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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