Question 1: Calculate the amount and the compound interest on:
per annum compounded annually.
per annum compounded yearly.
per annum compounded half-yearly.
Answer:
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:
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:
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:
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:
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:
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:
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:
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:
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:
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:
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:
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:
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:
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:
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:
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:
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:
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:
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:
For 1st year:
Therefore
and,
For 2nd year:
Therefore
and,