Compound Interest without Formula

Question 1: Find the amount and the compound interest on , at per annum for years, compounded annually.

Answer:

For the : We have,

Principal , Rate of Interest per annum,

Therefore

Therefore, the Amount at the end of

For the : We have,

Principal , Rate of Interest per annum,

Therefore

Therefore, the Amount at the end of year

Compound Interest for 2 years = Amount at the end of Year – Principal

Question 2: Find the amount and the compound interest on at per annum for years.

Answer:

For the : We have,

Principal , Rate of Interest per annum,

Therefore

Therefore, the Amount at the end of

For the : We have,

Principal , Rate of Interest per annum,

Therefore

Therefore, the Amount at the end of year

For the the next six months: We have,

Principal , Rate of Interest per annum,

Therefore

Therefore, the Amount at the end of year

Compound Interest for years = Amount at the end of Year – Principal

Question 3: Find the compound interest on for one year at the rate of , per annum, if the interest is compounded quarterly.

Answer:

Rate of Interest per quarter

For the : We have,

Principal , Rate of Interest per annum,

Therefore

Therefore, the Amount at the end of

For the : We have,

Principal , Rate of Interest per annum,

Therefore

Therefore, the Amount at the end of

For the : We have,

Principal , Rate of Interest per annum,

Therefore

Therefore, the Amount at the end of

For the : We have,

Principal , Rate of Interest per annum,

Therefore

Therefore, the Amount at the end of

Compound Interest for the year = Amount at the end of Year – Principal

Question 4: Calculate the amount and the compound interest on for years when the rates of interest for successive years are and respectively.

Answer:

For the : We have,

Principal , Rate of Interest per annum,

Therefore

Therefore, the Amount at the end of

For the : We have,

Principal , Rate of Interest per annum,

Therefore

Therefore, the Amount at the end of year

Compound Interest for 2 years = Amount at the end of Year – Principal

Question 5: The simple interest on a certain sum of money for years at per annum is . Find the amount and the compound interest on the same sum, at the same rate and for the same time, compounded annually.

Answer:

Simple interest on for years at per annum is

Hence the Principal

For the : We have,

Principal , Rate of Interest per annum,

Therefore

Therefore, the Amount at the end of

For the : We have,

Principal , Rate of Interest per annum,

Therefore

Therefore, the Amount at the end of year

Compound Interest for 2 years = Amount at the end of Year – Principal

Question 6: A man invested for years at per annum, compounded annually. Compute: (i) the amount at the end of first year. (ii) the compound interest for the second year. (iii) the compound interest for years.

Answer:

(i) For the : We have,

Principal , Rate of Interest per annum,

Therefore

Therefore, the Amount at the end of

(ii) For the : We have,

Principal , Rate of Interest per annum,

Therefore

Therefore, the Amount at the end of year

(iii) Compound Interest for 2 years = Amount at the end of Year – Principal

Question 7: A person invests for years at per annum compounded annually. If the income tax at is deducted at the end of each year on interest accrued, find the amount she received at the end of years.

Answer:

For the : We have,

Principal , Rate of Interest per annum,

Therefore

Income tax deducted

Therefore, the Amount at the end of

For the : We have,

Principal , Rate of Interest per annum,

Therefore

Income tax deducted

Therefore, the Amount at the end of year

Question 8: A man borrows at per annum compounded annually. If he repays at the end of first year and at the end of second year, find the amount of the loan outstanding at the beginning of the third year.

Answer:

For the : We have,

Principal , Rate of Interest per annum,

Therefore

Therefore, the Amount at the end of

Amount repaid after

For the : We have,

Principal , Rate of Interest per annum,

Therefore

Therefore, the Amount at the end of

Amount repaid after

For the : We have,

Outstanding Principal

Question 9: A person invested at a certain rate of interest compounded annually for two years. At the end of first year it amounts to . Calculate: (i) The rate of interest (ii) The amount at the end of second year

Answer:

For the : We have,

Principal , Rate of Interest per annum,

Therefore

For the : We have,

Principal , Rate of Interest per annum,

Therefore

Therefore, the Amount at the end of

Compound Interest Formula

Question 10: Find the amount and compound interest on for years at , interest being payable annually.

Answer:

Principal , Rate of Interest per annum,

Therefore compound interest

Question 11: Find the amount and compound interest on for years compounded annually and the rate of interest being and for three successive years respectively.

Answer:

Principal , Rate of Interest per annum,

Therefore compound interest

Question 12: Compute the interest earned and amount due if a sum of is invested for years at per annum compound interest, interest being compounded semi-annually.

Answer:

Principal , Rate of Interest semi-annually, years

Therefore compound interest

Question 13: A man borrows at per annum simple interest for years. He immediately lends this money out at compound interest at the same rate and for the same time. What is his gain at the end of years?

Answer:

Simple Interest:

Principal , Rate of Interest annually, years

Interest

Compound Interest:

Principal , Rate of Interest per annum,

Therefore compound interest

Therefore gain

Question 14: What sum of money will amount to in years at per annum, compounded annually?

Answer:

Principal , Rate of Interest per annum,

Question 15: What sum will become in months if the rate of interest is per is compounded half-yearly?

Answer:

Principal , Rate of Interest semi-annually, years

Question 16: The difference between the compound interest and the simple interest on a certain sum at per annum for years is . Find the sum.

Answer:

Simple Interest:

Principal , Rate of Interest annually, years

Interest

Compound Interest:

Principal , Rate of Interest per annum,

Compound Interest

Given

Question 17: The difference between the compound interest for a year payable half-yearly and the simple interest on a certain sum of money lent out at for a year is . Find the sum of money lent out.

Answer:

Simple Interest:

Principal , Rate of Interest annually, years

Interest

Compound Interest:

Principal , Rate of Interest semi-annually, year

Compound Interest

Given

Question 18: On a certain sum, lent out at per annum for , the difference between the compound interest reckoned yearly and the reckoned yearly half- is . Find the sum.

Answer:

Yearly:

Principal , Rate of Interest annually, year

Therefore Compound Interest

Half Yearly:

Principal , Rate of Interest semi-annually, year

Therefore Compound Interest

Given

Question 19: The compound interest on a certain sum for years at per annum is . Find the simple interest on the same sum for the the same period and at the same rate.

Answer:

Compound Interest:

Principal , Rate of Interest per annum,

Compound Interest

Simple Interest:

Principal , Rate of Interest annually, years

Interest

Question 20: The simple interest on a certain sum for years at per annum is . Find the corresponding compound interest.

Answer:

Simple Interest:

Principal , Rate of Interest annually, years

Interest

Compound Interest:

Principal , Rate of Interest per annum,

Compound Interest

Question 21: The simple interest on a sum of money for years at per annum is . Find the compound interest on the sum at the same rate for one year, compounded half -yearly.

Answer:

Simple Interest:

Principal , Rate of Interest annually, years

Interest

Compound Interest:

Principal , Rate of Interest semi-annually, year

Compound Interest

Question 22: A sum of money is lent out at compound interest for years at per annum interest being reckoned yearly. If the same sum of money is lent out at compound interest at the same rate per per annum, compound interest being reckoned half-yearly it will fetch more by way of interest. Calculate the sum of money-lent out.

Answer:

Compound Interest (yearly):

Principal , Rate of Interest per annum,

Compound Interest

Compound Interest (Half yearly):

Principal , Rate of Interest semi-annually, year

Compound Interest

Given

Question 23: What sum will amount to in years at compound interest, if the rates are and for the successive years?

Answer:

Principal , Rate of Interest per annum,

Question 24: A certain sum of money lent out at compound interest amounts to in one year and to in years. Find ii) the rate of interest (ii) the original sum.

Answer:

Compound Interest (yearly):

Principal , Rate of Interest per annum,

… … … … (i)

Principal , Rate of Interest per annum,

… … … … (ii)

Dividing (ii) by (i) we get

Now substituting in (i)

Question 25: The compound interest, calculated yearly on a certain sum of money for the second year is and for the third year is Calculate the rate of interest and the original money.

Answer:

Principal , Rate of Interest per annum,

… … … … (i)

Principal , Rate of Interest per annum,

… … … … (ii)

Principal , Rate of Interest per annum,

… … … … (iii)

Given: and

Therefore

… … … … (iv)

… … … … (v)

Dividing (v) by (iv) we get

Substituting in (iv)

Question 26: The compound interest on a sum of money for years is and the simple interest on the same sum for the same period and at the same rate is . Find: (i) the rate of interest (ii) the sum.

Answer:

Compound Interest:

Principal , Rate of Interest per annum,

Compound Interest

… … … … … (i)

Simple Interest:

Principal , Rate of Interest annually, years

Interest

… … … … … (ii)

Now solving (i) and (ii) we get

$latex )

Question 27: Find the rate percent per annum if amounts to in years, interest being compounded half-yearly.

Answer:

Principal , Rate of Interest semi-annually, year

per annum

Question 28: Find the rate at which a sum of money will double itself in years if the interest is compounded annually.

Answer:

Principal , Rate of Interest annually, year

per annum

Question 29: Find the rate at which a sum of money will become four amount times the original in years if the interest is compounded half yearly.

Answer:

Principal , Rate of Interest annually, year

per annum

Question 30: A sum compounded annually becomes times of itself in years. Determine the rate of interest.

Answer:

Principal , Rate of Interest annually, year

per annum

Question 31: Rishi invested in a finance company and received after years. Find the rate of interest per annum compounded semi-annually.

Answer:

Principal , Rate of Interest semi-annually, year

per annum

Question 32: In how much time would amounts to at per annum compound interest?

Answer:

Principal , Rate of Interest annually, year

Question 33: In what time will become at per annum interest compounded half-yearly?

Answer:

Principal , Rate of Interest annually, year

Question 34: The compound interest, calculated yearly, on a certain sum of money for the second year is and for the third year is . Calculate the rate of interest and the original sum of money.

Answer:

Principal , Rate of Interest per annum,

… … … … (i)

Principal , Rate of Interest per annum,

… … … … (ii)

Principal , Rate of Interest per annum,

… … … … (iii)

Given: and

Therefore

… … … … (iv)

… … … … (v)

Dividing (v) by (iv) we get

Substituting in (iv)

Question 35: On what sum of money will the difference between the compound interest and simple interest for years be equal to , if the rate of interest charged for both is per annum?

Answer:

Compound Interest:

Principal , Rate of Interest per annum,

Compound Interest

Simple Interest:

Principal , Rate of Interest annually, years

Interest

Given:

Question 36: Mr Kumar borrowed for two years. The rate of interest for the two successive years are and respectively. If he repays at the end of the first year, find the outstanding amount at the end of second year.

Answer:

For the : We have,

Principal , Rate of Interest per annum,

Therefore

Therefore, the Amount at the end of

For the : We have,

Principal , Rate of Interest per annum,

Therefore

Therefore, the Amount at the end of year

Depreciation Problems

Question 37: The value of a machine depreciates at the rate of per annum. what will be its value years hence if the present value is ? Also, find the total depreciation during this period.

Answer:

Present Value Rate of Depreciation No of Years

Total depreciation

Question 38: Pritam bought a plot of land for . Its value is increasing by of its previous value after every six months. What will be the value of the plot after years?

Answer:

Present Value , Rate of Interest half yearly ,

Question 39: The value of a machine depreciates at the rate of per annum. It was purchased years ago. If its present value is , find its purchase price.

Answer:

Present Value Rate of Depreciation No of Years Value 3 years back

Total depreciation

Question 40: The cost of a T.V. set was quoted at the beginning of 1999. In the beginning of 2000 the price was hiked by . Because of decrease in demand the cost was reduced by in the beginning of 2001. What was the cost of the T.V. set in 2001?

Answer:

Cost of TV at the beginning of 1999

Cost of TV at the beginning of 2000

Cost of TV at the beginning of 2001

Question 41: Ashish staffed the business with an initial investment of . In the first he incurred a loss of . However, during the second year he earned a profit of which in third year rose to . Calculate the net profit for the entire period of years.

Answer:

Initial Investment at the beginning of 1st Year

Capital at the beginning of 2nd Year

Capital at the beginning of 3rd Year

Capital at the beginning of 4th Year

Net profit

Population Questions

Question 42: The present population of a town is . If it increases at the rate of per annum, what will be its population after years?

Answer:

Population , Rate per annum, years

Population after years

Population after years

Question 43: The present population of a town is . It grows at first and during year, second year and third year respectively. Find lts population after years.

Answer:

Current Population , Rate per annum, years

Population after

Population after

Question 44: There is a continuous growth in population of a village at the rate of per annum. If its present population is , what was it years ago?

Answer:

Population 3 years ago Current Population , Rate per annum, years

Therefore

Question 45: In a factory the production of scooters rose to from in years. Find the annual rate of growth of the production of scooters.

Answer:

Question 46: The population of a town increases at the rate of per thousand. Its population after years will be . Find its present population.

Answer:

Rate of Increase (population in 2 years) (Initial population)

Question 47: The count of bacteria in a culture grows by in the first hour, decreases by in the second hour and again increase by in third hour. If the count of bacteria in the sample , what will be the count of bacteria after hour.

Answer:

Current bacteria Population , Rate per annum, hours

Bacteria Population after

Bacteria Population after

Question 48: workers were employed to construct a river bridge in four years. At the end First year, workers were retrenched. At the second year of those working at that time were retrenched. However, to complete the project in time, the number of workers was increased by the end of the third year. How many workers were working during the fourth year?

Answer:

Current worker Population , Rate per annum, years

Worker Population after

Worker Population after

Question 49: A man started a factory with an initial investment of . In the first year, he incurred a loss of . However, during the second year; he earned a profit of which in the third year rose to . Calculate the profit for the entire period of three years.

Answer:

Initial Investment , Rate per annum, years

Worker Population after

Worker Population after

Therefore net profit

Question 50: The population of a city increases each year by of what it had been at the beginning of each year. If the population in 1999 had been , find the population of the city in (i) 2001 (ii) 1997.

Answer: