1. 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?

2. 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?

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

4. 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)?

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

6. Determine the annual simple interest rate (percentage) at which the interest on a certain amount over 4 years becomes \(\frac{8}{25}\) of the principal.

7. 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.

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

9. Determine the annual simple interest rate (in percentage) at which the interest for 5 years becomes \(\cfrac{2}{5}\) of the principal amount.

10. What should the interest rate be so that the interest for 2 years on a certain amount of money equals \(\cfrac{1}{4}\) of the principal?

(a) 10% (b) 12.5% (c) 15% (d) 25%

11. 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

12. A borrowed ₹960 from B at an annual simple interest rate of 6%, with the condition that the loan will be repaid over the next 4 yearly installments. In the first 3 installments, A will pay only one-fourth of the principal each year. In the final (4th) installment, A will pay the remaining principal along with the total interest accrued over the 4 years. Find the total amount A will pay at the end of the 4th year.

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. Sure! The Bengali sentence: **"কোনো মূলধন বার্ষিক 6 \(\frac{1}{4}\)% সরল সুদের হারে কত বছরে দ্বিগুণ হবে তা লিখি ।"** translates to English as: **"Write how many years it will take for a principal to double at an annual simple interest rate of 6 \(\frac{1}{4}\)%."** Would you like help solving this too?

15. 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.

16. 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.

17. 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?

18. 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).

19. 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.

20. If the total amount becomes 966 rupees at an annual simple interest rate of 3% in 5 years, the principal amount will be -

(a) 480 rupees (b) 408 rupees (c) 404 rupees (d) 840 rupees

21. 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

22. What should be the annual simple interest rate so that the principal increases by 75% in 6 years?

(a) 8% (b) 20% (c) 12.5% (d) 15%

23. What should be the principal amount so that the compound amount becomes ₹169 in 2 years at a 4% interest rate?

(a) ₹ 156.25 (b) ₹160 (c) ₹150.50 (d) ₹ 154.75

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. 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.

26. 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.

27. ₹1200 is deposited for 4 years and ₹2000 for 3 years in a bank at the same rate of simple interest. If the total interest earned is ₹594, what is the annual rate of interest (percentage)?

28. 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.

29. If the amount becomes ₹\(y\) in \(x\) years at an annual interest rate of 4%, then the principal (original amount) will be –

(a) ₹ \(4xy\) (b) ₹\(\cfrac{4x}{100+y}\) (c) ₹ \(\cfrac{100y}{100+4x}\) (d) ₹\(\cfrac{100x}{4}\)

30. 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.