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Question 1: Calculate the amount and the compound interest on:

- per annum compounded annually.
- per annum compounded yearly.
- per annum compounded half-yearly.

Answer 1:

i)

For 1st year:

Therefore

and,

For 2nd year:

Therefore

and,

and

ii)

For 1st year:

Therefore

and,

For 2nd year:

Therefore

and,

and

iii)

For 1st half-year:

Therefore

and,

For 2nd half-year:

Therefore

and,

For 3rd half-year:

Therefore

and,

and

Question 2: Calculate the amount and the compound interest on years when the rates of interest for successive years are respectively:

Answer 2:

For 1st year:

Therefore

and,

For 2nd year:

Therefore

and,

For 3rd year:

Therefore

and,

and

Question 3: A Man lends per annum. Find the amount if the interest is compounded half-yearly and the duration is one year.

Answer 3:

For 1st half-year:

Therefore

and,

For 2nd half-year:

Therefore

and,

and

Question 4: A man borrows compound interest. If he repays at the end of each year, find the amount of the loan outstanding at the beginning of the third year.

Answer 4:

For 1st year:

Therefore

and,

For 2nd year:

Therefore

and,

and Amount left at the beginning of 3rd Year

Question 5: A man borrows per annum compound interest. He repays of the sum borrowed at the end of the first year and of the sum borrowed at the end of the second year. How much must he pay at the end of the third year in order the debt?

Answer 5:

For 1st year:

Therefore

and,

He repays

For 2nd year:

Therefore

and,

He repays

and Amount left at the beginning of 3rd Year

For 3rd year:

Therefore

and,

Question 6: Rachana borrows per annum interest compounded half-yearly. She repays at the end of every six months. Calculate the third payment she has to make at the end of months in order to clear the entire loan.

Answer 6:

For 1st half-year:

Therefore

and,

She repays

For 2nd half year:

Therefore

and,

She repays

For 3rd half-year:

Therefore

and,

Question 7: On a certain sum of money, invested at the rate of per annum compounded annually, the interest for the first year plus the interest for the third year is . Find the sum.

Answer 7:

For 1st year:

Therefore

and,

For 2nd year:

Therefore

and,

For 3rd year:

Therefore

and,

Question 8: A sum of money is lent at per annum compound interest. If the interest for the second year exceeds that for the first year by , find the sum of money.

Answer 8:

For 1st year:

Therefore

and,

For 2nd year:

Therefore

and,

Question 9: A person invested every year at the beginning of the year, at per annum compounded interest. Calculate his total savings at the beginning of the third year.

Answer 9:

For 1st year:

Therefore

and,

For 2nd year:

Therefore

and,

Therefore the amount at the start of third year

Question 10: A person saves every year and invests it at the end of the year at per annum compound interest. Calculate her total amount of savings at the end of the third year.

Answer 10:

For 1st year:

Therefore

and,

For 2nd year:

Therefore

and,

For 3rd year:

Therefore

and, Therefore the amount at the start of third year

Question 11: During every financial year, the value of the machine depreciates by . Find the original cost of the machine which depreciates by during the second financial year of its purchase.

Answer 11:

For 1st year:

Therefore

and,

For 2nd year:

Therefore

and,

Question 12: Find the sum on which the difference between the simple interest and the compound interest at a rate of per annum compounded annually be in years.

Answer 12:

Let the sum be

Simple Interest

Compound Interest

For 1st year:

Therefore

and,

For 2nd year:

Therefore

Total Compound Interest

Given

Question 13: A person borrows at simple interest. He immediately invests the money borrowed at compound interest compounded half yearly. How much money does he gain in one year.

Answer 13:

Sum borrowed

Simple Interest

Compound Interest

For 1st year:

Therefore

and,

For 2nd year:

Therefore

Total Compound Interest earned

Gain

Question 14: A sum of is invested at per annum compound interest for years. Calculate i) interest for the first year, ii) the amount at the end of the first year, iii) interest for the second year.

Answer 14:

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,

Hence,

i) the interest for 1st Year

ii) Amount at the end of 1st year

iii) the interest for 2nd Year

Question 15: A person invests for years at per annum compound interest. Calculate i) the interest for the first year, ii) the amount at the end of the 2nd year, iii) interest for the third year,

Answer 15:

For 1st year:

Therefore

and,

For 2nd year:

Therefore

and,

For 3rd year:

Therefore

and,

Hence,

i) the interest for 1st Year

ii) Amount at the end of 2nd year

iii) the interest for 2nd Year

Question 16: A person borrowed from another person at per annum compound interest. After years he gave back and a TV set to clear the debt. Find the value of the TV set.

Answer 16:

For 1st year:

Therefore

and,

For 2nd year:

Therefore

and,

.

Question 17: It is estimated that every year, the value of the asset depreciates at of its value at the beginning of the year.Calculate the original value of the asset if its value after two years is .

Answer 17:

For 1st year:

Therefore

and,

For 2nd year:

Therefore

and,

and,

Question 18: Find the sum that will amount to in years at compound interest, if the rates for the successive year are at respectively.

Answer 18:

For 1st year:

Therefore

and,

For 2nd year:

Therefore

and,

Given

Question 19: A person opens up a bank account on 1st jan 2010 with . If the bank pays per annum and the person deposits at the end of each year, find the sum in the account on 1st Jan 2012.

Answer 19:

For 2010 year:

Therefore

and,

For 2011 year:

Therefore

and,

For 2012 year:

Question 20: A person borrows at some rate per cent compound interest. After a year, the person paid back . If the compound interest for the second year is , find: i) the rate of interest charged ii) amount of debt at the end of the second year.

Answer 20:

For 1st year:

Therefore

and,

For 2nd year:

Therefore

and,