2 years and

interest is `1640.

4. Principal for 1st year = `8000

Rate of interest = 18% per annum

? 8000 ? 18 ? 1 ?

Interest for 1st year = ` ?

? = `1440

100

?

?

Amount at the end of 1st year = `(8000 + 1440)

= `9440

Principal for 2nd year = `9440

? 9440 ? 18 ? 1 ?

Interest for 2nd year = ` ?

?

100

?

?

= `1699.20

Amount at the end of 2nd year = `(9440 + 1699.20)

= `11139.20

Principal for 3rd year = `11139.20

? 11139.20 ? 18 ? 1 ?

Interest for 3rd year = ` ?

?

100

?

?

= `2005.06

Amount at the end of 3rd year

= `(11139.20 + 2005.06)

= `13144.26

1

? Compound interest = `(13144.26 每 8000)

Compound interest = `5144.26.

5. Principal for 1st year = `3000

Rate of interest = 4% per annum

? 3000 ? 4 ? 1 ?

Interest for 1st year = ` ?

?

100

?

?

= `120

Amount at the end of 1st year = `(3000 + 120)

= `3120

Principal for 2nd year = `3120

? 3120 ? 4 ? 1 ?

Interest for 2nd year = ` ?

?

100

?

?

= ` 124.80

Amount at the end of 2nd year = `(3120 + 124.80)

= `3244.80

? Compound interest = Amount 每 Principal

= `(3244.80 每 `3000)

= `244.80

6. Principal for 1st year = `4000

1

19

Rate of interest = 9 % ? % per annum

2

2

? 4000 ? 19 ? 1 ?

Interest for 1st year = ` ?

? = `380

? 100 ? 2 ?

Amount at the end of 1st year = `(4000 + 380)

= `4380

Principal for 2nd year = `4380

? 4380 ? 19 ? 1 ?

Interest for 2nd year = ` ?

?

? 100 ? 2 ?

= `416.10

Amount at the end of 2nd year = `(4380 + 416.10)

= `4796.10

Compound interest = Amount 每 Principal

= `(4796.10 每 4000)

Compound interest = `796.10.

7. Principal for 1st year = `2000

Rate of interest = 10% per annum

? 2000 ? 10 ? 1 ?

Interest for 1st year = ` ?

?

100

?

?

= `200

Amount at the end of 1st year = `(2000 + 200)

= `2200

Principal for 2nd year = `2200

2

? 2200 ? 10 ? 1 ?

Interest for 2nd year = ` ?

?

100

?

?

= `220

Amount at the end of 2nd year = `(2200 + 220)

= `2420

Principal for 3rd year = `2420

? 2420 ? 10 ? 1 ?

Interest for 3rd year = ` ?

?

100

?

?

= `242

Amount at the end of 3rd year = `(2420 + 242)

= `2662

Hence, he will repay `2662 after 3 years.

8. Principal for 1st year = `2500

Rate of interest = 8% per annum

? 2500 ? 8 ? 1 ?

Interest for 1st year = ` ?

?

100

?

?

= `200

Amount at the end of 1st year = `(2500 + 200)

= `2700

Principal for 2nd year = `2700

2700 ? 8 ? 1 ?

Interest for 2nd year = ` ??

?

100

?

?

= `216

Amount at the end of 2nd year = `(2700 + 216)

= `2916

? Compound interest = Amount 每 Principal

= `(2916 每 2500) = ` 416.

9. Principal for 1st year = `3500

Rate of interest = 20% per annum

? 3500 ? 20 ? 1 ?

Interest for 1st year = ` ?

?

100

?

?

= `700

Amount at the end of 1st year = `(3500 + 700)

= `4200

Principal for 2nd year = `4200

? 4200 ? 20 ? 1 ?

Interest for 2nd year = ` ?

?

100

?

?

= `840

Amount at the end of 2nd year = `(4200 + 840)

= `5040

? Compound interest = Amount 每 Principal

= `(5040 每 3500) = ` 1540

Hence, compound interest = `1540.

Answer Keys

10. Principal for 1st year = `20,000

Rate of interest = 12% per annum

2

20 ?

?

= `2700 ? ? 1 ?

?

300 ?

?

? 20,000 ? 12 ? 1 ?

Interest for 1st year = ` ?

?

100

?

?

2

1

= `2700 ? ?? 1 ? ??

15 ?

?

= `2400

Amount at the end of 1st year = `(20,000 + 2400)

= `22,400

Principal for 2nd year = `22,400

? 16 ?

= `2700 ? ? ?

? 15 ?

? 22400 ? 12 ? 1 ?

Interest for 2nd year = ` ?

?

100

?

?

? 2700 ? 16 ? 16 ?

= `?

?? = `3072

15 ? 15

?

= `2688

Amount at the end of 2nd year = `(22400 + 2688)

= `25088

Hence, Rahim has to pay `25088 after 2 years.

EXERCISE 10.2

= `2700 ?

1

15

3. P = `12800, R = 7 % per annum =

% per annum,

2

2

T = 1 year

If interest compounded semi-annually. Then

R=

T = 1 ? 2 = 2 half years.

T

R ?

A = P ?? 1 ?

?

100 ?

?

2

5 ?

?

= `6400 ? ? 1 ?

?

100 ?

?

?

15 ?

= `12800 ? ? 1 ?

4 ? 100 ??

?

2

1

= `6400 ? ?? 1 ? ??

20 ?

?

2

3

= `12800 ? ?? 1 ? ??

80 ?

?

? 64 ? 21 ? 21 ?

= `?

? = ` 7056

4

?

?

Compound interest = Amount 每 Principal

= `(7056 每 6400)

? Compound interest = ` 656

2

20

2. P = ` 2700, R = 6 % per annum =

% per annum,

3

3

T = 2 years

We have,

T

R ?

A = P ?? 1 ?

?

100 ?

?

?

20 ?

= `2700 ? ? 1 ?

3

?

100 ??

?

2

2

15 ?

= `12800 ? ?? 1 ?

?

400 ?

?

2

21 ? 21

= `6400 ?

20 ? 20

Mathematics In Everyday Life-8

15

15

=

% per half yearly

2?2

4

We have,

R ?

A = P ?? 1 ?

?

100 ?

?

? 21 ?

= `6400 ? ? ?

? 20 ?

16 16

?

15 15

? Compound interest = A 每 P

= `(3072 每 2700) = `372

1. Principal (P) = `6400, Rate (R) = 5% per annum

Time (T) = 2 years

We have,

T

2

? 83 ?

= `12800 ? ? ?

? 80 ?

= `12800 ?

2

83 83

?

80 80

? 128 ? 83 ? 83 ?

= `?

?

8?8

?

?

= `13778

Hence, Arun paid `13778 after one year.

11

% per annum

2

4. P = ` 6400, T = 2 years, R =

We have,

2

T

R ?

A = P ?? 1 ?

?

100

?

?

3

?

11 ?

= `6400 ? ? 1 ?

2 ? 100 ??

?

= `6400 ? ?? 1 ? 11 ??

200 ?

?

211 ?

= `6400 ? ??

?

? 200 ?

= `6400 ?

2

2

1 3

7. P = `2,50,000, R = 8% p.a., T = 1 = years

2 2

If interest compounded half yearly. Then,

2

211 211

?

200 200

? 64 ? 211 ? 211?

= `?

??

?

400

= `7123.36

? Compound interest = A 每 P

= `(7123.36 每 6400)

= `723.36

5. P = `30,000, R = 7% p.a., T = 2 years

We have,

T

R ?

A = P ?? 1 ?

?

100 ?

?

7 ?

= `30,000 ? ?? 1 ?

?

100 ?

?

? 107 ?

= `30,000 ? ?

?

? 100 ?

Compound interest = A 每 P

= `(18250.50 每 12000)

= `6250.50

? Compound interest = `6250.50

2

2

107 107

?

= `30,000 ?

100 100

= `(3 ? 107 ? 107)

= `34347

Hence, the amount is `34347.

6. P = `12000, R = 15% p.a., T = 3 years

We have,

R=

8

% = 4% per half year

2

T=

3

? 2 = 3 half years

2

Now, we have

T

R ?

A = P ?? 1 ?

?

100 ?

?

3

4 ?

?

= `2,50,000 ? ? 1 ?

?

100 ?

?

3

1

= `2,50,000 ? ?? 1 ? ??

25 ?

?

? 26 ?

= `2,50,000 ? ? ?

? 25 ?

26 26 26

?

?

25 25 25

= `(16 ? 26 ? 26 ? 26)

= `2,50,000 ?

A = `2,81,216

? Compound interest = A 每 P

= `(2,81,216 每 2,50,000)

= `31,216.

8. P = ` 25,000, R = 15% p.a., T = 2 years

? 25000 ? 15 ? 2 ?

Simple interest for 2 years = ` ?

?

100

?

?

T

R ?

A = P ?? 1 ?

?

100 ?

?

P?R?T?

?

?? S.I. ?

?

100 ?

?

3

15 ?

= `12,000 ? ?? 1 ?

?

100 ?

?

3 ?

?

= `12,000 ? ? 1 ? ?

20

?

?

? 23 ?

= `12,000 ? ? ?

? 20 ?

= `12,000 ?

3

3

23 23 23

?

?

20 20 20

? 12 ? 23 ? 23 ? 23 ?

= `?

?

8

?

?

A = `18250.50

4

3

= `7500

? Simple interest for 2 years = `7500

Amount to be paid by Ravi to Shishir after two years

= `(25000 + 7500) = `32500

But, Ravi lent same money to Rakesh at the same

rate of interest but compounded annually for 2 years.

Then,

T

R ?

A = P ?? 1 ?

?

100 ?

?

2

15 ?

?

= ` 25000 ? ? 1 ?

?

100 ?

?

Answer Keys

2

3 ?

?

= ` 25000 ? ? 1 ? ?

20 ?

?

23

= ` 25000 ? ?? ??

? 20 ?

2

= ` 8000 ?

? 250 ? 529 ?

A= `?

?

4

?

?

= ` 33062.50

Now, gain in this transaction

= `(33062.50 每 32500)

= ` 562.50

Hence, he gain `562.50 in this transaction.

9. P = `9000, R = 10% p.a., T = 3 years

T

R ?

A = P ?? 1 ?

?

100 ?

?

3

3

1

= `9000 ? ?? 1 ? ??

10 ?

?

3

11 11 11

?

?

10 10 10

= `(9 ? 1331) = `11979

Hence, Saurabh paid ` 11979 after three years.

10. Let principal be `P.

T = 2 years, R = 12% p.a., S.I. = `1920

?

?

Now,

P? R?T

100

= `(10035.20 每 `8000)

= `2035.20

? Compound interest = `2035.20

11. P = ` 15000, R = 20% p.a., T = 2 years

If interest compounded half yearly. Then,

R=

20

% = 10% per half year, T = 2 ℅ 2 = 4 half-years.

2

= `15000 ? ?? 1 ? 1 ??

?

10 ?

? 11 ?

= `15000 ? ? ?

? 10 ?

= `15000 ?

4

4

4

11 11 11 11

?

?

?

10 10 10 10

= `21961.50

Compound interest = A 每 P

= `(21961.50 每 15000)

= `6961.50

? Compound interest = `6961.50.

? 1920 ? 100 ?

P = ?

?

? 12 ? 2 ?

P = `8000

T

R ?

A = P ?? 1 ?

?

100

?

?

12 ?

= `8000 ? ?? 1 ?

?

100 ?

?

3 ?

?

= `8000 ? ? 1 ? ?

25 ?

?

T

R ?

A = P ?? 1 ?

?

100 ?

?

? 15000 ? 14641 ?

= `?

??

?

10000

? P ? 12 ? 2 ?

`1920 = ` ?

?

100 ??

Mathematics In Everyday Life-8

Compound interest = A 每 P

?

10 ?

= `15000 ? ? 1 ?

?

100 ??

= `9000 ?

?

28 28

?

25 25

We have,

10 ?

= `9000 ? ?? 1 ?

?

100 ?

?

? 11 ?

= `9000 ? ? ?

? 10 ?

2

? 64 ? 28 ? 28 ?

= `?

?

5

?

?

= ` 10035.20

23 23

?

20 20

= ` 25000 ?

S.I. =

? 28 ?

= ` 8000 ? ? ?

? 25 ?

2

3

1

12. P = ` 60000, R = 10% p.a., T = 1 years = years

2

2

If interest compounded half yearly. Then,

R=

10

= 5% per half-year

2

T=

3

? 2 = 3 half-years

2

2

5

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