ML Aggarwal Solutions for Class 8 Maths Chapter 8 Simple and Compound Interest has solutions prepared by experienced teachers at BYJU’S. Mathematics is one such subject where students score high marks with ease, if they practise on a regular basis. These solutions help them to improve conceptual knowledge, which assists them in acing the exam. For a better understanding of the concepts, students can make use of ML Aggarwal Solutions for Class 8 Maths Chapter 8 Simple and Compound Interest PDF from the links given below.
Chapter 8 discusses problems on finding the rate of interest, principal amount and time period, as per the current ICSE syllabus. Once they are through with the ML Aggarwal Solutions, students can cross-check their answers while solving textbook questions and also clear their doubts instantly. It also enhances their speed of solving problems, which is essential for better performance in academics.
ML Aggarwal Solutions for Class 8 Maths Chapter 8 Simple and Compound Interest
Access ML Aggarwal Solutions for Class 8 Maths Chapter 8 Simple and Compound Interest
Exercise 8.1
1. Find the simple interest on Rs 4000 at 7.5% p.a. for 3 years 3 months. Also, find the amount.
Solution:
Here
Principal (P) = Rs 4000
Rate of interest (R) = 7.5% p.a.
= (15 / 2) % p.a.
Time (T) = 3 years 3 months
=
years
=
years
= 13 / 4 years
Hence,
Simple Interest (I) = (P × R × T) / 100
= Rs {4000 × (15 / 2) × (13 / 4)} / 100
= Rs (4000 × 15 × 13) / (100 × 2 × 4)
On simplification, we get,
= Rs 5 × 15 × 13
= Rs 975
Therefore,
Amount = P + I
= Rs 4000 + Rs 975
= RS 4, 975
2. What sum of money will yield Rs 170.10 as simple interest in 2 years 3 months at 6% per annum?
Solution:
Here
I = Rs 170.10
T = 2 years 3 months
=
years
=
years
= 9 / 4 years
R = 6%
Hence,
P = (I × 100) / (R × T)
= Rs (170.10 × 100) / {6 × (9 / 4)}
On calculating further, we get,
= Rs (170.10 × 100 × 4) / (6 × 9)
= Rs (17010 × 4) / (6 × 9)
= Rs (17010 × 2) / (3 × 9)
= Rs 34020 / 27
= Rs 1260
3. Find the rate of interest when Rs 800 fetches Rs 130 as a simple interest in 2 years 6 months.
Solution:
Here
P = Rs 800
T = 2 years 6 months
=
years
=
years
= 5 / 2 years
Hence,
R = (I × 100) / (P × T)
= (130 × 100) / {800 × (5 / 2)} % p.a.
On simplification, we get,
= (130 × 100 × 2) / (800 × 5) % p.a.
= (130 × 2) / 40 %
= 130 / 20 % p.a.
= 13 / 2 %
= 6.5% p.a.
Therefore, the required rate of interest is 6.5% p.a.
4. Find the time when simple interest on Rs 3.3 lakhs at 6.5% per annum is Rs 75075.
Solution:
Here,
P = 3.3 lakhs
= Rs 3.3 × 100000
= Rs 330000
R = 6.5% per annum
I = Rs 75075
Hence,
T = (I × 100) / (P × R)
= (75075 × 100) / (330000 × 6.5) years
= (75075 × 100 × 10) / (330000 × 65) years
On further calculation, we get,
= (75075) / (330 × 65) years
= 1155 / 330 years
We get,
= 7 / 2 years
=
years
5. Find the sum of money when
(i) simple interest at 
% p.a. for years is Rs 2356.25
(ii) the final amount is Rs 11300 at 4% p.a. for 3 years 3 months.
Solution:
(i) Here,
I = Rs 2356.25
R =
% p.a.
= 29 / 4 % p.a.
T =
years
= 5 / 2 years
Hence,
P = (I × 100) / (R × T)
= Rs (2356.25 × 100) / (29 / 4) × (5 / 2)
On further calculation, we get,
= Rs (2356.25 × 100 × 4 × 2) / (29 × 5)
= Rs (235625 × 8) / (29 × 5)
We get,
= Rs (47125 × 8) / 29
= Rs 1625 × 8
= Rs 13000
(ii) Amount (A) = Rs 11300
Rate (R) = 4% p.a.
Time (T) = 3 years 3 months
=
years
=
years
= 13 / 4 years
Let the principal be Rs x
Hence,
S.I. = (P × R × T) / 100
= Rs (x × 4 × 13) / (100 × 4)
We get,
= Rs 13x / 100
Then,
Amount = Principal + Simple Interest
= Rs x + Rs 13x / 100
= Rs (x + 13x) / 100
We get,
= Rs (100x + 13x) / 100
= Rs (113x / 100)
But, the amount given is Rs 11300
Hence,
113x / 100 = 11300
x = 11300 × 100 / 113
x = 100 × 100
We get,
x = 10000
Therefore, principal (P) = Rs 10000
6. How long will it take a certain sum of money to triple itself at 
% per annum simple interest?
Solution:
Let the sum of money be x
Amount = 3 × Rs x
= Rs 3x
Interest = Amount – Principal
= Rs 3x – Rs x
= Rs 2x
Rate =
% p.a.
= 40 / 3 % p.a.
Time (T) = (I × 100) / (P × R)
= (2x × 100) / x × (40 / 3) years
On further calculation, we get,
= (2 × 100 × 3) / 40 years
= (100 × 3) / 20 years
We get,
= 5 × 3 years
= 15 years
7. At a certain rate of simple interest Rs 4050 amounts to Rs 4576.50 in 2 years. At the same rate of simple interest, how much would Rs 1 lakh amount to in 3 years?
Solution:
Here,
P = Rs 40000
A = Rs 4576.50
T = 2 years
Interest = Amount – Principal
= Rs 4576.50 – Rs 4050
= Rs 526.50
Let the rate of simple interest = R% per annum
Then,
R = (I × 100) / (P × T)
= (526.50 × 100) / (4050 × 2) % p.a.
On further calculation, we get,
= (526.50 × 10) / (405 × 2) % p.a.
= 5265 / 810 % p.a.
We get,
= 6.5% p.a.
Now,
P = Rs 1 lakh
= Rs 100000
R = 6.5% p.a.
T = 3 years
I = (P × R × T) / 100
= Rs (100000 × 6.5 × 3) / 100
We get,
= RS 1000 × 6.5 × 3
= Rs 19500
Amount = Principal + Interest
= Rs 100000 + Rs 19500
= Rs 119500
8. What sum of money invested at 7.5% p.a. simple interest for 2 years produces twice as much interest as Rs 9600 in 3 years 6 months at 10% p.a. simple interest?
Solution:
First Case:
Principal (P1) = Rs 9600
Rate (R1) = 10%
Period = (T) = 3 years 6 months
=
years = 7 / 2 years
Simple interest = (P × R × T) / 100
= (9600 × 10 × 7) / (100 × 2)
We get,
= Rs 3360
Second case:
Simple interest = Rs 3360 × 2
= Rs 6720
Rate (R) = 7.5% p.a. and
Period (T) = 2 years
Therefore,
Principal = (S.I × 100) / (R × T)
= (6720 × 100) / (7.5 × 2)
= Rs (6720 × 100 × 10) / (75 × 2)
= 6720000 / 150
We get,
= Rs 44800
Exercise 8.2
1. Calculate the compound interest on Rs 6000 at 10% per annum for two years.
Solution:
Given
Rate of interest = 10% per annum
Principal for the first year = Rs 6000
Interest for the first year = Rs (6000 × 10 × 1) / 100
= Rs 600
Amount at the end of first year = Rs 6000 + Rs 600
= Rs 6600
Principal for the second year = Rs 6600
Interest for the second year = Rs (6600 × 10 × 1) / 100
= Rs 660
Amount for the second year = Rs 6600 + Rs 660
= Rs 7260
Therefore, compound interest for 2 years = final amount – (original) Principal
= Rs 7260 – Rs 6000
We get,
= Rs 1260
2. Salma borrowed from Mahila Samiti a sum of Rs 1875 to purchase a sewing machine. If the rate of interest is 4% per annum, what is the compound interest that she has to pay after 2 years?
Solution:
Principal for the first year = Rs 1875
Rate of interest = 4% p.a.
Interest for the first year = Rs (1875 × 4 × 1) / 100
= 75
Amount at the end of first year = Rs 1875 + Rs 75
= Rs 1950
Principal for the second year = Rs 1950
Interest for the second year = Rs (1950 × 4 × 1) / 100
= 78
Amount at the end of second year = Rs 1950 + Rs 78
= Rs 2028
Hence,
Compound interest paid by Salma = Final amount – (original) Principal
= Rs 2028 – Rs 1875
= Rs 153
3. Jacob invests Rs 12000 for 3 years at 10% per annum. Calculate the amount and the compound interest that Jacob will get after 3 years.
Solution:
Principal for the first year = Rs 12000
Rate of interest = 10% p.a.
Interest for the first year = Rs (12000 × 10 × 1) / 100
= Rs 1200
Amount at the end of first year = Rs 12000 + Rs 1200
= 13200
Principal for the second year = Rs 13200
Interest for the second year = Rs (13200 × 10 × 1) / 100
= Rs 1320
Amount at the end of second year = Rs 13200 + Rs 1320
= Rs 14520
Principal for the third year = Rs 14520
Interest for the third year = Rs (14520 × 10 × 1) / 100
= Rs 1452
Amount at the end of third year = Rs 14520 + Rs 1452
= Rs 15972
Hence,
Compound interest for 3 year = Final amount – (original) Principal
= Rs 15972 – Rs 12000
= Rs 3972
4. A man invests Rs 46875 at 4% per annum compound interest for 3 years.
Calculate:
(i) the interest for the first year
(ii) the amount standing to his credit at the end of second year
(iii) the interest for the third year
Solution:
(i) Principal for the first year = Rs 46875
Rate of interest = 4% per annum
Therefore,
Interest for the first year = Rs (46875 × 4 × 1) / 100
We get,
= Rs 46875 / 25
= Rs 1875
Hence, interest for the first year is Rs 1875
(ii) Amount at the end of first year
= Rs 46875 + Rs 1875
We get,
= Rs 48750
Principal for the second year = Rs 48750
Interest for the second year = Rs (48750 × 4 × 1) / 100
= Rs 48750 / 25
We get,
= Rs 1950
Amount at the end of second year = Rs 48750 + Rs 1950
We get,
= Rs 50700
Hence, the amount at the end of second year is Rs 50700
(iii) Principal for the third year = Rs 50700
Interest for the third year = Rs (50700 × 4 × 1) / 100
We get,
= Rs 507 × 4
= Rs 2028
Hence, the interest for the third year is Rs 2028
5. Calculate the compound interest for the second year on Rs 6000 invested for 3 years at 10% p.a. Also find the sum due at the end of third year.
Solution:
Principal for the first year = Rs 6000
Rate of interest = 10% p.a.
Interest for the first year = Rs (6000 × 10 × 1) / 100
= Rs 600
Amount at the end of first year = Rs 6000 + Rs 600
= Rs 6600
Principal for the second year = Rs 6600
Interest for the second year = Rs (6600 × 10 × 1) / 100
We get,
= Rs 660
Amount at the end of second year = Rs 6600 + Rs 660
= Rs 7260
Compound interest for the second year = Final amount – (original) Principal
= Rs 7260 – Rs 6000
= Rs 1260
Principal for the third year = Rs 7260
Interest for the third year = Rs (7260 × 10 × 1) / 100
We get,
= Rs 726
Amount at the end of third year = Rs 7260 + Rs 726
= Rs 7986
6. Calculate the amount and the compound interest on Rs 5000 in 2 years when the rate of interest for successive years is 6% and 8% respectively.
Solution:
Principal for the first year = Rs 5000
Rate of interest = 6% p.a.
Interest for the first year = Rs (5000 × 6 × 1) / 100
= Rs 50 × 6
= Rs 300
Amount at the end of first year = Rs 5000 + Rs 300
= Rs 5300
Principal for the second year = Rs 5300
Rate of interest = 8% p.a.
Interest for the second year = Rs (5300 × 8 × 1) / 100
= Rs 53 × 8
We get,
= Rs 424
Amount for the second year = Rs 5300 + Rs 424
= Rs 5724
Compound interest for two years = Final amount – (original) Principal
= Rs 5724 – Rs 5000
We get,
= Rs 724
7. Calculate the difference between the compound interest and the simple interest on Rs 20000 in 2 years at 8% per annum.
Solution:
Principal (P) = Rs 20000
Rate (R) = 8% p.a.
Period (T) = 2 years
Hence,
Simple interest (S.I.) = PRT / 100
= Rs (20000 × 8 × 2) / 100
We get,
= Rs 3200
Now,
Amount on compound interest
A = P {1 + (R / 100)}n
= RS 20000 {1 + (8 / 100)}2
On further calculation,
We get,
= Rs 20000 × (27 / 25) × (27 / 25)
= Rs 32 × 729
= Rs 23328
Therefore,
Compound interest = Final amount – (original) Principal
= Rs 23328 – Rs 20000
We get,
= Rs 3328
Hence,
Difference in compound interest – simple interest
= Rs 3328 – Rs 3200
= Rs 128
Exercise 8.3
1. Calculate the amount and compound interest on
(i) Rs 15000 for 2 years at 10% per annum compounded annually.
(ii) Rs 156250 for 
years at 8% per annum compounded half-yearly.
(iii) Rs 100000 for 9 months at 4% per annum compounded quarterly.
Solution:
(i) Given
Principal (P) = Rs 15000
Rate (R) = 10% p.a.
Period (n) = 2 years
Hence,
Amount (A) = P {1 + (R / 100)}n
= Rs 15000 {1 + (10 / 100)}2
On further calculation, we get,
= Rs 15000 × (11 / 10) × (11 / 10)
We get,
= Rs 18150
Therefore,
Compound interest = Amount – Principal
= Rs 18150 – 15000
We get,
= Rs 3150
(ii) Principal (P) = Rs 156250
Rate (R) = 8% p.a. or 4% half-yearly
Period (n) =
years
= 3 half-year
Therefore,
Amount (A) = P {1 + (R / 100)}n
= Rs 156250 {1 + (4 / 100)}3
On further calculation, we get,
= Rs 156250 × (26 / 25)3
= Rs 156250 × (26 / 25) × (26 / 25) × (26 / 25)
We get,
= Rs 175760
Hence,
Compound interest = Amount – Principal
= Rs 175760 – Rs 156250
= Rs 19510
2. Find the difference between the simple interest and compound interest on Rs 4800 for 2 years at 5% per annum, compound interest being reckoned annually.
Solution:
Given
Principal (P) = Rs 4800
Rate (R) = 5% p.a.
Period (n) = 2 years
Therefore,
S.I. = PRT / 100
= (4800 × 5 × 2) / 100
We get,
= Rs 480
And when interest is compounded annually
Amount (A) = P {1 + (R / 100)}n
= Rs 4800 {1 + (5 / 100)}2
= Rs 4800 × (21 / 20) × (21 / 20)
We get,
= Rs 5292
Hence,
Compound interest = Amount – Principal
= Rs 5292 – Rs 4800
= Rs 492
Now,
Difference in compound interest and simple interest = Rs 492 – Rs 480
= Rs 12
3. Find the compound interest on Rs 3125 for 3 years if the rates of interest for the first, second and third year are respectively 4%, 5% and 6% per annum.
Solution:
Given
Principal (P) = Rs 3125
Rate of interest for continuous 3 years = 4%, 5%, 6%
Period (n) = 3 years
Therefore,
Amount = P {1 + (r / 100)}n
= 3125 {1 + (4 / 100)} {1 + (5 / 100)} {1 + (6 / 100)}
On further calculation, we get,
= 3125 × (26 / 25) × (21 / 20) × (53 / 50)
We get,
= Rs 14469 / 4
= Rs 3617.25
Hence,
Compound interest = Amount – Principal
= Rs 3617. 25 – Rs 3125
= Rs 492. 25
4. Kamla borrowed Rs 26400 from a Bank to buy a scooter at a rate of 15% p.a. compounded yearly. What amount will she pay at the end of 2 years and 4 months to clear the loan?
Solution:
Given
Money borrowed (P) = Rs 26400
Rate (R) = 15% p.a.
Period (n) = 2 years 4 months
=
=
years
Therefore,
Amount = P {1 + (R / 100)}n
= Rs 26400 {1 + (5 / 100)2} × [1 + {15 / (3 × 100)}]1
On further calculation, we get,
= Rs 26400 × (23 / 20) × (23 / 20) × (21 / 20)
We get,
= Rs 366597 / 10
= Rs 36659.70
5. Anil borrowed Rs 18000 from Rakesh at 8% per annum simple interest for 2 years. If Anil had borrowed this sum at 8% per annum compound interest, what extra amount would he has to pay?
Solution:
Given
Money borrowed (P) = Rs 18000
Rate (R) = 8% p.a.
Time (n) = 2 years
Simple Interest = PRT / 100
= Rs (18000 × 8 × 2) / 100
= Rs 2880
In case of compound interest
A = P {1 + (R / 100)}n
= Rs 18000 {1 + (8 / 100)}2
= Rs 18000 × (27 / 25)2
= Rs 18000 × (27 / 25) × (27 / 25)
We get,
= Rs 104976 / 5
= Rs 20995.20
Hence,
Compound interest = Amount – Principal
= Rs 20995.20 – Rs 18000
= Rs 2995.20
Now,
Difference between compound interest and simple interest
= Rs 2995.20 – Rs 2880
= Rs 115.20
6. Mukesh borrowed 75000 from a bank. If the rate of interest is 12% per annum, find the amount he would be paying after 
years if the interest is
(i) compounded annually
(ii) compounded half-yearly
Solution:
Given
Money borrowed (P) = Rs 75000
Rate (R) = 12% p.a. or 6% half- yearly
Period (n) =
years or 3 half-years
(i) When the interest compounded yearly
Amount (A) = P {1 + (R / 100)}n
= Rs 75000 {1 + (12 / 100)} {1 + (6 / 100)}
= Rs 75000 × (28 / 25) × (53 / 50)
On simplification, we get,
= Rs 89040
(ii) When the interest compounded half-yearly
Then,
Amount = Rs 75000 {1 + (6 / 100)}3
= Rs 75000 × (53 / 50)3
= Rs 75000 × (53 / 50) × (53 / 50) × (53 / 50)
We get,
= Rs 446631 / 5
= Rs 89326.20
7. Aryaman invested Rs 10000 in a company, he would be paid interest at 7% per annum compounded annually. Find
(i) the amount received by him at the end of 2 years
(ii) the interest for the 3rd year
Solution:
(i) Given
Investment to a company (P) = Rs 10000
Rate of interest (R) = 7% p.a.
Period (n) = 2 years
Hence,
Amount (A) = P {1 + (R / 100)}n
= Rs 10000 {1 + (7 / 100)}2
= Rs 10000 × (107 / 100) × (107 / 100)
On simplification, we get,
= Rs 11449
(ii) Amount after 3rd year = Rs 11449 × (107 / 100)
We get,
= Rs 12250.43
Therefore,
Interest on the 3rd year = Rs 12250.43 – 11449
= Rs 801.43
8. What sum of money will amount to Rs 9261 in 3 years at 5% per annum compound interest?
Solution:
Given
Amount (A) = Rs 9261
Rate of interest = 5% p.a.
Time (T) = 3 years
Principal (P) =?
A = P {1 + (r / 100)}t
9261 = P {1 + (5 / 100)}3
We get,
9261 = P (21 / 20)3
P = (9261 × 20 × 20 × 20) / (21 × 21 × 21)
On simplification, we get,
= Rs 8000
Therefore, the sum of money = Rs 8000
9. What sum invested for 
years compounded half-yearly at the rate of 8% p.a. will amount to Rs 140608?
Solution:
Given
Amount (A) = Rs 140608
Rate (R) = 8% p.a. = 4% half-yearly
Period (n) =
years = 3 half-year
A = P {1 + (R / 100)}n
140608 = P {1 + (4 / 100)}3
140608 = P (26 / 25)3
Therefore,
P = 140608 × (25 / 26) × (25 / 26) × (25 / 26)
On further calculation, we get,
P = Rs 125000
Hence,
Principal = Rs 125000
10. At what rate percent will Rs 2000 amount to Rs 2315.25 in 3 years at compound interest?
Solution:
Given
Principal (P) = Rs 2000
Amount (A) = Rs 2315.25
Period (n) = 3 years
Let the rate of interest be r% p.a.
WKT
A / P = {1 + (r / 100)}n
2315.25 / 2000 = {1 + (r / 100)}3
{1 + (r / 100)}3 = (231525) / (100 × 2000)
On calculating, we get,
{1 + (r / 100)}3 = 9261 / 8000
{1 + (r / 100)}3 = (21 / 20)3
We get,
1 + (r / 100) = 21 / 20
r / 100 = (21 / 20) – 1
r / 100 = 1 / 20
We get,
r = 100 / 20
r = 5
Therefore, rate of interest = 5% p.a.
11. If Rs 40000 amounts to Rs 46305 in 
years, compound interest payable half-yearly, find the rate of interest per annum.
Solution:
Given
Principal (P) = Rs 40000
Amount (A) = Rs 46305
Period (n) =
years = 3/2 years
So half yearly, 2n = 2 × (3/2) = 3 years.
Let the rate of interest be r% p.a.
WKT
A / P = (1 + r / 100)n
46305 / 40000 = (1 + r / 100)3
(1 + r / 100)3 = 46305 / 40000
On further calculation, we get,
(1 + r / 100)3 = 9261 / 8000
(1 + r / 100)3 = (21 / 20)3
We get,
(1 + r / 100) = (21 / 20)
r / 100 = (21 / 20) – 1
r / 100 = 1 / 20
r = 100 / 20
We get,
r = 5
Therefore, rate of interest = 5% for half year.
So, 2 × 5 = 10% per annum.
12. In what time will Rs 15625 amount to Rs 17576 at 4% per annum compound interest?
Solution:
Given
Amount (A) = Rs 17576
Principal (P) = Rs 15625
Rate (R) = 4% p.a.
Let period be n years
WKT
A / P = {1 + (r / 100)}n
17576 / 15625 = {1 + (4 / 100)}n
We get,
(26 / 25)3 = (26 / 25)n
n = 3
Therefore, time = 3 years
13. Rs 16000 invested at 10% p.a. compounded semi-annually, amounts to Rs 18522. Find the time period of investment.
Solution:
Given
Principal (P) = Rs 16000
Amount (A) = Rs 18522
Rate (R) = 10% p.a. or 5% semi-annually
Let period be n half-years
WKT
A / P = {1 + (r / 100)}n
18522 / 16000 = {1 + (5 / 100)}n
On further calculation, we get,
9261 / 8000 = (21 / 20)n
(21 / 20)3 = (21 / 20)n
So,
n = 3 half years
Therefore,
Time = 3 / 2 =
years
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