1. What should be the annual compound interest rate for a certain amount of money to become 1.96 times that amount in 2 years?

2. What should be the annual rate of simple interest (in percent) so that the interest on a sum of money for 10 years becomes \(\frac{2}{5}\) of the total amount (principal + interest)?

3. What should be the annual simple interest rate (in percentage) so that the interest on a sum of money for 6 years becomes \(\frac{18}{25}\) of the principal?

4. Some money becomes 5 times its original amount in 5 years at simple interest. At the same rate of interest, the time required for that principal to become 17 times is:

(a) 17 years (b) 20 years (c) 18 years (d) 19 years

5. Uday Babu lent a certain amount of money to one person at an annual simple interest rate of 4% for 4 years, and twice that amount to another person at an annual simple interest rate of 10% for the same duration. He received ₹960 more interest from the second person than from the first. Find the total amount of money Uday Babu lent.

6. 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.

7. Bimal Babu lent a certain amount of money to one person at an annual simple interest rate of 8% for 4 years, and twice that amount to another person at an annual simple interest rate of 10% for the same duration. Bimal Babu received ₹960 more interest from the second person than from the first. Find the total amount of money Bimal Babu lent.

8. A man left ₹28,000 for his 13-year-old son and 15-year-old daughter with the instruction that, at the age of 18, the amount each receives — including simple interest at an annual rate of 10% — should be equal. Determine the amount allocated to each child.

9. At an annual interest rate of 4%, how much money should be invested so that the total amount becomes ₹3600 in 5 years?

10. 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.

11. If the difference between the compound interest and simple interest on a certain sum of money for 3 years at an annual rate of 10% is ₹930, then what is the amount of that sum?

12. 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?

13. What would be the annual simple interest rate (percentage) if the interest for 4 years on a certain amount is \(\cfrac{8}{25}\) of the principal?

14. What should be the annual simple interest rate so that the interest for 5 years becomes \(\cfrac{1}{4}\) of the principal?

15. At an annual interest rate of 9%, if the difference between the compound interest and simple interest on a certain amount for 2 years is ₹129.60, then calculate and write that principal amount.

16. What should be the annual rate of simple interest (in percentage) so that the interest earned in 4 years becomes \( \frac{2}{5} \) of the principal amount?

17. What should be the annual rate of simple interest (in percentage) so that the interest earned in 4 years becomes \(\frac{8}{25}\) of the principal amount?

18. What should be the annual rate of simple interest so that the interest for 5 years becomes \(\frac{1}{4}\) of the principal?

19. Mr. Bimal deposited ₹5,600 in a bank at a simple interest rate of 10% for his 13-year-old son and 15-year-old daughter in such a way that when both turn 18 years old, they each receive the same amount including interest. How much money did he deposit separately for his son and daughter?

20. Ronit borrowed some money on the condition that: - \(\cfrac{1}{4}\) of it has an interest rate of 8% - \(\cfrac{2}{3}\) of it has an interest rate of 9% - The remaining portion has an interest rate of 12% If he had to pay a total interest of ₹480, then the loan amount is—?

(a) ₹5334 (b) ₹6000 (c) ₹5333.33 (d) ₹5000

21. If the interest on a certain amount of money at an annual rate of 5% for 8 years is ₹246 more than the interest at an annual rate of 7% for 4 years, what is the principal amount?

(a) ₹ 5020 (b) ₹ 2000 (c) ₹ 2050 (d) ₹ 2005

22. Mr. Rahim divided ₹9600 between his two daughters, aged 12 and 16, and deposited the amounts in a bank at an annual interest rate of 5% so that both daughters would receive the same amount upon reaching adulthood. How did he distribute the money?

(a) ₹ 3000 ,₹ 6600 (b) ₹ 4400,₹ 5200 (c) ₹5600,₹ 4000 (d) ₹ 5000, ₹ 4600

23. If the simple interest on a certain amount at an annual interest rate of 8% for 2 years is ₹850, then what will be the compound interest for the same period?

(a) ₹ 1684 (b) ₹984 (c) ₹ 884 (d) none of the above

24. If the difference between the compound interest and simple interest on a certain sum at a rate of 20% per annum for 3 years is ₹800, what is the principal amount?

(a) ₹ 5250 (b) ₹ 8650 (c) ₹ 6250 (d) none of the above

25. 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.

26. At an annual compound interest rate of 5%, if the compound interest on a certain sum of money for 2 years is ₹615, determine the principal amount.

27. Bimal Kaku deposited ₹187,500 in a bank at an annual simple interest rate of 5% for his 12-year-old son and 14-year-old daughter, in such a way that when both children turn 18, they each receive the same amount (principal plus interest). Let us calculate how much money he deposited for his son and daughter individually.

28. Chhanda Devi borrowed some money for 2 years at an annual compound interest rate of 8%. If the compound interest amounts to ₹2496, determine how much money she borrowed.

29. If the difference between the compound interest and simple interest on a certain amount for 3 years at an annual interest rate of 10% is ₹930, then calculate and write that principal amount.

30. A principal amount doubles in 20 years at a certain simple interest rate. At the same rate of simple interest, the time required for the principal to become three times will be:

(a) 30 Years (b) 35 Years (c) 40 Years (d) 45 Years