1. At an annual percentage rate of interest, the simple interest and compound interest on a principal amount are equal after —— years.

2. At the same interest rate, the simple interest on a certain amount for 3 years is ₹1200, and the compound interest for 2 years is ₹832. Determine the interest rate and the principal amount.

3. At the same annual interest rate, the compound interest and simple interest on a principal amount will be equal.

(a) 1 years (b) 2 years (c) 3 years (d) 4 years

4. At an equal annual interest rate, determine the number of years required for the simple interest and compound interest on a given principal to become equal.

5. ₹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

6. 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.

7. 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.

8. 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) \(\frac{1}{2}\)

9. If the simple interest for 1 year on a certain principal amount is 500 rupees and the compound interest for 2 years is 1020 rupees, determine the principal amount and the annual simple interest rate.

10. 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.

11. At the same annual interest rate, simple interest and compound interest will be equal in _____ years.

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

13. Determine the principal and the annual simple interest rate if a sum of money amounts to ₹7100 in 7 years and ₹6200 in 4 years at the same annual rate of simple interest.

14. Determine the annual simple interest rate (percentage) at which the interest on a certain amount over 10 years becomes \(\frac{2}{5}\) of the total amount (principal + interest).

15. If a certain principal earns ₹560 in 3 years and ₹600 in 5 years at the same annual simple interest rate, determine the principal amount and the annual percentage rate of simple interest.

16. 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.

17. 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.

18. If the simple interest on a certain principal for 1 year is ₹50 and the compound interest for 2 years is ₹102, then calculate and write the amount of the principal and the annual rate of interest.

19. 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.

20. If the annual simple interest on a principal is \(\cfrac{1}{9}\) of it, then what will be the accumulated amount in 4 years if the total sum becomes 1326 rupees?

(a) ₹ 1080 (b) ₹ 1120 (c) ₹ 918 (d) ₹ 750

21. If the simple interest on ₹850 for 3 years and on ₹1250 for 4 years at the same rate amounts to ₹302 in total, then what will be the annual rate of interest?

(a) 3% (b) 5% (c) 7% (d) None of the above

22. 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

23. 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?

24. 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.

25. 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.

26. 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.

27. At an annual interest rate of 10%, compounded semi-annually, the difference between the compound interest and simple interest over 2 years is ₹124.05. Find the principal amount.

28. Bimalkaku deposited ₹187,500 in a bank at an annual 5% simple interest for his 12-year-old son and 14-year-old daughter, in such a way that when both of them turn 18, they will each receive the same amount of money (principal + interest). How much money did he deposit for his son and daughter respectively?

29. 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)?

30. If a principal amount yields a total of ₹7,100 (principal + simple interest) in 7 years and ₹6,200 in 4 years at the same annual rate of simple interest, find the principal and the annual rate of simple interest.