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Question 1: A sum is invested at compound interest compounded yearly. If the interest for two successive years be and . calculate the rate of interest.

Answer 1:

Question 2: A certain sum of money is put at compound interest, compounded half-yearly. If the interests for two successive half-years are and ; find the rate of interest.

Answer 2:

is the interest on

Question 3: A certain sum amounts to in two years and in three years, interest being compounded annually. Find; The rate of interest. The original sum.

Answer 3:

is the interest on

Let the sum of money

Therefore Interest on it for 1st Year

When amount in two year

, then

Question 4: The compound interest, calculated yearly, on a certain sum of money for the second year is and for the third year it is . Calculate the rate of interest and the sum of money.

Answer 4:

is the interest on

Let the sum of money

Therefore Interest on it for 1st Year

When interest of 2nd year

, then

Question 5: A person invests for years at a certain rate of interest, compounded annually. At the end of one year it amounts to . Calculate;

- The rate of interest per annum.
- The amount at the end of the second year.
- The interest accrued in the third year.

Answer 5:

For 1st year:

Therefore

and,

For 2nd year:

Therefore

and,

For 3rd year:

Therefore

Question 6: A person borrowed for months at a certain rate of interest compounded semi-annually. If at the end of six months it amounted to ; calculate:

- The rate of interest per annum;
- The total amount of money that person must pay at the end of months in order to clear the account.

Answer 6:

For 1st year:

Therefore

For 2nd year:

Therefore

and,

For 3rd year:

Therefore

and,

Question 7: Ramesh invests for three years at the rate of per annum compound interest. Find;

- The sum due to that person at the end of the first year.
- The interest he earns for the second year.
- The total amount due to him at the end of the third year. [2007]

Answer 7:

For 1st year:

Therefore

and,

For 2nd year:

Therefore

and,

For 3rd year:

Therefore

and,

Question 8: The simple interest on a certain sum computes to years, whereas the compound interest on the same sum at the same rate and for the same time computes to . Find the rate per cent and the sum.

Answer 8:

Let the amount be and the rate be

Simple Interest

Compound Interest

For 1st year:

Therefore

and,

For 2nd year:

Therefore

Therefore

Question 9: On the certain sum and at a certain rate percent, the simple interest for the first year is and the compound interest for the first two years is . Find the sum and the rate per cent.

Answer 9:

Let the amount be and the rate be

Simple Interest

Compound Interest

For 1st year:

Therefore

and,

For 2nd year:

Therefore

Question 10: The interest charged on a certain sum is for one year and for two years. Find, whether the interest is simple or compound. Also, calculate the rate per cent and the sum.

Answer 10:

Interest charged for 1st Year

Interest Charged for 2 years

Interest charged for the 2nd year

Since the interest for the 2nd year is more than the 1st year, it is not simple interest. It is compound interest.

Difference between the Compound interest of two successive years

is the interest on

or you could also do it directly using the following approach:

Sum borrowed is

Question 11: 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 compound interest on the same sum and at the same rate, for the fourth year.

Answer 11:

Difference between the Compound interest of two successive years

is the interest on

or you could also do it directly using the following approach:

For 1st year:

Therefore

and,

For 2nd year:

Therefore

Given

For 3rd year:

Therefore

and,

For 4th year:

Therefore

Question 12: A sum of money to in years and to in years. Calculate:

- The rate of interest.
- Amount in years and
- Amount in years.

Answer 12:

Difference between the Compound interest of two successive years

is the interest on

For 1st year:

Therefore

and,

For 2nd year:

Therefore

and,

For 3rd year:

Therefore

and,

For 4th year:

Therefore

and,

For 5th year:

Therefore

and,

Question 13: is lent out at compound interest for years. At the end of the first year are returned. Calculate:

- The interest paid for the second year.
- The total interest paid in two years.
- The total amount of money paid in two years to clear the debt.

Answer 13:

For 1st year:

Therefore

and,

For 2nd year:

Therefore

and,

i) Interest paid for 2nd year

ii) Total interest paid in 2 years

iii) Total money paid to clear the dues

Question 14: A sum of is lent out for years at compound interest, the rate of interest being per year. The borrower returns some money at the end of the first year and on paying at the end of the second year the total debt is cleared. Calculate the amount of money returned at the end of the first year.

Answer 14:

For 1st year:

Therefore

and,

For 2nd year:

Therefore

and,

Question 15: A man invests for two years at compound interest. After one year his money amounts to . Find the interest for the second year correct to the nearest rupee.

Answer 15:

For 1st year:

Therefore

and,

For 2nd year:

Therefore

Question 16: 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 sum of money. [1995]

Answer 16:

Difference between the Compound interest of two successive years

is the interest on

or you could also do it directly using the following approach:

For 1st year:

Therefore

and,

For 2nd year:

Therefore

Given

Question 17: The cost of a machine depreciated by during the first year and by during the second year. Calculate:

- The rate of depreciation.
- The original cost of the machine.
- Its cost at the end of the third year.

Let the value of the machine is Rs. x and the rate of depreciation is r%.

For 1st year:

Therefore

and,

For 2nd year:

Therefore

Given

and