1. 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).

2. 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.

3. If the annual interest rate is the same, the compound interest on a principal amount for one year will be higher than the simple interest.

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

5. 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.

6. My aunt wants to will ₹56,000 between her two sons, aged 13 and 15, in such a way that by the time each turns 18, the total amount (principal + interest) received by both sons is equal. The interest is calculated at an annual simple interest rate of 10%. Determine how much should be allotted to each son in the will.

7. ₹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

8. 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

9. Which one will be less: the simple interest for 2 years or the compound interest with annual compounding for 2 years, on a fixed principal, if the rate of interest is the same?

10. 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?

11. 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.

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

13. 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?

14. 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.

15. 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?

16. 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?

17. 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

18. 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.

19. My aunt wants to will 56,000 INR between her two sons, aged 13 and 15, in such a way that when they turn 18, the total amount received (principal + interest) for each son will be equal, given a 10% annual simple interest rate. Determine the amount allocated for each son in the will.

20. If the compounding period is 1 year, the simple interest and compound interest for 1 year on a certain amount of money will be equal.

21. 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.

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

23. 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.

24. 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?

25. 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.

26. 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.

27. 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

28. 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%

29. If a sum of money becomes 4 times its original amount in *n* years at a fixed annual compound interest rate, then in how many years will it become 4 times?

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