1. 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?

2. 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?

3. 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?

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. 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.

6. 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).

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

8. 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.

9. 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?

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

11. At an annual simple interest rate of 10%, if the interest for 5 years is x rupees, then the principal amount:

(a) ₹ 2x (b) ₹ 4x (c) ₹ 10x (d) ₹ 20x

12. 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

13. At an annual simple interest rate of \(r\%\), if the total interest on a principal for \(n\) years is \(\cfrac{pnr}{25}\) rupees, then the amount of the principal is –

(a) \(2p\) rupees (b) \(4p\) rupees (c) \(\cfrac{p}{2}\) rupees (d) \(\cfrac{p}{4}\) rupees

14. The principal amount, if the simple interest for 5 years at an annual rate of 6% is ₹75, would be?

(a) ₹ 200 (b) ₹ 250 (c) ₹ 300 (d) ₹ 325

15. 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

16. If the simple interest for \(n\) years at an annual rate of \(r\%\) is \(\frac{pnr}{25}\) rupees, then the principal amount will be _____ rupees.

17. 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.

18. 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?

19. ₹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)?

20. 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.

21. If the total simple interest on a principal amount at an annual rate of \(x\%\) for \(y\) years is \(\frac{pyx}{25}\) rupees, then the principal amount will be:

(a) \(2p\) rupees (b) \(4p\) rupees (c) \(\cfrac{p}{2}\) rupees (d) \(\cfrac{p}{4}\) rupees

22. Doubling the principal means Principal \((p) =\) Interest \((I) = x\) taka Rate of interest \((r) = 6\frac{1}{4}\% = \frac{25}{4}\%\) \[ \therefore \text{Time } (t) = \frac{100 \times I}{p \times r} \text{ years} = \frac{100 \times x}{x \times \frac{25}{4}} = \frac{100 \times 4}{25} = 16 \text{ years} \] \[ \therefore \text{At an annual simple interest rate of } 6\frac{1}{4}\%, \text{ any principal will double in 16 years.} \]

23. 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.

24. 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.

25. 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?

26. At an annual simple interest rate of \(\cfrac{a}{5}\)%, if the interest on ₹\(a^2\) for \(\cfrac{a}{3}\) years equals the principal amount, then what is the value of \(\cfrac{a^3}{60}\)?

27. If the simple interest on a certain principal for 2 years at an annual rate of 15% is ₹160, find the compound interest.

(a) ₹ 205 (b) ₹ 172 (c) ₹ 200 (d) none of the above

28. 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.

29. 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.

30. 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%