Question 1: Find the money, invested at compounded annually, on which the sum of interest for the first year and the third year is
.
Answer:
For 1st year:
Therefore
and,
For 2nd year:
Therefore
and,
For 3rd year:
Therefore
and,
Given
Question 2: A sum of money is invested at compound interest payable annually. The interest in first two successive years is and
respectively. Find;
- The rate of interest
- The original Sum
- The interest earned in the third year.
Answer:
For 1st year:
and,
For 2nd year:
Therefore
and,
For 3rd year:
Therefore
and,
Question 3: A sum of money amounts to in
year and to
in
years at compound interest, compounded semi-annually. Find the sum and the rate of interest per annum.
Answer:
For 1st half year:
and,
For 2nd half year:
Question 4: The cost of machine in . Its value depreciates at the rate of
every year. Find the total depreciation in its value by the end of
years.
Answer:
For 1st year:
and,
For 2nd year:
and,
Question 5: Find the sum, invested at compounded annually, on which the interest for the third year exceeds the interest of the first year by
.
Answer:
For 1st year:
and,
For 2nd year:
and,
For 3rd year:
and,
Given
Question 6: The compound interest, compounded annually, on a certain sum is in second year and is
in third year. Calculate;
- The rate of interest, sum borrowed
- The interest of
year.
Answer:
is the interest on
Let the sum of money
Therefore Interest on it for 1st Year
When interest of 2nd year
, then
Question 7: A man borrows at
compound interest compounded yearly. At the end of each year, he pays back
of the sum borrowed. How much money is left unpaid just after the second year?
Answer:
For 1st year:
and,
For 2nd year:
and,
Question 8: A man borrows at
compound interest compounded yearly. At the end of each year, he pays back
of the amount for that year. How much money is left unpaid just after the second year?
Answer:
For 1st year:
and,
For 2nd year:
and,
Question 9: The population of a town increases every
years. If the present population of the town is
, calculate:
- Its population after
years;
- Its population
years ago;
Answer:
For 2 years ago:
and,
For 1 year ago:
and,
Given
For 1st year:
and,
For 2nd year:
and,
Question 10: 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 sum of money. [2014]
Answer:
is the interest on
Let the sum of money
Therefore Interest on it for 1st Year
When interest of 2nd year
, then