Question 1: Find the amount and the compound interest on Rs. 10,000 at 8 per cent per annum and in 2 years.

Answer:

Question 2: Find the amount and the compound interest on Rs. 10,000 at 8 per cent per annum and in 1 year; interest being compounded half-yearly.

Answer:

Question 3: Calculate the compound interest accrued on Rs. 16,000 in 3 years, when the rates of interest for successive years are 10%, 12% and 15% respectively.

Answer:

Question 4: A person borrows Rs. 20,000 at 12 per cent C.I. If he repays Rs. 8,400 at the end of first year and Rs. 9,680 at the end of second year, find the amount of loan outstanding at the beginning of the third year. **[ ICSE Board 2014]**

Answer:

Since, the man pays Rs. 8400 at the end of 1st year Principal for 2nd year

Since, the man pays Rs. 9680 at the end of 2nd year Principal for 3rd year

Question 5: A man borrows Rs. 8,000 at 10% compound interest payable every six months. He repays Rs. 2500 at the end of every six months. Calculate the third payment he has to make at the end of 18 months in order to clear the entire loan.

Answer:

Money repaid Balance

Money repaid Balance

The 3rd instalment to be made to clear the entire loan

Question 6: On a certain sum of money, invested at the rate of 5% per annum compounded annually, the difference between the interest of the first year and the interest of the third year is Rs. 61.50. Find the sum.

Answer:

Question 7: Mrs. Kapoor invested Rs. 6,000 every year at the beginning of the year, at 10% per annum compound interest. Calculate the amount of her total savings :

(i) up to the end of the second year. (ii) at the beginning of the third year.

Answer:

For 1st Year :

2nd Year :

Since, Rs. 6000 is invested again at the beginning of the second year,

Therefore, for the second year, principal

Amount of her total savings upto the end of the second year

Since, Rs. 6000 is invested again at the beginning of the third year,

Amount of her total savings at the beginning of the third year

Question 8: During every financial year, the value of a machine depreciates by 10%. Find the original value (cost) of a machine which depreciates by Rs. 2250 during the second year.

Answer:

Let the original cost of the machine

Depreciation during 1st year

Value of the machine at the beginning of 2nd year

Depreciation during 2nd year

Now, when depreciation during 2nd year

Therefore when depreciation during 2nd year

Question 9: Calculate the difference between the compound interest and the simple interest on Rs. 4000 at 8 per cent per annum and in 2 years.

Answer:

Required difference between C.I. and S.I.

Question 10: Ashok borrowed Rs. 16000 at 10% simple interest. He immediately invested this money at 10% compound interest compounded half-yearly. Calculate Ashok’s gain in 18 months.

Answer:

Compound Interest

Ashok’s gain in 18 months = C.I. earned – S.I. paid

Question 11: A sum of money is invested at C.I. payable annually. The amounts of interest in two successive years are Rs. 2700 and Rs. 2,880. Find the rate of interest.

Answer:

Directly:

Question 12: A certain sum of money, placed out at compound interest, amounts to Rs. 6272 in 2 years and to Rs. 7024.64 in 3 years. Find the rate of interest and the sum of money.

Answer:

Directly:

Question 13: A person invests Rs. 10000 for three years at a certain rate of interest compounded annually. At the end of one year this sum amounts to Rs. 11200. Calculate:

(i) the rate of interest per annum.

(ii) the amount at the end of the second year.

(iii) the amount at the end of the third year **[ ICSE Board 2006]**

Answer:

(i) For the first year:

(ii) For the second year:

(iii) For the third year:

Question 14: The simple interest on a certain sum computes to Rs. 600 in 3 years and the compound interest on the same sum, at the same rate and for 2 years computes to Rs. 410. Find the rate per cent.

Answer:

Therefore Rs. 10 is the interest for one year on the interest of 1st year i.e. on Rs. 200

Question 15: The compound interest calculated yearly at 10% on a certain sum of money amounts to Rs. 665.50 in the fifth year. Calculate :

(i) C.I. for the sixth year at the same rate and on the same sum.

(ii) C.I. for the fourth year on the same sum and at the same rate.

Answer:

(ii)

Since, C.I. for 5th year = C.I. of 4th year + Interest on it for 1 year.

Question 16: Asum of money, at compound interest, amounts to Rs. 8100 in 5 years and to Rs. 8748 in 6 years. Find :

(i) the rate per cent (ii) amount in 7 years and (iii) amount in 4 years

Answer:

(i) Since Amount in 5 years = Rs. 8100

Amount 6 years = Rs. 8748

Therefore 8748-8100 = Rs. 648 is the interest of 1 year on Rs. 8100

(iii)

Amount in 5 years = Amount in 4 years + interest on it for 1 year

Question 17: A sum of Rs. 9600 is invested for 3 years at 10% annum at compound interest.

(i) What is the sum due at the end of the first year ?

(ii) What is the sum due at the end of the second year.

(iii) Find the difference between the answers in (ii) and (i) and find the interest on this sum (difference) for one year.

(iv) Hence, write down the compound interest for the third year **[ ICSE Board 1996]**

Answer:

Question 18: The cost of a machine depreciated by Rs. 4752 during the second year and by Rs. 4181.76 during the third year. Calculate :

(i) the rate of depreciation;

(ii) the original cost;

(iii) the cost at the end of the third year.

Answer:

(iii) Since, total depreciation during all the three years

= Depreciation during (1st year + 2nd year + 3rd year)

The cost of machine at the end of the third year