1. 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?

2. 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)?

3. 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?

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

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

6. 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.

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

8. 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.

9. 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).

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. 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?

12. 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?

13. 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

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

15. 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) ₹\(\cfrac{100x}{4}\)

16. The annual simple interest rate decreases from \( 4\% \) to \( 3\frac{3}{4}\% \), causing a person's yearly income to reduce by 60 rupees. Find the principal amount of that person.

17. Due to the decrease in the annual simple interest rate from 4% to 3\(\frac{3}{4}\)%, a person's annual income decreases by 60 rupees. What is the principal amount of that person?

18. In compound interest, if an amount becomes \(\cfrac{27}{8}\) times the principal in 3 years, what will be the annual rate of interest? Let me know if you'd like the full solution as well—I'm ready when you are.

19. Mannan Miah saw that after 6 years of borrowing a sum of money, the amount of simple interest had become \(\frac{3}{8}\) of the principal. Determine the annual rate of simple interest.

20. 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%

21. At an annual simple interest rate of \(x\%\), if the interest on a principal amount for \(x\) years is \(x\) rupees, what is the principal amount?

(a) \(x\) rupees (b) \(100x\) rupees (c) \(\cfrac{100}{x}\) rupees (d) \(\cfrac{100}{x^2}\) rupees

22. At what annual interest rate will the interest on a principal amount become \(\cfrac{5}{16}\) of the principal in 6\(\cfrac{1}{4}\) years?

(a) 3% (b) 4% (c) 5% (d) 6%

23. At what annual percentage rate of interest will the interest on an amount in 4 years become \(\cfrac{1}{6}\) of the total amount?

(a) 4% (b) 5% (c) 6% (d) 8%

24. At an annual simple interest rate of 12%, if the ratio of principal to interest after \(x\) years is 25:24, what is the value of \(x\)?

(a) 8 (b) 10 (c) 12 (d) 5

25. 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

26. 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.

27. At an annual simple interest rate of \(\cfrac{r}{2}\%\), the amount after \(t\) years on ₹\(2p\) becomes \(\left(2p + \cfrac{prt}{100}\right)\).

28. If a principal amount becomes ₹6325 in 3 years and ₹6737.50 in 4\(\frac{1}{2}\) years at compound interest, find the rate of interest and the principal.

29. 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.

30. If \(\frac{1}{6}\) of a principal amount is earned as annual simple interest, what will be the percentage rate of interest?

(a) 10\(\cfrac{2}{3}\%\) (b) 16\(\cfrac{2}{3}\%\) (c) 12% (d) 9\(\cfrac{2}{3}\%\)