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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