1. For a fixed amount of money, at a fixed annual rate of interest, the compound interest and simple interest will be equal in -- years.

2. If the ratio of a certain principal amount to its compound amount after a certain period is 15:21 and the annual simple interest rate is 5%, then the duration of time is –

(a) 4 years (b) 2 years (c) 8 years (d) 10 years

3. Rokeya takes a loan from the bank under the condition that she will pay interest at an annual simple interest rate of 10% and repay \(\frac{1}{5}\) of the principal every two years. If she pays 10,000 currency units as the first installment after two years, determine the amount she borrowed.

4. At the same annual percentage interest rate, the simple interest and compound interest on a principal amount become equal in _____ years (interest period: 1 year).

5. In compound interest, if the interest rates for the first, second, and third years are \(r_1\%\), \(r_2\%\), and \(2r_3\%\) respectively, then the amount after 3 years on a principal of ₹\(P\) will be: \[ P\left(1 + \cfrac{r_1}{100}\right)\left(1 + \cfrac{r_2}{100}\right)\left(1 + \cfrac{r_3}{100}\right) \]

6. If the simple interest and compound interest on a certain principal for 2 years are ₹8400 and ₹8652 respectively, then calculate and write the amount of the principal and the annual rate of interest.

7. For a fixed amount of money at a fixed annual interest rate, the amount of compound interest and simple interest after 1 year will be equal.

8. If the simple interest and compound interest on a certain principal for 2 years are 840 rupees and 869.40 rupees respectively, then let’s calculate and write down the principal amount and the annual rate of interest.

9. A fixed amount of money is given at a fixed annual interest rate. In one year, the compound interest and the simple interest amounts are equal.

10. If the time period and the annual simple interest rate are equal, then at what annual interest rate will the interest amount be \(\cfrac{1}{25}\) of the principal?

(a) 25% (b) 10% (c) 2% (d) 2.5%

11. ₹1200 is lent at an annual interest rate of 6\(\frac{1}{4}\)% and ₹1000 is lent at an annual interest rate of 4\(\frac{1}{3}\)% on the same day. After how much time will the amounts (principal + interest) of both loans become equal?

(a) 20 years (b) 24 years (c) 15 years (d) 30 years

12. A person deposited ₹100 in a bank, and after 2 years received ₹121 as the total amount under compound interest. What is the annual percentage rate of compound interest?

13. A farmer deposited some money in the village post office. After 4 years, he found that the total amount including interest had become ₹434. He calculated that the interest he received was \(\frac{6}{25}\) of his principal amount. Find how much money he had originally deposited and what annual rate of simple interest the post office gave.

14. The simple interest for 2 years and the compound interest for 1 year (with annual compounding) on the same principal at the same rate are ₹800 and ₹820 respectively. Find the principal and the rate of interest.

15. If after one year the ratio of the principal to the amount (principal + interest) is 10 : 12, what is the annual rate of simple interest (in percentage)?

16. A bank gives simple interest at an annual rate of 5%. A person deposited ₹15,000 at the beginning of the year. After 3 months, he withdrew ₹3,000, and 3 months after the withdrawal, he deposited ₹8,000 again. Calculate the total amount (principal + interest) he will receive at the end of the year.

17. Mr. Amal bequeaths ₹56,000 in his will for his two sons aged 13 and 15 in such a way that, when they each turn 18, the simple interest earned at an annual rate of 10% will be equal to the principal for each. What will be the allocated amount for each son in the will?

18. If the simple interest and compound interest on a certain principal for 2 years are ₹8400 and ₹8652 respectively, then determine the principal and the annual rate of interest.

19. If the difference between the compound interest and the simple interest on a certain sum of money for 2 years at an annual interest rate of 9% is ₹129.60, then find the principal amount.

20. If the difference between the compound interest and simple interest on a certain principal for 2 years at an annual rate of 5% is ₹25, then what is the amount of the principal?

21. The compound interest and simple interest on a fixed amount of money at a fixed annual rate for 1 year are ______.

22. If the principal is \(p\) rupees and the annual compound interest rates for the first, second, and third years are \(r_1\%\), \(r_2\%\), and \(r_3\%\) respectively, then what will be the total compound amount after 3 years?

23. If the simple interest and compound interest for 2 years on a certain principal are ₹840 and ₹869.40 respectively, determine the principal amount and annual interest rate.

24. Anil Babu wants to allocate ₹56,000 between his two sons, aged 13 and 15, such that when they turn 18, the simple interest earned at an annual rate of 10% is equal to their respective principal amounts. Determine the amount allocated to each son in the will.

25. In how many years will the amounts of simple interest and compound interest be equal for the same principal at the same annual interest rate?

(a) 3 years (b) 2 years (c) 1 years (d) \(\frac{1}{2}\)

26. Rahim took a loan from a bank at an annual simple interest rate of 10%, and on the same day, Ram took a separate loan from the same bank at the same interest rate. After 2 years, the total amount the bank received from Rahim was exactly the same as the total amount it received from Ram after 3 years. Determine the ratio of Rahim's loan to Ram's loan.

27. Rambabu divided his total money between two banks in such a way that he received equal interest from both banks after one year. The annual interest rates of the two banks are 4% and 5%, respectively. The amount of money deposited in the second bank is — of the amount deposited in the first bank.

(a) \(\frac{1}{2}\) part (b) \(\frac{1}{3}\) part (c) \(\frac{1}{6}\) part (d) twice

28. Bimal Kaku deposited 56,000 INR in a bank for his two sons, aged 13 and 15 years, in such a way that when they turn 18, the simple interest earned at an annual rate of 10% on each deposit equals the respective principal amount. Determine how much he deposited in each son's name.

29. At an annual interest rate of 4%, the difference between the simple interest and compound interest on a principal amount for 2 years is 40 rupees. Determine the principal amount.

30. If the simple interest and compound interest for 2 years on a principal amount are ₹8,400 and ₹8,652 respectively, find the principal amount and the annual simple interest rate.