RS Aggarwal Solutions: Exercise 11B - Compound Interest | Mathematics (Maths) Class 8 PDF Download

 Page 1


Q u e s t i o n : 1
Find the amount and the compound interest on Rs 2500 for 2 years at 10% per annum, compounded annually.
S o l u t i o n :
Principal for the first year = Rs. 2500Interest for the first year = Rs. 
2500×10×1
100
= Rs. 250Amount at the end of the first year = Rs. 2500 +250  = Rs. 2750Principal for the second
Q u e s t i o n : 2
Find the amount and the compound interest on Rs 15625 for 3 years at 12% per annum, compounded annually.
S o l u t i o n :
Principal for the first year = Rs. 15625Interest for the first year = Rs. 
15625×12×1
100
= Rs. 1875Amount at the end of the first year = Rs.  15625 + 1875 = Rs. 17500Principal for the
Q u e s t i o n : 3
Find the difference between the simple interest and the compound interest on Rs 5000 for 2 years at 9% per annum.
S o l u t i o n :
Principal amount = Rs. 5000Simple interest = Rs. 
5000×2×9
100
= Rs. 900The compound interest can be calculated as follows: Principal for the first year = Rs. 5000Interest for the first 
Q u e s t i o n : 4
Ratna obtained a loan of Rs 25000 from the Syndicate Bank to renovate her house. If the rate of interest is 8% per annum, what amount will she have to pay to the bank after 2 years to
discharge her debt?
S o l u t i o n :
Principal for the first year = Rs. 25000Interest for the first year = Rs. 
25000×8×1
100
= Rs. 2000Amount at the end of the first year = Rs. 25000 +2000 = Rs. 27000Principal for the second
Q u e s t i o n : 5
Harpreet borrowed Rs 20000 from her friend at 12% per annum simple interest. She lent it to Alam at the same rate but compounded annually. Find her gain after 2 years.
S o l u t i o n :
Principal amount = Rs. 20000Simple interest = Rs. 
20000×2×12
100
= Rs. 4800The compound interest can be calculated as follows: Principal for the first year = Rs. 20000Interest for the
Q u e s t i o n : 6
Manoj deposited a sum of Rs 64000 in a post office for 3 years, compounded annually at 7
1
2
% per annum. What amount will he get on maturity?
S o l u t i o n :
Principal for the first year = Rs. 64000Interest for the first year = Rs. 
64000×15×1
100×2
= Rs. 4800Now, amount at the end of the first year = Rs. 64000 +4800 = Rs. 68800Principal for
Q u e s t i o n : 7
Divakaran deposited a sum of Rs 6250 in the Allahabad Bank for 1 year, compounded half-yearly at 8% per annum. Find the compound interest he gets.
S o l u t i o n :
Principal amount = Rs. 6250Rate of interest = 8 % per annum = 4 % for half yearTime = 1 year = 2 half yearsPrincipal for the first half year = Rs. 6250Interest for the first half year 
Q u e s t i o n : 8
Michael borrowed Rs 16000 from a finance company at 10% per annum, compounded half-yearly. What amount of money will discharge his debt after 1
1
2
 years?
S o l u t i o n :
Principal amount = Rs. 16000Rate of interest = 10 % per annum = 5 % for half yearTime = 1
1
2
 years = 3 half yearsPrincipal for the first half year = Rs. 16000Interest for the first half
Q u e s t i o n : 9
By using the formula, find the amount and compound interest on:
Rs 6000 for 2 years at 9% per annum compounded annually.
S o l u t i o n :
Principal amount, P = Rs 6000Rate of interest, R = 9 % per annumTime, n = 2 years. The formula for the amount including the compound interest is given below: A = Rs. P 1 +
R
100
n
 
Q u e s t i o n : 1 0
By using the formula, find the amount and compound interest on:
Rs 10000 for 2 years at 11% per annum compounded annually.
S o l u t i o n :
Principal amount, P = Rs. 10000Rate of interest, R = 11 % per annum. Time, n = 2 years. The formula for the amount including the compound interest is given below: A = Rs. P 1 +
R
100
Q u e s t i o n : 1 1
By using the formula, find the amount and compound interest on:
Rs 31250 for 3 years at 8% per annum compounded annually.
S o l u t i o n :
Principal amount, P = Rs. 31250Rate of interest, R = 8 % per annum. Time, n = 3 years. The formula for the amount including the compound interest is given below: A = Rs. P 1 +
R
100
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Page 2


Q u e s t i o n : 1
Find the amount and the compound interest on Rs 2500 for 2 years at 10% per annum, compounded annually.
S o l u t i o n :
Principal for the first year = Rs. 2500Interest for the first year = Rs. 
2500×10×1
100
= Rs. 250Amount at the end of the first year = Rs. 2500 +250  = Rs. 2750Principal for the second
Q u e s t i o n : 2
Find the amount and the compound interest on Rs 15625 for 3 years at 12% per annum, compounded annually.
S o l u t i o n :
Principal for the first year = Rs. 15625Interest for the first year = Rs. 
15625×12×1
100
= Rs. 1875Amount at the end of the first year = Rs.  15625 + 1875 = Rs. 17500Principal for the
Q u e s t i o n : 3
Find the difference between the simple interest and the compound interest on Rs 5000 for 2 years at 9% per annum.
S o l u t i o n :
Principal amount = Rs. 5000Simple interest = Rs. 
5000×2×9
100
= Rs. 900The compound interest can be calculated as follows: Principal for the first year = Rs. 5000Interest for the first 
Q u e s t i o n : 4
Ratna obtained a loan of Rs 25000 from the Syndicate Bank to renovate her house. If the rate of interest is 8% per annum, what amount will she have to pay to the bank after 2 years to
discharge her debt?
S o l u t i o n :
Principal for the first year = Rs. 25000Interest for the first year = Rs. 
25000×8×1
100
= Rs. 2000Amount at the end of the first year = Rs. 25000 +2000 = Rs. 27000Principal for the second
Q u e s t i o n : 5
Harpreet borrowed Rs 20000 from her friend at 12% per annum simple interest. She lent it to Alam at the same rate but compounded annually. Find her gain after 2 years.
S o l u t i o n :
Principal amount = Rs. 20000Simple interest = Rs. 
20000×2×12
100
= Rs. 4800The compound interest can be calculated as follows: Principal for the first year = Rs. 20000Interest for the
Q u e s t i o n : 6
Manoj deposited a sum of Rs 64000 in a post office for 3 years, compounded annually at 7
1
2
% per annum. What amount will he get on maturity?
S o l u t i o n :
Principal for the first year = Rs. 64000Interest for the first year = Rs. 
64000×15×1
100×2
= Rs. 4800Now, amount at the end of the first year = Rs. 64000 +4800 = Rs. 68800Principal for
Q u e s t i o n : 7
Divakaran deposited a sum of Rs 6250 in the Allahabad Bank for 1 year, compounded half-yearly at 8% per annum. Find the compound interest he gets.
S o l u t i o n :
Principal amount = Rs. 6250Rate of interest = 8 % per annum = 4 % for half yearTime = 1 year = 2 half yearsPrincipal for the first half year = Rs. 6250Interest for the first half year 
Q u e s t i o n : 8
Michael borrowed Rs 16000 from a finance company at 10% per annum, compounded half-yearly. What amount of money will discharge his debt after 1
1
2
 years?
S o l u t i o n :
Principal amount = Rs. 16000Rate of interest = 10 % per annum = 5 % for half yearTime = 1
1
2
 years = 3 half yearsPrincipal for the first half year = Rs. 16000Interest for the first half
Q u e s t i o n : 9
By using the formula, find the amount and compound interest on:
Rs 6000 for 2 years at 9% per annum compounded annually.
S o l u t i o n :
Principal amount, P = Rs 6000Rate of interest, R = 9 % per annumTime, n = 2 years. The formula for the amount including the compound interest is given below: A = Rs. P 1 +
R
100
n
 
Q u e s t i o n : 1 0
By using the formula, find the amount and compound interest on:
Rs 10000 for 2 years at 11% per annum compounded annually.
S o l u t i o n :
Principal amount, P = Rs. 10000Rate of interest, R = 11 % per annum. Time, n = 2 years. The formula for the amount including the compound interest is given below: A = Rs. P 1 +
R
100
Q u e s t i o n : 1 1
By using the formula, find the amount and compound interest on:
Rs 31250 for 3 years at 8% per annum compounded annually.
S o l u t i o n :
Principal amount, P = Rs. 31250Rate of interest, R = 8 % per annum. Time, n = 3 years. The formula for the amount including the compound interest is given below: A = Rs. P 1 +
R
100
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( )
( )
(
Q u e s t i o n : 1 2
By using the formula, find the amount and compound interest on:
Rs 10240 for 3 years at 12
1
2
% per annum compounded annually.
S o l u t i o n :
Principal amount, P = Rs. 10240Rate of interest, R = 12
1
2
% p. a. Time, n = 3 yearsThe formula for the amount including the compound interest is given below: A = Rs. P 1 +
R
100
n
 ?
Q u e s t i o n : 1 3
By using the formula, find the amount and compound interest on:
Rs 10240 for 3 years at 12
1
2
% per annum compounded annually.
S o l u t i o n :
Principal amount, P = Rs 62500Rate of interest, R = 12 % p. a. Time, n = 2 years 6 months =
5
2
= 2
1
2
 yearsThe formula for the amount including the compound interest is given below: A 
Q u e s t i o n : 1 4
By using the formula, find the amount and compound interest on:
Rs 9000 for 2 years 4 months at 10% per annum compounded annually.
S o l u t i o n :
Principal amount, P = Rs. 9000Rate of interest, R = 10 % p. a. Time, n = 2 years 4 months = 2
1
3
years = 
7
3
 yearsThe formula for the amount including the compound interest is given below
Q u e s t i o n : 1 5
Find the amount of Rs 8000 for 2 years compounded annually and the rates being 9% per annum during the first year and 10% per annum during the second year.
S o l u t i o n :
Principal amount, P = Rs. 8000Rate of interest for the first year, p = 9 % p. a. Rate of interest for the second year, q = 10 % p. a. Time, n = 2 years. Formula for the amount including the
Q u e s t i o n : 1 6
Anand obtained a loan of Rs 125000 from the Allahabad Bank for buying computers. The bank charges compound interest at 8% per annum, compounded annually. What amount wil he
have to pay after 3 years to clear the debt?
S o l u t i o n :
Principal amount, P = Rs. 125000Rate of interest, R = 8 % p. a. Time, n = 3 yearsThe amount including the compound interest is calculated using the formula, A = Rs. P 1 +
R
100
n
  = 
Q u e s t i o n : 1 7
Three years ago, Beeru purchased a buffalo from Surjeet for Rs 11000. What payment will discharge his debt now, the rate of interest being 10% per annum, compounded annually?
S o l u t i o n :
Principal amount, P = Rs. 11000Rate of interest, R = 10 % p. a. Time, n = 3 yearsThe amount including the compound interest is calculated using the formula, A = Rs. P 1 +
R
100
n
  =
Q u e s t i o n : 1 8
Shubhalaxmi took a loan of Rs 18000 from surya Finance to purchase a TV set. If the company charges compound interest at 12% per annum during the first year and 12
1
2
% per annum
during the second year, how much will she have to pay after 2 years?
S o l u t i o n :
Principal amount, P = Rs. 18000Rate of interest for the first year, p = 12 % p. a. Rate of interest for the second year, q = 12
1
2
% p. a. Time, n = 2 yearsThe formula for the amount including
Q u e s t i o n : 1 9
Neha borrowed Rs 24000 from the State Bank of India to buy a scooter. If the rate of interest be 10% per annum compounded annually, what payment will she have to make after 2 years
3 months?
S o l u t i o n :
Principal amount, P = Rs. 24000Rate of interest, R = 10 % p. a. Time, n = 2 years 3 months = 2
1
4
 yearsThe formula for the amount including the compound interest is given below: A =
Q u e s t i o n : 2 0
Abhay borrowed Rs 16000 at 7
1
2
% per annum simple interest. On the same day, he lent it to Gurmeet at the same rate but compounded annually. What does he gain at the end of 2
years?
S o l u t i o n :
Principal amount, P = Rs 16000Rate of interest, R = 
15
2
% p. a. Time, n = 2 yearsNow, simple interest = Rs 
16000×2×15
100×2
= Rs. 2400Amount including the simple interest = Rs (16000
Q u e s t i o n : 2 1
The simple interest on a sum of money for 2 years at 8% per annum is Rs 2400. What will be the compound interest on that sum at the same rate and for the same period?
S o l u t i o n :
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Page 3


Q u e s t i o n : 1
Find the amount and the compound interest on Rs 2500 for 2 years at 10% per annum, compounded annually.
S o l u t i o n :
Principal for the first year = Rs. 2500Interest for the first year = Rs. 
2500×10×1
100
= Rs. 250Amount at the end of the first year = Rs. 2500 +250  = Rs. 2750Principal for the second
Q u e s t i o n : 2
Find the amount and the compound interest on Rs 15625 for 3 years at 12% per annum, compounded annually.
S o l u t i o n :
Principal for the first year = Rs. 15625Interest for the first year = Rs. 
15625×12×1
100
= Rs. 1875Amount at the end of the first year = Rs.  15625 + 1875 = Rs. 17500Principal for the
Q u e s t i o n : 3
Find the difference between the simple interest and the compound interest on Rs 5000 for 2 years at 9% per annum.
S o l u t i o n :
Principal amount = Rs. 5000Simple interest = Rs. 
5000×2×9
100
= Rs. 900The compound interest can be calculated as follows: Principal for the first year = Rs. 5000Interest for the first 
Q u e s t i o n : 4
Ratna obtained a loan of Rs 25000 from the Syndicate Bank to renovate her house. If the rate of interest is 8% per annum, what amount will she have to pay to the bank after 2 years to
discharge her debt?
S o l u t i o n :
Principal for the first year = Rs. 25000Interest for the first year = Rs. 
25000×8×1
100
= Rs. 2000Amount at the end of the first year = Rs. 25000 +2000 = Rs. 27000Principal for the second
Q u e s t i o n : 5
Harpreet borrowed Rs 20000 from her friend at 12% per annum simple interest. She lent it to Alam at the same rate but compounded annually. Find her gain after 2 years.
S o l u t i o n :
Principal amount = Rs. 20000Simple interest = Rs. 
20000×2×12
100
= Rs. 4800The compound interest can be calculated as follows: Principal for the first year = Rs. 20000Interest for the
Q u e s t i o n : 6
Manoj deposited a sum of Rs 64000 in a post office for 3 years, compounded annually at 7
1
2
% per annum. What amount will he get on maturity?
S o l u t i o n :
Principal for the first year = Rs. 64000Interest for the first year = Rs. 
64000×15×1
100×2
= Rs. 4800Now, amount at the end of the first year = Rs. 64000 +4800 = Rs. 68800Principal for
Q u e s t i o n : 7
Divakaran deposited a sum of Rs 6250 in the Allahabad Bank for 1 year, compounded half-yearly at 8% per annum. Find the compound interest he gets.
S o l u t i o n :
Principal amount = Rs. 6250Rate of interest = 8 % per annum = 4 % for half yearTime = 1 year = 2 half yearsPrincipal for the first half year = Rs. 6250Interest for the first half year 
Q u e s t i o n : 8
Michael borrowed Rs 16000 from a finance company at 10% per annum, compounded half-yearly. What amount of money will discharge his debt after 1
1
2
 years?
S o l u t i o n :
Principal amount = Rs. 16000Rate of interest = 10 % per annum = 5 % for half yearTime = 1
1
2
 years = 3 half yearsPrincipal for the first half year = Rs. 16000Interest for the first half
Q u e s t i o n : 9
By using the formula, find the amount and compound interest on:
Rs 6000 for 2 years at 9% per annum compounded annually.
S o l u t i o n :
Principal amount, P = Rs 6000Rate of interest, R = 9 % per annumTime, n = 2 years. The formula for the amount including the compound interest is given below: A = Rs. P 1 +
R
100
n
 
Q u e s t i o n : 1 0
By using the formula, find the amount and compound interest on:
Rs 10000 for 2 years at 11% per annum compounded annually.
S o l u t i o n :
Principal amount, P = Rs. 10000Rate of interest, R = 11 % per annum. Time, n = 2 years. The formula for the amount including the compound interest is given below: A = Rs. P 1 +
R
100
Q u e s t i o n : 1 1
By using the formula, find the amount and compound interest on:
Rs 31250 for 3 years at 8% per annum compounded annually.
S o l u t i o n :
Principal amount, P = Rs. 31250Rate of interest, R = 8 % per annum. Time, n = 3 years. The formula for the amount including the compound interest is given below: A = Rs. P 1 +
R
100
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( )
(
Q u e s t i o n : 1 2
By using the formula, find the amount and compound interest on:
Rs 10240 for 3 years at 12
1
2
% per annum compounded annually.
S o l u t i o n :
Principal amount, P = Rs. 10240Rate of interest, R = 12
1
2
% p. a. Time, n = 3 yearsThe formula for the amount including the compound interest is given below: A = Rs. P 1 +
R
100
n
 ?
Q u e s t i o n : 1 3
By using the formula, find the amount and compound interest on:
Rs 10240 for 3 years at 12
1
2
% per annum compounded annually.
S o l u t i o n :
Principal amount, P = Rs 62500Rate of interest, R = 12 % p. a. Time, n = 2 years 6 months =
5
2
= 2
1
2
 yearsThe formula for the amount including the compound interest is given below: A 
Q u e s t i o n : 1 4
By using the formula, find the amount and compound interest on:
Rs 9000 for 2 years 4 months at 10% per annum compounded annually.
S o l u t i o n :
Principal amount, P = Rs. 9000Rate of interest, R = 10 % p. a. Time, n = 2 years 4 months = 2
1
3
years = 
7
3
 yearsThe formula for the amount including the compound interest is given below
Q u e s t i o n : 1 5
Find the amount of Rs 8000 for 2 years compounded annually and the rates being 9% per annum during the first year and 10% per annum during the second year.
S o l u t i o n :
Principal amount, P = Rs. 8000Rate of interest for the first year, p = 9 % p. a. Rate of interest for the second year, q = 10 % p. a. Time, n = 2 years. Formula for the amount including the
Q u e s t i o n : 1 6
Anand obtained a loan of Rs 125000 from the Allahabad Bank for buying computers. The bank charges compound interest at 8% per annum, compounded annually. What amount wil he
have to pay after 3 years to clear the debt?
S o l u t i o n :
Principal amount, P = Rs. 125000Rate of interest, R = 8 % p. a. Time, n = 3 yearsThe amount including the compound interest is calculated using the formula, A = Rs. P 1 +
R
100
n
  = 
Q u e s t i o n : 1 7
Three years ago, Beeru purchased a buffalo from Surjeet for Rs 11000. What payment will discharge his debt now, the rate of interest being 10% per annum, compounded annually?
S o l u t i o n :
Principal amount, P = Rs. 11000Rate of interest, R = 10 % p. a. Time, n = 3 yearsThe amount including the compound interest is calculated using the formula, A = Rs. P 1 +
R
100
n
  =
Q u e s t i o n : 1 8
Shubhalaxmi took a loan of Rs 18000 from surya Finance to purchase a TV set. If the company charges compound interest at 12% per annum during the first year and 12
1
2
% per annum
during the second year, how much will she have to pay after 2 years?
S o l u t i o n :
Principal amount, P = Rs. 18000Rate of interest for the first year, p = 12 % p. a. Rate of interest for the second year, q = 12
1
2
% p. a. Time, n = 2 yearsThe formula for the amount including
Q u e s t i o n : 1 9
Neha borrowed Rs 24000 from the State Bank of India to buy a scooter. If the rate of interest be 10% per annum compounded annually, what payment will she have to make after 2 years
3 months?
S o l u t i o n :
Principal amount, P = Rs. 24000Rate of interest, R = 10 % p. a. Time, n = 2 years 3 months = 2
1
4
 yearsThe formula for the amount including the compound interest is given below: A =
Q u e s t i o n : 2 0
Abhay borrowed Rs 16000 at 7
1
2
% per annum simple interest. On the same day, he lent it to Gurmeet at the same rate but compounded annually. What does he gain at the end of 2
years?
S o l u t i o n :
Principal amount, P = Rs 16000Rate of interest, R = 
15
2
% p. a. Time, n = 2 yearsNow, simple interest = Rs 
16000×2×15
100×2
= Rs. 2400Amount including the simple interest = Rs (16000
Q u e s t i o n : 2 1
The simple interest on a sum of money for 2 years at 8% per annum is Rs 2400. What will be the compound interest on that sum at the same rate and for the same period?
S o l u t i o n :
( )
( )
( )
( )
( )
Simple interest SI = Rs. 2400Rate of interest, R = 8 %Time, n = 2 yearsThe principal can be calculated using the formula: Sum = 
100×SI
R×T
? Sum = Rs. 
100×2400
8×2
= Rs. 15000i
Q u e s t i o n : 2 2
The difference between the compound interest and the simple interest on a certain sum for 2 years at 6% per annum is Rs 90. Find the sum.
S o l u t i o n :
Let Rs P be the sum. Then SI = 
P×2×6
100
= Rs. 
12P
100
= Rs.
3P
25
Also, CI = P × 1 +
6
100
2
-P = Rs. P ×
100+6
100
2
-P = Rs. P ×
53
50
2
-P = Rs. 
2809P
2500
-P = Rs. 
2809P-2500P
2500
= Rs.
309P
2500
N
Q u e s t i o n : 2 3
The difference between the compound interest and the simple interest on a certain sum for 3 years at 10% per annum is Rs 93. Find the sum.
S o l u t i o n :
Let P be the sum. Then SI = Rs 
P×3×10
100
= Rs 
30P
100
= Rs 
3P
10
Also, CI = Rs. P × 1 +
10
100
3
-P = Rs. P ×
100+10
100
3
-P = Rs. P ×
11
10
3
-P = Rs. 
1331P
1000
-P = Rs. 
1331P-1000P
1000
= Rs
Q u e s t i o n : 2 4
A sum of money amounts to Rs 10240 in 2 years at 6
2
3
% per annum, compounded annually. Find the sum.
S o l u t i o n :
Let P be the sum. Rate of interest, R = 6
2
3
% = 
20
3
%Time, n = 2 yearsNow, A = P × 1 +
20
100×3
2
= Rs. P × 1 +
20
300
2
= Rs. P ×
300+20
300
2
= Rs. P × 
320
300
2
 = Rs. P × 
16
15
×
16
15
= Rs. 
Q u e s t i o n : 2 5
What sum of money will amount to Rs 21296 in 3 years at 10% per annum, compounded annually?
S o l u t i o n :
Let P be the sum. Rate of interest, R = 10 %Time, n = 3 yearsNow, A = P × 1 +
10
100
3
= Rs. P ×
100+10
100
3
= Rs. P × 
110
100
3
 = Rs. P × 
11
10
×
11
10
×
11
10
= Rs. 
1331P
1000
However, amount = Rs
Q u e s t i o n : 2 6
At what rate per cent per annum will Rs 4000 amount to Rs 4410 in 2 years when compounded annually?
S o l u t i o n :
Let R % p. a. be the required rate. A = 4410P = 4000n = 2 yearsNow, A = P 1 +
R
100
n
? 4410 = 4000 1 +
R
100
2
?
4410
4000
= 1 +
R
100
2
?
441
400
= 1 +
R
100
2
?
21
20
2
= 1 +
R
100
2
?
21
20
-1
Q u e s t i o n : 2 7
At what rate per cent per annum will Rs 640 amount to Rs 774.40 in 2 years when compounded annually?
S o l u t i o n :
Let the required rate be R % p. a. A = 774. 40P = 640 n = 2 yearsNow, A = P 1 +
R
100
n
? 774. 40 = 640 1 +
R
100
2
?
774.40
640       
= 1 +
R
100
2
? 1. 21 = 1 +
R
100
2
? (1. 1)
2
= 1 +
R
100
2
? 1
Q u e s t i o n : 2 8
In how many years will Rs 1800 amount to Rs 2178 at 10% per annum when compounded annually?
S o l u t i o n :
Let the required time be n years. Rate of interest, R = 10 %Principal amount, P = Rs. 1800Amount with compound interest, A = Rs. 2178Now, A = P × 1 +
R
100
n
= Rs. 1800 × 1 +
10
100
Q u e s t i o n : 2 9
In how many years will Rs 6250 amount to Rs 7290 at 8% per annum, compounded annually?
S o l u t i o n :
Let the required time be n years. Rate of interest, R = 8 %Principal amount, P = Rs. 6250Amount with compound interest, A = Rs. 7290Then, A = P × 1 +
R
100
n
? A = Rs. 6250 ×
Q u e s t i o n : 3 0
The population of a town is 125000. It is increasing at the rate of 2% per annum. What will be its population after 3 years?
S o l u t i o n :
Population of the town, P = 125000Rate of increase, R = 2 %Time, n = 3 yearsThen the population of the town after 3 years is given byPopulation = P × 1 +
R
100
3
= 125000 × 1 +
2
100
Q u e s t i o n : 3 1
Three years ago, the population of a town was 50000. If the annual increase during three successive years be at the rate of 5%, 4% and 3% respectively, what is its present population?
S o l u t i o n :
Let the population of the town be 50000. Rate of increase for the first year, p = 5 %Rate of increase for the second year, q = 4 %Rate of increase for the third year, r = 3 %Time = 3 years
Q u e s t i o n : 3 2
The population of a city was 120000 in the year 2009. During next year it increased by 6% but due to an epidemic it decreased by 5% in the following year. what is its population in the
year 2011?
S o l u t i o n :
Population of the city in 2009, P = 120000Rate of increase, R = 6 %Time, n = 3  yearsThen the population of the city in the year 2010 is given byPopulation = P × 1 +
R
100
n
= 120000
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Page 4


Q u e s t i o n : 1
Find the amount and the compound interest on Rs 2500 for 2 years at 10% per annum, compounded annually.
S o l u t i o n :
Principal for the first year = Rs. 2500Interest for the first year = Rs. 
2500×10×1
100
= Rs. 250Amount at the end of the first year = Rs. 2500 +250  = Rs. 2750Principal for the second
Q u e s t i o n : 2
Find the amount and the compound interest on Rs 15625 for 3 years at 12% per annum, compounded annually.
S o l u t i o n :
Principal for the first year = Rs. 15625Interest for the first year = Rs. 
15625×12×1
100
= Rs. 1875Amount at the end of the first year = Rs.  15625 + 1875 = Rs. 17500Principal for the
Q u e s t i o n : 3
Find the difference between the simple interest and the compound interest on Rs 5000 for 2 years at 9% per annum.
S o l u t i o n :
Principal amount = Rs. 5000Simple interest = Rs. 
5000×2×9
100
= Rs. 900The compound interest can be calculated as follows: Principal for the first year = Rs. 5000Interest for the first 
Q u e s t i o n : 4
Ratna obtained a loan of Rs 25000 from the Syndicate Bank to renovate her house. If the rate of interest is 8% per annum, what amount will she have to pay to the bank after 2 years to
discharge her debt?
S o l u t i o n :
Principal for the first year = Rs. 25000Interest for the first year = Rs. 
25000×8×1
100
= Rs. 2000Amount at the end of the first year = Rs. 25000 +2000 = Rs. 27000Principal for the second
Q u e s t i o n : 5
Harpreet borrowed Rs 20000 from her friend at 12% per annum simple interest. She lent it to Alam at the same rate but compounded annually. Find her gain after 2 years.
S o l u t i o n :
Principal amount = Rs. 20000Simple interest = Rs. 
20000×2×12
100
= Rs. 4800The compound interest can be calculated as follows: Principal for the first year = Rs. 20000Interest for the
Q u e s t i o n : 6
Manoj deposited a sum of Rs 64000 in a post office for 3 years, compounded annually at 7
1
2
% per annum. What amount will he get on maturity?
S o l u t i o n :
Principal for the first year = Rs. 64000Interest for the first year = Rs. 
64000×15×1
100×2
= Rs. 4800Now, amount at the end of the first year = Rs. 64000 +4800 = Rs. 68800Principal for
Q u e s t i o n : 7
Divakaran deposited a sum of Rs 6250 in the Allahabad Bank for 1 year, compounded half-yearly at 8% per annum. Find the compound interest he gets.
S o l u t i o n :
Principal amount = Rs. 6250Rate of interest = 8 % per annum = 4 % for half yearTime = 1 year = 2 half yearsPrincipal for the first half year = Rs. 6250Interest for the first half year 
Q u e s t i o n : 8
Michael borrowed Rs 16000 from a finance company at 10% per annum, compounded half-yearly. What amount of money will discharge his debt after 1
1
2
 years?
S o l u t i o n :
Principal amount = Rs. 16000Rate of interest = 10 % per annum = 5 % for half yearTime = 1
1
2
 years = 3 half yearsPrincipal for the first half year = Rs. 16000Interest for the first half
Q u e s t i o n : 9
By using the formula, find the amount and compound interest on:
Rs 6000 for 2 years at 9% per annum compounded annually.
S o l u t i o n :
Principal amount, P = Rs 6000Rate of interest, R = 9 % per annumTime, n = 2 years. The formula for the amount including the compound interest is given below: A = Rs. P 1 +
R
100
n
 
Q u e s t i o n : 1 0
By using the formula, find the amount and compound interest on:
Rs 10000 for 2 years at 11% per annum compounded annually.
S o l u t i o n :
Principal amount, P = Rs. 10000Rate of interest, R = 11 % per annum. Time, n = 2 years. The formula for the amount including the compound interest is given below: A = Rs. P 1 +
R
100
Q u e s t i o n : 1 1
By using the formula, find the amount and compound interest on:
Rs 31250 for 3 years at 8% per annum compounded annually.
S o l u t i o n :
Principal amount, P = Rs. 31250Rate of interest, R = 8 % per annum. Time, n = 3 years. The formula for the amount including the compound interest is given below: A = Rs. P 1 +
R
100
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Q u e s t i o n : 1 2
By using the formula, find the amount and compound interest on:
Rs 10240 for 3 years at 12
1
2
% per annum compounded annually.
S o l u t i o n :
Principal amount, P = Rs. 10240Rate of interest, R = 12
1
2
% p. a. Time, n = 3 yearsThe formula for the amount including the compound interest is given below: A = Rs. P 1 +
R
100
n
 ?
Q u e s t i o n : 1 3
By using the formula, find the amount and compound interest on:
Rs 10240 for 3 years at 12
1
2
% per annum compounded annually.
S o l u t i o n :
Principal amount, P = Rs 62500Rate of interest, R = 12 % p. a. Time, n = 2 years 6 months =
5
2
= 2
1
2
 yearsThe formula for the amount including the compound interest is given below: A 
Q u e s t i o n : 1 4
By using the formula, find the amount and compound interest on:
Rs 9000 for 2 years 4 months at 10% per annum compounded annually.
S o l u t i o n :
Principal amount, P = Rs. 9000Rate of interest, R = 10 % p. a. Time, n = 2 years 4 months = 2
1
3
years = 
7
3
 yearsThe formula for the amount including the compound interest is given below
Q u e s t i o n : 1 5
Find the amount of Rs 8000 for 2 years compounded annually and the rates being 9% per annum during the first year and 10% per annum during the second year.
S o l u t i o n :
Principal amount, P = Rs. 8000Rate of interest for the first year, p = 9 % p. a. Rate of interest for the second year, q = 10 % p. a. Time, n = 2 years. Formula for the amount including the
Q u e s t i o n : 1 6
Anand obtained a loan of Rs 125000 from the Allahabad Bank for buying computers. The bank charges compound interest at 8% per annum, compounded annually. What amount wil he
have to pay after 3 years to clear the debt?
S o l u t i o n :
Principal amount, P = Rs. 125000Rate of interest, R = 8 % p. a. Time, n = 3 yearsThe amount including the compound interest is calculated using the formula, A = Rs. P 1 +
R
100
n
  = 
Q u e s t i o n : 1 7
Three years ago, Beeru purchased a buffalo from Surjeet for Rs 11000. What payment will discharge his debt now, the rate of interest being 10% per annum, compounded annually?
S o l u t i o n :
Principal amount, P = Rs. 11000Rate of interest, R = 10 % p. a. Time, n = 3 yearsThe amount including the compound interest is calculated using the formula, A = Rs. P 1 +
R
100
n
  =
Q u e s t i o n : 1 8
Shubhalaxmi took a loan of Rs 18000 from surya Finance to purchase a TV set. If the company charges compound interest at 12% per annum during the first year and 12
1
2
% per annum
during the second year, how much will she have to pay after 2 years?
S o l u t i o n :
Principal amount, P = Rs. 18000Rate of interest for the first year, p = 12 % p. a. Rate of interest for the second year, q = 12
1
2
% p. a. Time, n = 2 yearsThe formula for the amount including
Q u e s t i o n : 1 9
Neha borrowed Rs 24000 from the State Bank of India to buy a scooter. If the rate of interest be 10% per annum compounded annually, what payment will she have to make after 2 years
3 months?
S o l u t i o n :
Principal amount, P = Rs. 24000Rate of interest, R = 10 % p. a. Time, n = 2 years 3 months = 2
1
4
 yearsThe formula for the amount including the compound interest is given below: A =
Q u e s t i o n : 2 0
Abhay borrowed Rs 16000 at 7
1
2
% per annum simple interest. On the same day, he lent it to Gurmeet at the same rate but compounded annually. What does he gain at the end of 2
years?
S o l u t i o n :
Principal amount, P = Rs 16000Rate of interest, R = 
15
2
% p. a. Time, n = 2 yearsNow, simple interest = Rs 
16000×2×15
100×2
= Rs. 2400Amount including the simple interest = Rs (16000
Q u e s t i o n : 2 1
The simple interest on a sum of money for 2 years at 8% per annum is Rs 2400. What will be the compound interest on that sum at the same rate and for the same period?
S o l u t i o n :
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Simple interest SI = Rs. 2400Rate of interest, R = 8 %Time, n = 2 yearsThe principal can be calculated using the formula: Sum = 
100×SI
R×T
? Sum = Rs. 
100×2400
8×2
= Rs. 15000i
Q u e s t i o n : 2 2
The difference between the compound interest and the simple interest on a certain sum for 2 years at 6% per annum is Rs 90. Find the sum.
S o l u t i o n :
Let Rs P be the sum. Then SI = 
P×2×6
100
= Rs. 
12P
100
= Rs.
3P
25
Also, CI = P × 1 +
6
100
2
-P = Rs. P ×
100+6
100
2
-P = Rs. P ×
53
50
2
-P = Rs. 
2809P
2500
-P = Rs. 
2809P-2500P
2500
= Rs.
309P
2500
N
Q u e s t i o n : 2 3
The difference between the compound interest and the simple interest on a certain sum for 3 years at 10% per annum is Rs 93. Find the sum.
S o l u t i o n :
Let P be the sum. Then SI = Rs 
P×3×10
100
= Rs 
30P
100
= Rs 
3P
10
Also, CI = Rs. P × 1 +
10
100
3
-P = Rs. P ×
100+10
100
3
-P = Rs. P ×
11
10
3
-P = Rs. 
1331P
1000
-P = Rs. 
1331P-1000P
1000
= Rs
Q u e s t i o n : 2 4
A sum of money amounts to Rs 10240 in 2 years at 6
2
3
% per annum, compounded annually. Find the sum.
S o l u t i o n :
Let P be the sum. Rate of interest, R = 6
2
3
% = 
20
3
%Time, n = 2 yearsNow, A = P × 1 +
20
100×3
2
= Rs. P × 1 +
20
300
2
= Rs. P ×
300+20
300
2
= Rs. P × 
320
300
2
 = Rs. P × 
16
15
×
16
15
= Rs. 
Q u e s t i o n : 2 5
What sum of money will amount to Rs 21296 in 3 years at 10% per annum, compounded annually?
S o l u t i o n :
Let P be the sum. Rate of interest, R = 10 %Time, n = 3 yearsNow, A = P × 1 +
10
100
3
= Rs. P ×
100+10
100
3
= Rs. P × 
110
100
3
 = Rs. P × 
11
10
×
11
10
×
11
10
= Rs. 
1331P
1000
However, amount = Rs
Q u e s t i o n : 2 6
At what rate per cent per annum will Rs 4000 amount to Rs 4410 in 2 years when compounded annually?
S o l u t i o n :
Let R % p. a. be the required rate. A = 4410P = 4000n = 2 yearsNow, A = P 1 +
R
100
n
? 4410 = 4000 1 +
R
100
2
?
4410
4000
= 1 +
R
100
2
?
441
400
= 1 +
R
100
2
?
21
20
2
= 1 +
R
100
2
?
21
20
-1
Q u e s t i o n : 2 7
At what rate per cent per annum will Rs 640 amount to Rs 774.40 in 2 years when compounded annually?
S o l u t i o n :
Let the required rate be R % p. a. A = 774. 40P = 640 n = 2 yearsNow, A = P 1 +
R
100
n
? 774. 40 = 640 1 +
R
100
2
?
774.40
640       
= 1 +
R
100
2
? 1. 21 = 1 +
R
100
2
? (1. 1)
2
= 1 +
R
100
2
? 1
Q u e s t i o n : 2 8
In how many years will Rs 1800 amount to Rs 2178 at 10% per annum when compounded annually?
S o l u t i o n :
Let the required time be n years. Rate of interest, R = 10 %Principal amount, P = Rs. 1800Amount with compound interest, A = Rs. 2178Now, A = P × 1 +
R
100
n
= Rs. 1800 × 1 +
10
100
Q u e s t i o n : 2 9
In how many years will Rs 6250 amount to Rs 7290 at 8% per annum, compounded annually?
S o l u t i o n :
Let the required time be n years. Rate of interest, R = 8 %Principal amount, P = Rs. 6250Amount with compound interest, A = Rs. 7290Then, A = P × 1 +
R
100
n
? A = Rs. 6250 ×
Q u e s t i o n : 3 0
The population of a town is 125000. It is increasing at the rate of 2% per annum. What will be its population after 3 years?
S o l u t i o n :
Population of the town, P = 125000Rate of increase, R = 2 %Time, n = 3 yearsThen the population of the town after 3 years is given byPopulation = P × 1 +
R
100
3
= 125000 × 1 +
2
100
Q u e s t i o n : 3 1
Three years ago, the population of a town was 50000. If the annual increase during three successive years be at the rate of 5%, 4% and 3% respectively, what is its present population?
S o l u t i o n :
Let the population of the town be 50000. Rate of increase for the first year, p = 5 %Rate of increase for the second year, q = 4 %Rate of increase for the third year, r = 3 %Time = 3 years
Q u e s t i o n : 3 2
The population of a city was 120000 in the year 2009. During next year it increased by 6% but due to an epidemic it decreased by 5% in the following year. what is its population in the
year 2011?
S o l u t i o n :
Population of the city in 2009, P = 120000Rate of increase, R = 6 %Time, n = 3  yearsThen the population of the city in the year 2010 is given byPopulation = P × 1 +
R
100
n
= 120000
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Q u e s t i o n : 3 3
The count of bacteria in a certain experiment was increasing at the rate of 2% per hour. Find the bacteria at the end of 2 hours if the count was initially 500000.
S o l u t i o n :
Initial count of bacteria, P = 500000Rate of increase, R = 2 %Time, n = 2 hoursThen the count of bacteria at the end of 2 hours is given byCount of bacteria = P × 1 +
R
100
n
= 500000 ×
Q u e s t i o n : 3 4
The bacteria in a culture grows by 10% in the first hour, decreases by 10% in the second hour and again increases by 10% in the third hour. Find the bacteria at the end of 3 hours if the
count was initially 20000.
S o l u t i o n :
Initial count of bacteria, P = 20000Rate of increase, R = 10 %Time, n = 3 hoursThen the count of bacteria at the end of the first hour is given byCount of bacteria = P × 1 +
10
100
n
= 20000
Q u e s t i o n : 3 5
A machine is purchased for Rs 625000. Its value depreciates at the rate of 8% per annum. What will be its value after 2 years?
S o l u t i o n :
Initial value of the machine, P = Rs 625000Rate of depreciation, R = 8 %Time, n = 2 yearsThen the value of the machine after two years is given byValue = P × 1 -
R
100
n
= Rs 625000
Q u e s t i o n : 3 6
A scooter is bought at Rs 56000. Its value depreciates at the rate of 10% per annum. What will be its value after 3 years?
S o l u t i o n :
Initial value of the scooter, P = Rs 56000Rate of depreciation, R = 10 %Time, n = 3 yearsThen the value of the scooter after three years is given byValue = P × 1 -
R
100
n
= Rs. 56000
Q u e s t i o n : 3 7
A car is purchased for Rs 348000. Its value depreciates at 10% per annum during the first year and at 20% per annum during the second year. What will be its value after 2 years?
S o l u t i o n :
Initial value of the car, P = Rs 348000Rate of depreciation for the first year, p = 10 %Rate of depreciation for the second year, q = 20 %Time, n = 2 years. Then the value of the car after
Q u e s t i o n : 3 8
The value of a machine depreciates at the rate of 10% per annum. It was purchased 3 years ago. If its present value is Rs 291600, for how much was it purchased?
S o l u t i o n :
                                  
                  
                                  
                  
                                   
                  
                                   
                  
                                   
                                 
    
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