1. If the interest on a principal for 5 years is \(\cfrac{1}{4}\) of the principal, then the annual interest rate will be –

(a) 5% (b) 10% (c) 15% (d) 20%

2. Divide ₹549 into two parts such that the interest on the first part at an annual rate of 7% for 6 years is equal to the interest on the second part at an annual rate of 10% for 8 years. Determine the two parts.

(a) ₹ 320,₹ 229 (b) ₹510,₹ 39 (c) ₹360, ₹ 189 (d) none of the above

3. Bimal Babu deposited ₹1,87,500 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 turn 18, they receive equal amounts, including interest. Determine how much he deposited separately for his son and daughter.

4. 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.

5. At an annual simple interest rate of 6%, the interest for 5 months is \(\cfrac{x}{10}\) rupees. What will the principal be?

(a) ₹ 2x (b) ₹ 4x (c) ₹ 10x (d) ₹ 20x

6. If the total interest on a principal amount in 4 years is \(\cfrac{1}{5}\) of the principal, the annual rate of interest is:

(a) 4% (b) 5% (c) 10% (d) 20%

7. The simple interest for \( a \) rupees at an annual rate of 10% for \( b \) months is—

(a) \(\cfrac{ab}{100}\) rupees (b) \(\cfrac{ab}{120}\) rupees (c) \(\cfrac{ab}{1200}\) rupees (d) \(\cfrac{ab}{10}\) rupees

8. If interest is compounded every 6 months, then at an annual compound interest rate of 10%, what will be the compound amount and compound interest on ₹8000 for 1½ years?

9. If the compound interest on ₹5,000 for 2 years is ₹408, what is the annual rate of interest?

10. 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?

11. 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.

12. Prakash Babu invested ₹48,000 for 2 years at an annual compound interest rate of 10%. If 20% income tax is deducted from the interest earned each year, how much money will he receive at the end of the second year?

13. 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?

14. When Mr. Subir retired from his job, he received a lump sum of ₹6,00,000 from his Provident Fund and Gratuity. He wants to divide this amount between the post office and the bank in such a way that he earns ₹34,000 annually as interest. If the annual simple interest rates of the post office and the bank are 6% and 5% respectively, determine how much money he should deposit in each.

15. 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.

16. If the interest is compounded every 6 months at an annual rate of 10%, then calculate the compound interest and the total amount on ₹1600 for \(1\cfrac{1}{2}\) years.

17. Here's the English translation of your sentence: Calculate the compound interest and the total amount on ₹2,400 for 1½ years at an annual compound interest rate of 10%, compounded semi-annually.

18. 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

19. If the interest on a certain principal for 4 years is \(\cfrac{7}{16}\) of it, find the annual interest rate.

(a) 9% (b) 10.9% (c) 12% (d) 12.9%

20. If the annual interest rate is 5% and interest is compounded every 4 months, what will be the compound interest on ₹4800 for 1 year?

(a) ₹ 254 (b) ₹ 244.02 (c) ₹ 444.02 (d) ₹ 344

21. If the annual interest rate is \(12\%\) and interest is compounded every 4 months, then the compound interest on ₹\(6840\) for \(\cfrac{2}{3}\) years is?

(a) ₹ 780 (b) ₹ 330.14 (c) ₹ 758 (d) ₹ 558.14

22. If interest is compounded every 4 months, then the compound interest on ₹5600 for 1 year at an interest rate of 9% per annum is?

(a) ₹ 719 (b) ₹ 519.27 (c) ₹ 419.27 (d) ₹ 6019.27

23. Determine the principal amount for which the difference between the simple interest and compound interest for 2 years at an annual rate of 4% is 40 rupees.

24. Determine the principal amount for which the difference between the simple interest and compound interest for 2 years at an annual rate of 4% is 80 rupees.

25. If the total simple interest for 5 years is \(\cfrac{1}{5}\) of the principal, determine the annual simple interest rate.

(a) 4% (b) 5% (c) 10% (d) 25%

26. If the ratio of the principal to the total amount (principal + interest) in one year is \(4:9\), determine the annual simple interest rate.

27. Determine the compound interest on ₹6,250 for 9 months at an annual compound interest rate of 10%, compounded every 3 months.

28. If interest is compounded every 6 months, find the difference between compound interest and simple interest for ₹10,000 at an annual rate of 10% after one year.

(a) ₹ 50 (b) ₹ 25 (c) ₹ 75 (d) ₹ 0

29. 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.

30. If the interest period is 6 months and the annual compound interest rate is 10%, determine the compound interest and the total amount for ₹16,000 in \(1\frac{1}{2}\) years.