1. If the ratio of a principal amount and its amount after 5 years is 5 : 6, then find the annual simple interest rate.

2. If the ratio of principal to amount after 1 year is 20 : 21, what is the annual rate of simple interest (in percentage)?

3. If the ratio of principal to amount after 1 year is 4:9, then the annual simple interest rate will be 5%.

4. If after one year the ratio of the principal to the amount (principal + interest) is 10 : 12, what is the annual rate of simple interest (in percentage)?

5. If the ratio of principal to amount after 1 year is 4:9, then the annual simple interest rate is 12.5%.

6. If the ratio of principal to interest for 5 years is 16:9, find the annual interest rate.

(a) 11.25% (b) 13% (c) 12.25% (d) 16%

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

8. If the ratio of the principal amount and the amount with interest after 1 year is 8:9, then the annual simple interest rate is 12.5%.

9. If the ratio of principal to amount after one year is \(8:9\), then the annual simple interest rate is _____%.

10. If the ratio of principal to interest-principal in a year is 8:9, then what is the annual simple interest rate?

(a) 12\(\cfrac{1}{2}\)% (b) 15\(\cfrac{1}{2}\)% (c) 12% (d) 15%

11. 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

12. If the ratio of the principal to its total amount after one year is 25:28, then the annual interest rate is—?

(a) 3% (b) 12% (c) 10\(\frac{5}{7}\)% (d) 8%

13. A person deposited ₹100 in a bank, and after 2 years received ₹121 as the total amount under compound interest. What is the annual percentage rate of compound interest?

14. At an annual interest rate, the compound interest on a principal for 2 years is greater than the simple interest.

15. At an annual percentage rate of interest, the simple interest and compound interest on a principal amount are equal after —— 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. A farmer deposits ₹100 at the post office on the first day of every month. If the annual rate of simple interest is 5%, what will be the total amount (principal + interest) he receives at the end of the year?

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. If the ratio of a principal amount to its annual amount with interest is 20:25, then the annual interest rate will be 4%.

21. 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.

22. At an annual compound interest rate of 5%, if the compound interest on a certain amount of money over 2 years is ₹615, determine the principal.

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

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. 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?

26. Mr. Jayanta deposits ₹1,000 on the first day of every month in a monthly scheme. If the annual simple interest rate is 5%, then how much total amount (principal + interest) will he receive at the end of the year?

27. Jayanta deposits ₹100 on the first day of each month in a monthly savings scheme. He continues this for one year. If the annual simple interest rate is 6%, how much total amount (principal + interest) will he receive at the end of the year?

28. If the principal and interest ratio in 5 years is 5:3, the annual simple interest rate is-

(a) 12% (b) 10% (c) 8% (d) 4%

29. 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%

30. 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