Compound Interest
Class 8th Mathematics RD Sharma Solution
- Find the compound interest when principal = Rs. 3000, rate = 5% per annum and…
- What will be the compound interest on Rs. 4000 in two years when rate of…
- Rohit deposited Rs. 8000 with a finance company for 3 years at an interest of…
- Find the compound interest on Rs. 1000 at the rate of 8% per annum for 1 1/2…
- Find the compound interest on Rs. 160000 for one year at the rate of 20% per…
- Swati took a loan of Rs. 16000 against her insurance policy at the rate of 12…
- Roma borrowed Rs. 64000 from a bank for 1 1/2 years at the rate of 10% per…
- Mewa lal borrowed Rs. 20000 from his friend Rooplal at 18% per annum simple…
- Find the compound interest on Rs. 8000 for 9 months at 20% per annum compounded…
- Find the compound interest at the rate of 10% per annum for two years on that…
- Find the compound interest on Rs. 64000 for 1 year at the rate of 10% per…
- Ramesh deposited Rs. 7500 in a bank which pays him 12% interest per annum…
- Anil borrowed a sum of Rs. 9600 to install a handpump in his dairy. If the…
- Surabhi borrowed a sum of Rs. 12000 from a finance company to purchase a…
- Daljit received a sum of Rs. 40000 as a loan from a finance company. If the…
- Compute the amount and the compound interest in each of the following by using…
- Find the amount of Rs. 2400 after 3 years, when the interest is compounded…
- Rahman lent Rs. 16000 to Rasheed at the rate of 12 1/2 % per annum compound…
- Meera borrowed a sum of Rs. 1000 from Sita for two years. If the rate of…
- Find the difference between the compound interest and simple interest. On a sum…
- Amit borrowed Rs. 16000 at 17 1/2 % per annum simple interest. On the same day,…
- Find the amount of Rs. 406 for 18 months at 12 1/2 % per annum, the interest…
- Find the amount and the compound interest on Rs. 8000 for 1 1/2 years at 10%…
- Kamal borrowed Rs. 57600 from LIC against her policy at 12 1/2 % per annum to…
- Abha purchased a house from Avas Parishad on credit. If the cost of the house…
- Rakesh lent out Rs. 10000 for 2 years at 20% per annum, compounded annually.…
- Romesh borrowed a sum of Rs. 245760 at 12.5% per annum, compounded annually.…
- Find the amount that David would receive if he invests Rs. 8192 for 18 months…
- Find the compound interest on Rs. 15625 for 9 months, at 16% per annum,…
- Rekha deposited Rs. 16000 in a foreign bank which pays interest at the rate of…
- Find the amount of Rs. 12500 for 2 years compounded annually, the rate of…
- Ramu borrowed Rs. 15625 from a finance company to buy scooter. If the rate of…
- What will Rs. 125000 amount to at the rate of 6%, if the interest is…
- Find the compound interest at the rate of 5% for three years on that principal…
- A sum of money was lent for 2 years at 20% compounded annually. If the…
- Simple interest on a sum of money for 2 years at 6 1/2 % per annum is Rs.…
- What will be the compound interest at the rate of 5% per annum for 3 years on…
- On what sum will the compound interest at 5% per annum for 2 years compounded…
- Find the principal if the interest compounded annually at the rate of 10% for…
- A sum amounts to Rs. 756.25 at 10% per annum in 2 years, compounded annually.…
- What sum will amount to Rs. 4913 in 18 months, if the rate of interest is 12…
- The difference between the compound interest and simple interest on a certain…
- Rachna borrowed a certain sum at the rate of 15% per annum. If she paid at the…
- The interest on a sum of Rs. 2000 is being compounded annually at the rate of…
- In how much time would Rs. 5000 amount to Rs. 6655 at 10% per annum compound…
- In what time will Rs. 4400 become Rs. 4576 at 8% per annum interest compounded…
- The difference between the S.I. and C.I. on a certain sum of money for 2 years…
- In what time will Rs. 1000 amount to Rs. 1331 at 10% per annum, compound…
- At what rate percent compound interest per annum will Rs. 640 amount to Rs.…
- Find the rate percent per annum if Rs. 2000 amount to Rs. 2662 in 1 1/2 years,…
- Kamala borrowed from Ratan a certain sum at a certain rate for two years…
- Find the rate percent per annum, if Rs. 2000 amount to Rs. 2315.25 in an year…
- Find the rate at which a sum of money will double itself in 3 years, if the…
- Find the rate at which a sum of money will become four times the original…
- A certain sum amounts to Rs. 5832 in 2 years at 8% compounded interest. Find…
- The difference between the compound interest and simple interest on a certain…
- The difference in simple interest and compound interest on a certain sum of…
- Ishita invested a sum of Rs. 12000 at 5% per annum compound interest. She…
- At what rate percent per annum will a sum of Rs. 4000 yield compound interest…
- A sum of money deposited at 2% per annum compounded annually becomes Rs. 10404…
- In how much time will a sum of Rs. 1600 amount to Rs. 1852.20 at 5% per annum…
- At what rate percent will a sum of Rs. 1000 amount to Rs. 1102.50 in 2 years…
- The compound interest on Rs. 1800 at 10% per annum for a certain period of…
- What sum of money will amount to Rs. 45582.25 at 6 3/4 % per annum in two…
- Sum of money amounts to Rs. 453690 in 2 years at 6.5% per annum compounded…
- The present population of a town is 28000. If it increases at the rate of 5%…
- The population of a city is 125000. If the annual birth rate and death rate are…
- The present population of a town is 25000. It grows at 4%, 5% and 8% during…
- Three years ago, the population of a town was 50000. If the annual increase…
- There is a continuous growth in population of a village at the rate of 5% per…
- In a factory the production of scooters rose to 46305 from 40000 in 3 years.…
- The annual rate of growth in population of a certain city is 8%. If its present…
- The population of a town increases at the rate of 50 per thousand. Its…
- The count of bacteria in a culture grows by 10% in the first hour, decreases by…
- The population of a certain city was 72000 on the last day of the year 1998.…
- 6400 workers were employed to construct a river bridge in four years. At the…
- Aman started a factory with an initial investment of Rs. 100000. In the first…
- The population of a town increases at the rate of 40 per thousand annually. If…
- The population of a mixi company in 1996 was 8000 mixies. Due to increase in…
- The population of a city increases each year by 4% of what it had been at the…
- Jitendra set up a factory by investing Rs. 2500000. During the first two…
- Ms. Cherian purchases a boat for Rs. 16000. If the total cost of the boat is…
- The value of a machine depreciates at the rate of 10% per annum. What will be…
- Pritam bought a plot of land for Rs. 640000. Its value is increasing by 5% of…
- Mohan purchased a house for Rs. 30000 and its value is depreciating at the rate…
- The value of a machine depreciates at the rate of 10% per annum. It was…
- The value of a refrigerator which was purchased 2 years ago, depreciates at 12%…
- The cost of a T.V. set was quoted Rs. 17000 at the beginning of 1999. In the…
- Ashish started the business with an initial investment of Rs. 500000. In the…
Exercise 14.1
Question 1.Find the compound interest when principal = Rs. 3000, rate = 5% per annum and time = 2 years.
Answer:
Given:
Principal =Rs.3000
Rate = 5%
Time = 2 years
Hence,
Compound interest = 
= 
Question 2.
What will be the compound interest on Rs. 4000 in two years when rate of interest is 5% per annum?
Answer:
Given,
Principal = Rs.4000
Time = 2 years
Rate = 5 % per annum
Compound interest =
= 
Question 3.
Rohit deposited Rs. 8000 with a finance company for 3 years at an interest of 15% per annum. What is the compound interest that Rohit gets after 3 years?
Answer:
Given,
Principal=Rs.8000
Time = 3 years
Rate = 15% p.a
Hence,
Compound interest =
=
Question 4.
Find the compound interest on Rs. 1000 at the rate of 8% per annum for 1
years when interest is compounded half yearly.
Answer:
Given,
Principal = Rs.1000
Rate = 8% p.a = 
Time = 
years = 
Compound interest =
= 
Question 5.
Find the compound interest on Rs. 160000 for one year at the rate of 20% per annum, if the interest is compounded quarterly.
Answer:
Given,
Principal = Rs.160000
Rate = 20% p.a = 
Time = 1 year = 
Compound interest =
= 
Question 6.
Swati took a loan of Rs. 16000 against her insurance policy at the rate of 12% per annum. Calculate the total compound interest payable by Swati after 3 years.
Answer:
Given,
Principal = Rs.16000
Rate = 12
%
Time = 3 years
Compound interest =
= 
Question 7.
Roma borrowed Rs. 64000 from a bank for 1years at the rate of 10% per annum. Compare the total compound interest payable by Roma after 1years, if the interest is compounded half-yearly.
Answer:
Given,
Principal = Rs. 64000
Time = 1
years = 
Rate= 10% = 
Compound interest =
= 
Question 8.
Mewa lal borrowed Rs. 20000 from his friend Rooplal at 18% per annum simple interest. He lent it to Rampal at the same rate but compounded annually. Find his gain after 2 years.
Answer:
Given,
Principal= Rs. 20000
Rate = 18% p.a
Time = 2 years
Hence,
Interest that Mewa lal has to pay = 
And,
Interest paid by Rampal to Mewalal = Compound interest =
= 
Gain of Mewa lal = Rs.(7848 – 7200 ) = Rs. 648
Question 9.
Find the compound interest on Rs. 8000 for 9 months at 20% per annum compounded quarterly.
Answer:
Principal = Rs.8000
Time =9 months
Rate = 20% per annum
∵ Interest is compounded quarterly, So Rate of interest will be counted as 20/4 = 5% and time will be 9/3 = 3 Quarter
We know that, 
Hence, Compound Interest = Rs. 9261 – Rs 8000 = Rs. 1261
Question 10.
Find the compound interest at the rate of 10% per annum for two years on that principal which in two years at the rate of 10% per annum given Rs. 200 as simple interest.
Answer:
Given,
Rate of simple interest = 10%
Time = 2 years
Simple interest = RS.200
So,
=
= 200 = 
= 
Rate of compound interest = 10%
Time = 2years
= Compound interest = 
= 1000
Question 11.
Find the compound interest on Rs. 64000 for 1 year at the rate of 10% per annum compounded quarterly.
Answer:
Given,
Principal = Rs.64000
Time = 1 year = 1×4 = 4 quarters
Rate = 10% = 
Hence,
Compound interest = 
= 
Question 12.
Ramesh deposited Rs. 7500 in a bank which pays him 12% interest per annum compounded wuarterly. What is the amount which he receives after 9 months.
Answer:
Given,
Principal = Rs.7500
Rate = 12% = 
Time = 9 months = 
Hence,
Compound interest = 
= 
Amount he receives after 9 months = principal + compound interest
= 7500+695.45 = Rs.8195.45
Question 13.
Anil borrowed a sum of Rs. 9600 to install a handpump in his dairy. If the rate of interest is 5% per annum compounded annually, determine the compound interest which Anil will have to pay after 3 years.
Answer:
Given,
Principal = Rs. 9600
Rate of interest = 5% = 
Time = 3 years
Hence,
Compound interest = 
= 9600× 0.174 = Rs.1672.72
So,
Compound interest paid by Anil after 3 years = Rs.1672.72
Question 14.
Surabhi borrowed a sum of Rs. 12000 from a finance company to purchase a refrigerator. If the rate of interest is 5% per annum compounded annually, calculate the compound interest that Surabhi has to pay to the company after 3 years.
Answer:
Given,
Principal = Rs.12000
Rate = 5%
Time = 3 years
Hence,
Compound interest = 
= 
So,
Compound interest paid by Surabhi to the company = Rs.1891.50
Question 15.
Daljit received a sum of Rs. 40000 as a loan from a finance company. If the rate of interest is 7% per annum compounded annually, calculate the compound interest that Daljit pays after 2 years.
Answer:
Given,
Principal = Rs.40000
Rate of interest = 7 %
Time = 2 years
Hence,
Compound interest = 
= 
So,
Compound interest paid by Daljit = Rs.5796
Exercise 14.2
Question 1.Compute the amount and the compound interest in each of the following by using the formulae when :
(i) Principal = Rs. 3000, Rate = 5%, Time = 2 years
(ii) Principal = Rs. 3000, Rate = 18%, Time = 2 years
(iii) Principal = Rs. 5000, Rate = 10 paise per annum, Time = 2 years
(iv) Principal = Rs. 2000, Rate = 4 paise per annum, Time = 3 years
(v) Principal = Rs. 12800, Rate = 7
%, Time = 3 years
(vi) Principal = Rs. 10000, Rate = 20% per annum compounded half-yearly, Time = 2 years
(vii) Principal = Rs. 160000, Rate = 10 paise per rupee per annum compounded half yearly, Time = 2 years.
Answer:
(i) Given,
Principal = Rs.3000
Rate = 5%
Time = 2 years
Compound interest = 
= 
Amount = principal + Compound interest
= 3000 + 307.50 = Rs. 3307.50
(ii) Given,
Principal = Rs.3000
Rate = 18%
Time = 2 years
Compound interest = 
= 
Amount = Principal + compound interest
= 3000 + 1177.20 = Rs.4177.20
(iii) Given,
Principal = Rs.5000
Rate = 10% p.a
Time = 2 years
Compound interest = 
= 
Amount = Principal + compound interest
= 5000 + 1050 = Rs. 6050
(iv) Given,
Principal = Rs.2000
Rate = 4% p.a
Time = 3 years
Compound interest = 
= 
Amount = Principal + compound interest
= 2000 + 249.72 = Rs.2249.73
(v) Given,
Principal = Rs.12800
Rate = 7% = 
Time = 3 years
Compound interest = 
= 
= Rs.3101.40
Amount = principal + compound interest
= 12800 + 3101.40 = Rs. 15901.40
(vi) Given,
Principal = Rs.10000
Rate = 20% p.a = 
Time = 2 years = 2×2 = 4 quarter
Compound interest = 
= 100
Amount = Principal + Compound interest
= 10000 + 4641 = Rs.14641
(vii) Given,
Principal = Rs.160000
Rate = 10% p.a =
Time = 2 years = 2×2 = 4 quarters
Compound interest = 
=160000
Amount = principal + Compound interest
= 160000+34481 = Rs.194481
Question 2.
Find the amount of Rs. 2400 after 3 years, when the interest is compounded annually at the rate of 20% per annum.
Answer:
Given,
Principal = Rs.2400
Rate = 20% per annum
Time = 3 years
Hence,
Compound interest = 
= 
So,
Amount = principal + compound interest
= 2400 + 1747.20 = Rs.4147.20
Question 3.
Rahman lent Rs. 16000 to Rasheed at the rate of 12% per annum compound interest. Find the amount payable by Rasheed to Rahman after 3 years.
Answer:
Given,
Principal = Rs.16000
Rate = 12% per annum = 
Time = 3 years
Hence,
Compound interest = 
= 
So,
Amount payable by Rasheed to Rahman after 3 years = Rs(16000+6781.25) = Rs.22781.25
Question 4.
Meera borrowed a sum of Rs. 1000 from Sita for two years. If the rate of interest is 10% compounded annually, find the amount that Meera has to pay back.
Answer:
Given,
Principal = Rs.1000
Rate of interest = 10% p.a
Time = 2 years
Hence,
Compound interest =
= 
So,
Amount that Meera has to pay back = Rs.(1000+210) = Rs.1210
Question 5.
Find the difference between the compound interest and simple interest. On a sum of Rs. 50,000 at 10% per annum for 2 years.
Answer:
Given,
Principal = Rs.50000
Rate = 10% per annum
Time = 2 years
Hence,
= 
Compound interest = 
= 
So,
Difference between compound interest and simple interest = Rs.(10500 – 10000) = Rs.500
Question 6.
Amit borrowed Rs. 16000 at 17% per annum simple interest. On the same day, he lent it to Ashu at the same rate but compounded annually. What does he gain at the end of 2 years?
Answer:
Given,
Principal = Rs.406
Rate = 12
% per annum = 
semi annually
Time = 18 months = 
Hence,
Amount = Principal = Rs.16000
Rate = 17 % = 
Time = 2 years
Hence ,
Interest paid by Amit on this sum = 
Interest that Amit get from Ashu = Compound interest = 
Hence,
Gain of Amit = Rs.(6090 – 5600 ) = Rs. 490
Question 7.
Find the amount of Rs. 406 for 18 months at 12% per annum, the interest being compounded semi-annually.
Answer:
Given,
Principal = Rs.406
Time = 18 Months = 
=
Rate = 12 % per annum = 
So,
= 
Amount = Rs.486.98
Question 8.
Find the amount and the compound interest on Rs. 8000 for 1years at 10% per annum, compounded half-yearly.
Answer:
Given,
Principal = Rs.8000
Time = 1- years =
Rate = 10% per annum =
Hence,
Compound interest = 
= 8000
Amount = Principal + compound interest
= 8000+1261 = Rs.9261
Question 9.
Kamal borrowed Rs. 57600 from LIC against her policy at 12% per annum to build a house. Find the amount that she pays to the LIC after 1years if the interest is calculated half-yearly.
Answer:
Given,
Principal = Rs.57600
Rate = 12-% per annum = 
Time = 1 years =
Hence,
Compound interest = 
= 57600
So,
Amount that Kamal pays to LIC after 1- years = Rs.(57600 + 11489.06) = Rs.69089.06
Question 10.
Abha purchased a house from Avas Parishad on credit. If the cost of the house is Rs. 64000 and the rate of interest is 5% per annum compounded half-yearly, find the interest paid by Abha after one year and a half.
Answer:
Given,
Principal = Rs.64000
Rate of interest = 5% per annum = 
% half yearly
Time = 1-
years =
Hence,
Compound interest = 
= 
= 
So, interest paid by Abha = Rs.4921
Question 11.
Rakesh lent out Rs. 10000 for 2 years at 20% per annum, compounded annually. How much more he could earn if the interest be compounded half-yearly?
Answer:
Given,
Principal = Rs.10000
Rate = 20%
Time = 2 year
Hence,
Compound interest = 
= 
If interest compounded half yearly ,
Rate = 
Time = 2×2 = 4 half years
Hence,
Compound interest = 
= 10000
So,
If Rakesh can earn = Rs.(4641 – 4400 ) = Rs.241 more
Question 12.
Romesh borrowed a sum of Rs. 245760 at 12.5% per annum, compounded annually. On the same day, he lent out his money to Ramu at the same rate of interest, but compounded semi-annually. Find his gain after 2 years.
Answer:
Given,
For Romesh,
Principal = Rs. 245760
Rate = 12.5% per annum
Time = 2 years
Hence,
Compound interest = 
= 
For Ramu,
Principal = Rs.245760
Rate = 
Time = 2×2 = 4 half years
Compound interest = 
= 245760
Hence,
Gain for Romesh = Rs.(67443.75 – 65280 ) = Rs. 2163.75
Question 13.
Find the amount that David would receive if he invests Rs. 8192 for 18 months at 12c% per annum, the interest being compounded half-yearly.
Answer:
Given,
Principal = Rs.8192
Rate = 12% p.a = 
Time = 18 months = years = 
Hence,
Amount = 
= 
= 
So,
David receives Rs.9826 after 18 months
Question 14.
Find the compound interest on Rs. 15625 for 9 months, at 16% per annum, compounded quarterly.
Answer:
Given,
Principal = Rs. 15625
Rate = 16% per annum = 
Time = 9 months = 
Hence,
Compound interest = 
= 
Question 15.
Rekha deposited Rs. 16000 in a foreign bank which pays interest at the rate of 20% per annum compounded wuarterly, find the interest received by Rekha after one year
Answer:
Given,
Principal = Rs. 16000
Rate = 20% per annum = 
Time = 1 year = 4 quarters
Hence,
Compound interest = 
= 
So,
Interest received by Rekha after one year = Rs.3448.10
Question 16.
Find the amount of Rs. 12500 for 2 years compounded annually, the rate of interest being 15% for the first year and 16% for the second year.
Answer:
Given,
Principal = Rs.12500
Time = 2 years
=
= 15%
= 
= 16%
Hence,
Amount = 
= 12500
Question 17.
Ramu borrowed Rs. 15625 from a finance company to buy scooter. If the rate of interest be 16% per annum compounded annually, what payment will he have to make after 2
years?
Answer:
Given,
Principal = Rs.15625
Rate = 16% per annum
Time = 2-
years
Amount = 
= 15625 
So,
Ramu has to make a payment of Rs.21866
Question 18.
What will Rs. 125000 amount to at the rate of 6%, if the interest is calculated after every four months?
Answer:
Principal = Rs. 125000
Time = 1 year
Rate = 6% per annum
∵ Interest is compounded after 4 months, So Rate of interest will be counted as 6/3 = 2% and time will be 12/4 = 3
We know that,
Question 19.
Find the compound interest at the rate of 5% for three years on that principal which in three years at the rate of 5% per annum gives Rs. 12000 as simple interest.
Answer:
Given,
Simple interest = Rs.12000
Rate = 5% per annum
Time = 3 years
So,
= 
= P = 
We get ,
Principal = Rs.80000
Rate = 5% per annum
Time = 3 years
Compound interest = 
= 80000
= 
Question 20.
A sum of money was lent for 2 years at 20% compounded annually. If the interest is payable half-yearly instead of yearly, then the interest is Rs. 482 more. Find the sum.
Answer:
Given,
Rate of interest = 20% p.a = 
Time = 2 years = 
Let principal = Rs. P
According to the question,
= 
= 
= 
Hence,
Principal = Rs.20000
Question 21.
Simple interest on a sum of money for 2 years at 6
% per annum is Rs. 5200. What will be the compound interest on the sum at the same rate for the same period.
Answer:
S.I = Rs.5200
Rate of simple interest = 
time = 2 years
Let principal = Rs. P
so, by formula
= 
= 
Hence,
Principal = Rs. 40000
now,
Rate of compound interest =
Time = 2 years
so,
compound interest = 
compound interest 
compound interest = 45369 – 40000 = Rs.5369
Question 22.
What will be the compound interest at the rate of 5% per annum for 3 years on that principal which in 3 years at the rate of 5% per annum gives Rs. 1200 as simple interest,
Answer:
Given,
S.I = Rs.1200
Rate of simple interest = 5%
time = 3 years
Let principal = Rs. P
so, by formula
= 
= 
Hence,
Principal = Rs.8000
now,
Rate of compound interest = 5%
Time = 3 years
so,
compound interest = 
Exercise 14.3
Question 1.On what sum will the compound interest at 5% per annum for 2 years compounded annually be Rs 164?
Answer:
Given,
Rate of interest= 5% p.a
Time = 2 years
Compound interest = Rs.164
Let principal = P
By applying formula ,
Compound interest =
= 
= 
= 
= P
Hence,
Principal = Rs. 1600.
Question 2.
Find the principal if the interest compounded annually at the rate of 10% for two years is Rs. 210.
Answer:
Given,
Rate = 10% p.a
Time = 2 years
Compound interest = Rs.210
Let principal = P
So,
Compound interest =
= 
= 
= 
= 
Hence,
Principal = Rs.1000.
Question 3.
A sum amounts to Rs. 756.25 at 10% per annum in 2 years, compounded annually. Find the sum .
Answer:
Given,
Amount = Rs.756.25
Rate = 10% p.a
Time = 2 years
Let principal = P
So,
A = 
= 
= P
= 
Hence,
Principal = Rs.625
Question 4.
What sum will amount to Rs. 4913 in 18 months, if the rate of interest is 12
% per annum, compounded half-yearly?
Answer:
Given,
Amount = Rs.4913
Time = 18 months = 
Rate = 12-% = 
Let principal = P
So,
A =
= P
= 
= 
= 
Hence ,
Principal = Rs. 4096
Question 5.
The difference between the compound interest and simple interest on a certain sum at 15% per annum for 3 years is Rs. 283.50. Find the sum.
Answer:
Given,
Rate = 15 % p.a
Time = 3 years
C.I – S.I = Rs.283.50
Let principal = P
So,
= 
= 
= 
= 
= 
Hence,
Principal = Rs. 4000
Question 6.
Rachna borrowed a certain sum at the rate of 15% per annum. If she paid at the end of two years Rs. 1290 as interest compounded annually, find the sum she borrowed.
Answer:
Given,
Rate = 15% p.a
Time = 2 years
C.I = Rs. 1290
Let principal = P
So,
Compound interest =
= P
= 
= 
= 
Hence,
Principal = Rs. 4000
Question 7.
The interest on a sum of Rs. 2000 is being compounded annually at the rate of 4% per annum. Find the period for which the compound interest is Rs. 163.20.
Answer:
Given,
Principal = Rs. 2000
Rate = 4 % p.a
C.I = Rs.163.20
Let time = T years
So,
Compound interest =
= 
= 
= 
= 
= 
= T = 2years
Hence,
Time = 2 years
Question 8.
In how much time would Rs. 5000 amount to Rs. 6655 at 10% per annum compound interest?
Answer:
Given,
Principal = Rs.5000
Rate = 10%
Amount = Rs.6655
Let time = T years
So,
A =
= 
= 
= 
= T= 3 years
Hence,
Time = 3 years.
Question 9.
In what time will Rs. 4400 become Rs. 4576 at 8% per annum interest compounded half-yearly?
Answer:
Given,
Principal = Rs. 4400
Amount = Rs.4576
Rate = 8% p.a = 
Let time = T years = 2T half years
So,
A =
= 
= 
= 2T = 1
= 
Hence,
Time = 
Question 10.
The difference between the S.I. and C.I. on a certain sum of money for 2 years at 4$ per annum is Rs. 20. Find the sum.
Answer:
Given,
Rate = 4%
Time = 2 years
C.I – S.I = Rs.20
Let principal = P
So,
=
= 
= 
= 
Hence,
Principal = Rs. 12500
Question 11.
In what time will Rs. 1000 amount to Rs. 1331 at 10% per annum, compound interest?
Answer:
Given,
Principal = Rs.1000
Amount = Rs. 1331
Rate = 10% p.a
Let time = T years
So,
A =
= 
= 
= T = 3 years
Hence,
Time = 3 years
Question 12.
At what rate percent compound interest per annum will Rs. 640 amount to Rs. 774.40 in 2 years?
Answer:
Given,
Principal = Rs.640
Amount = Rs.774.40
Time = 2 years
Let rate = R%
So,
A = 
= 
= 
= 
= 
= 
Hence,
Rate = 10% per annum
Question 13.
Find the rate percent per annum if Rs. 2000 amount to Rs. 2662 in 1years, interest being compounded half-yearly?
Answer:
Given,
Principal = Rs.2000
Amount = Rs.2662
Time = 1- years =
Let rate = R% per annum , 
So,
A =
= 
= 
= 
= 
= 
Hence ,
Rate = 20% per annum
Question 14.
Kamala borrowed from Ratan a certain sum at a certain rate for two years simple interest. She lent this sum at the same rate to Harti for two years compound interest. At the end of two years she received Rs. 210 as compound interest, but paid Rs. 200 only as simple interest. Find the sum and the rate of interest.
Answer:
Given,
C.I that Kamla receive = Rs.210
S.I that Kamla paid = Rs.200
Time = 2 years
So,
S.I = 
Also,
C.I = 
210 = 
(a + b)2 = a2 + b2 + 2ab
R = 10%
From equation (i)
P × R = 10000
Question 15.
Find the rate percent per annum, if Rs. 2000 amount to Rs. 2315.25 in an year and a half, interest being compounded six monthly.
Answer:
Given,
Principal = Rs.2000
Amount = Rs.2315.25
Time = 1 years = 
Let rate = R % per annum
A =
= 
= 
= 
= 
= 
Hence ,
Rate = 10.25%
Question 16.
Find the rate at which a sum of money will double itself in 3 years, if the interest is compounded annually.
Answer:
Given,
Time = 3 years
Let rate = R %
Let principal = P
So, amount becomes = 2P
A =
= 
= 
= 
Rate = 25.99%
Question 17.
Find the rate at which a sum of money will become four times the original amount in 2 years, if the interest is compounded half-yearly.
Answer:
Given,
Time = 2 years = 2×2 = 4 half years
Let rate = R % per annum =
Let principal = P
Amount becomes = 4P
So,
A =
= 
= 
= 
= 
Hence ,
Rate = 82.84 %
Question 18.
A certain sum amounts to Rs. 5832 in 2 years at 8% compounded interest. Find the sum.
Answer:
Given,
Amount = Rs.5832
Time = 2 years
Rate = 8%
Let principal = P
So,
A =
= 
= 
= 
Hence,
Principal = Rs.5000
Question 19.
The difference between the compound interest and simple interest on a certain sum for 2 years at 7.5% per annum is Rs. 360. Find the sum.
Answer:
Given,
C.I – S.I = Rs.360
Time = 2 years
Rate = 7.5 % per annum
Let principal = Rs. P
So,
= 
= 
= 
= 
= 
Hence,
Principal = Rs. 64000
Question 20.
The difference in simple interest and compound interest on a certain sum of money at 6
% per annum for 3 years in Rs. 46. Determine the sum.
Answer:
Given,
S.I – C.I = Rs. 46
Rate = 6
%= 
Time = 3 years
Let principal = Rs. P
So,
= 
= 
= 
= P = 
Hence,
Principal = Rs. 3375
Question 21.
Ishita invested a sum of Rs. 12000 at 5% per annum compound interest. She received an amount of Rs. 13230 after n years. Find the value of n.
Answer:
Given,
Principal = Rs.12000
Rate = 5% per annum
Amount = Rs.13230
Let time = T years
So,
A =
= 
= 
= T= 2 years
Hence ,
Time = 2 years
Question 22.
At what rate percent per annum will a sum of Rs. 4000 yield compound interest of Rs. 410 in 2 years?
Answer:
Given,
Principal = Rs.4000
C.I = Rs.410
Time = 2 years
Let rate of interest = R %
So,
= 
= 
= 
= 
= 
= 
=
= R
Hence,
Rate of interest = 5% per annum
Question 23.
A sum of money deposited at 2% per annum compounded annually becomes Rs. 10404 at the end of 2 years. Find the sum deposited.
Answer:
Given,
Rate of interest = 2% p.a
Time = 2 years
Amount = Rs.10404
Let principal = Rs. P
So,
A =
= 
= 
= 
Hence,
Principal = Rs.10000
Question 24.
In how much time will a sum of Rs. 1600 amount to Rs. 1852.20 at 5% per annum compound interest?
Answer:
Given,
Principal = Rs.1600
Amount = Rs.1852.20
Rate = 5 % per annum
Let time = T years
So,
A =
= 
= 
= T = 3 years
Hence,
Time = 3 years
Question 25.
At what rate percent will a sum of Rs. 1000 amount to Rs. 1102.50 in 2 years at compound interest?
Answer:
Given,
Principal = Rs.1000
Amount = Rs.1102.50
Time = 2 years
Let rate of interest = R % per annum
So,
A =
= 
= 
=
= 
= 
Hence,
Rate of interest = 5 % per annum
Question 26.
The compound interest on Rs. 1800 at 10% per annum for a certain period of timeos Rs. 378. Find the time in years.
Answer:
Given,
Compound interest = Rs.375
Principal = Rs.1800
Rate = 10% p.a
Let time = T years
So,
=
= 
= 
= 
=
= 
Hence.
Time = 2 years
Question 27.
What sum of money will amount to Rs. 45582.25 at 6
% per annum in two years, interest being compounded annually?
Answer:
Given,
Amount = Rs.45582.25
Rate = 6
% = 
Time = 2 years
Let principal = Rs.P
So,
A =
= 
= 
= 
Hence,
Principal = Rs. 40000
Question 28.
Sum of money amounts to Rs. 453690 in 2 years at 6.5% per annum compounded annually. Find the sum.
Answer:
Given,
Amount = Rs.453690
Time = 2 years
Rate = 6.5 % p.a
Let principal = Rs. P
So,
A =
= 
= 
= 
Hence ,
Principal = Rs. 400000
Exercise 14.4
Question 1.The present population of a town is 28000. If it increases at the rate of 5% per annum, what will be its population after 2 years?
Answer:
Given,
Present population of town = 28000
Rate of increase = 5% per annum
Hence,
Population of town after 2 years = 
Question 2.
The population of a city is 125000. If the annual birth rate and death rate are 5.5% and 3.5% respectively, calculate the population of city after 3 years.
Answer:
Given,
Population of city = 125000
Annual birth rate = 5.5 %
Annual death rate = 3.5 %
Annual increasing rate = 5.5 – 3.5 = 2 %
Hence,
Population of city after 3 years = 125000
Question 3.
The present population of a town is 25000. It grows at 4%, 5% and 8% during first year, second year and third year respectively. Find its population after 3 years.
Answer:
Given,
Present population of town = 25000
Growth rate in 3 years = 4% , 5% ,8% respectively
Hence,
Population of town after 3 years = 2500
= 
Question 4.
Three years ago, the population of a town was 50000. If the annual increase during three successive years be at the rate of 4%, 5% and 3% respectively, find the present population.
Answer:
Given,
Population of town 3 years ago was = 50000
Annual increasing in 3 years = 4% ,5%, 3% respectively
Let present population = X
So,
= 
= 
X
= 
56238
Hence,
Present population of town = 56238
Question 5.
There is a continuous growth in population of a village at the rate of 5% per annum. If its present population is 9261, what it was 3 years ago?
Answer:
Given,
Present population of village = 9261
Continuous growth rate = 5%
Let 3 years ago population of village was = X
So,
= 
= 
= X = 
= 8000
Hence,
3 years ago population of village was = 8000
Question 6.
In a factory the production of scooters rose to 46305 from 40000 in 3 years. Find the annual rate of growth of the production of scooters.
Answer:
Given,
Initial production of scooters = 40000
Final production of scooters = 46305
Time duration = 3 years
Let annual growth rate = R%
So,
= 
= 
=
= 
=
Hence,
Annual growth rate of production of scooters = 5 %
Question 7.
The annual rate of growth in population of a certain city is 8%. If its present population is 196830, what it was 3 years ago?
Answer:
Given,
Annual growth rate of population of city = 8%
Present population of city = 196830
Let population of city 3 years ago was = X
So,
= 
= 
= 
Hence,
Population of city 3 years ago was = 156250.
Question 8.
The population of a town increases at the rate of 50 per thousand. Its population after 2 years will be 22050. Find its present population.
Answer:
Given,
Growth rate of population of town = 
Population after 2 years = 22050
Let present population of town = X
So,
= 
= 
= 
Hence,
Present population of town = 20000
Question 9.
The count of bacteria in a culture grows by 10% in the first hour, decreases by 8% in the second hour and again increases by 12% in the third hour. If the count of bacteria in the sample is 13125000, what will be the count of bacteria after 3 hours?
Answer:
Given,
Count of bacteria in sample = 13125000
According to increase and decrease of growth rates,
Let count of bacteria after 3 hours = X
So,
= 
= 
= 
Hence,
Count of bacteria after 3 hours will be = 14876400
Question 10.
The population of a certain city was 72000 on the last day of the year 1998. During next year it increased by 7% but due to an epidemic it decreased by 10% in the following year. What was its population at the end of the year 2000?
Answer:
Given,
Population of city on last day of year 1998 = 72000
Increasing rate in 1999 = 7%
Decreasing rate in 2000 = 10 %
So,
Population at the end of 2000 = 
Question 11.
6400 workers were employed to construct a river bridge in four years. At the end of the first year, 25% workers were retrenched. At the end of the second year, 25% of those working at that time were retrenched. However, to complete the project in time, the number of workers was increased by 25% at the end of the third year. How many workers were working during the fourth year?
Answer:
Given,
Intial number of workers = 6400
At the end of first year = 25% retrenched
At the end of second year = 25% retrenched
At the end of third year = 25% increased
So,
Number of workers working during fourth year = 
= 
Question 12.
Aman started a factory with an initial investment of Rs. 100000. In the first year, he incurred a loss of 5%. However, during the second year, he earned a profit of 10% which in the third year rose to 12%. Calculate his net profit for the entire period of three years.
Answer:
Given,
Initial investment by Aman = Rs.100000
In first year = loss of 5%
In second year = profit of 10%
In third year = profit of 12 %
So,
His net profit for entire period of three years = 
= 
Profit = 117040 – 100000= Rs.17040
Question 13.
The population of a town increases at the rate of 40 per thousand annually. If the present population be 175760, what was the population three years ago.
Answer:
Given,
Increase rate of population of town = 
Present population of town = 175760
Let population of town 3 years ago was = X
So,
= 
= 
= 
Hence,
Population of town 3 years ago was = 156250
Question 14.
The population of a mixi company in 1996 was 8000 mixies. Due to increase in demand it increases its production by 15% in the next two years and after two years its demand decreases by 5%. What eill its production after 3 years?
Answer:
Given,
Population of mixi company in 1996 = 8000
Production growth rate in next 2 years = 15 %
Decrease rate in 3rd year = 5%
So,
Production after 3 years = 
= 
Question 15.
The population of a city increases each year by 4% of what it had been at the beginning of each year. If the population in 1999 had been 6760000, find the population of the city in (1) 2001 (ii) 1997.
Answer:
Given,
Annually increase rate of population of city = 4%
Population in 1999 = 6760000
So ,
i) Population of city in 2001 (2 years after)
= 
= 
ii) Population of city in 1997 (2 years ago)
= 
=
= 6250000
Question 16.
Jitendra set up a factory by investing Rs. 2500000. During the first two successive years his profits were 5% and 10% respectively. If each year the profit was on previous year’s capital, compute his total profit.
Answer:
Given,
Initial investment by Jitendra = Rs.2500000
Profit in first 2 successive years = 5% & 10%
Final investment after two successive profits = 
Hence,
His total profit = 2805000 – 2500000 = Rs.387500
Exercise 14.5
Question 1.Ms. Cherian purchases a boat for Rs. 16000. If the total cost of the boat is depreciating at the rate of 5% per annum, calculate its value after 2 years.
Answer:
Given,
Price of boat = Rs.16000
Depreciation rate = 5% per annum
So,
Value of boat after 2 years = 
Question 2.
The value of a machine depreciates at the rate of 10% per annum. What will be its value 2 years hence, if the present value is Rs 100000? Also, find the total depreciation during this period.
Answer:
Given,
Present value of machine = Rs.100000
Rate of depreciation = 10% per annum
So,
Value of machine after 2 years = 
Total depreciation during this period = Rs.(100000 – 8100) = Rs.19000
Question 3.
Pritam bought a plot of land for Rs. 640000. Its value is increasing by 5% of its previous value after every six
months. What will be the value of the plot after 2 years?
Answer:
Given,
Price of land = Rs.640000
Rate of increase = 5% in every six month
So,
Value of plot after 2 years = 
= 
Question 4.
Mohan purchased a house for Rs. 30000 and its value is depreciating at the rate of 25% per year. Find the value of the house after 3 years.
Answer:
Given,
Price of house = Rs.30000
Depreciating rate = 25% per year
Value of house after 3 years = 
= 
Question 5.
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. 43740, find its purchase price.
Answer:
Given,
Depreciation rate of machine = 10% p.a
Present value of machine = Rs.43740
Let its purchase price 3 years ago = Rs. X
So,
=X
= X 
= X = 
Hence,
Purchase price of machine was = Rs.60000
Question 6.
The value of a refrigerator which was purchased 2 years ago, depreciates at 12% per annum. If its present value is Rs. 9680, for how much was it purchased?
Answer:
Given,
Present value of refrigerator = Rs. 9680
Rate of depreciation = 12%
Let price of it 2 years ago = Rs.X
So,
= 
= X
= X = 
= 12500
Hence,
Price of refrigerator 2 years ago was = Rs.12500
Question 7.
The cost of a T.V. set was quoted Rs. 17000 at the beginning of 1999. In the beginning of 2000 the price was hiked by 5%. Because of decrease in demand the cost was reduced by 4% in the beginning of 2001. What was the cost of the T.V. set in 2001?
Answer:
Given,
Cost of T.V at beginning og 1999 = Rs.17000
Hiked in price in 2000 = 5%
Depreciation in 2001 = 4%
So,
Price of T.V in 2001 = 
Question 8.
Ashish started the business with an initial investment of Rs. 500000. In the first year he incurred a loss of 4%. However during the second year he earned a profit of 5% which in third year rose to 10%. Calculate the net profit for the entire period of 3 years.
Answer:
Given,
Initial investment by Ashish = Rs.500000
Loss in first year = 4%
Profit in 2nd year = 5 %
Profit in 3rd year = 10%
Hence,
Finally investment becomes = 
= Rs.5090400
Net profit = Rs.(5090400 – 500000) = Rs.554400