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)