1. At an annual simple interest rate of \(\frac{r}{2}\%\), the amount after \(t\) years on ₹\(2p\) will be ₹\((2p +\) ___\()\).

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. 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).

4. At an annual simple interest rate of 5%, a person deposits some money in the bank. After 5 years, how much total amount will he receive, if the principal is 12,500 rupees less than the total amount (principal + interest?

5. At an annual percentage rate of interest, the simple interest and compound interest on a principal amount are equal after —— years.

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. 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)?

8. A bank gives simple interest at an annual rate of 5%. A person deposited ₹15,000 at the beginning of the year. After 3 months, he withdrew ₹3,000, and 3 months after the withdrawal, he deposited ₹8,000 again. Calculate the total amount (principal + interest) he will receive at the end of the year.

9. Rahim took a loan from a bank at an annual simple interest rate of 10%, and on the same day, Ram took a separate loan from the same bank at the same interest rate. After 2 years, the total amount the bank received from Rahim was exactly the same as the total amount it received from Ram after 3 years. Determine the ratio of Rahim's loan to Ram's loan.

10. Rokeya takes a loan from the bank under the condition that she will pay interest at an annual simple interest rate of 10% and repay \(\frac{1}{5}\) of the principal every two years. If she pays 10,000 currency units as the first installment after two years, determine the amount she borrowed.

11. 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.

12. 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.

13. Jayanta deposits ₹1000 on the first day of each month into a monthly savings scheme. If the bank offers an annual simple interest rate of 5%, let's calculate the total amount (principal + interest) he will receive after 6 months.

14. I have ₹5000. I deposited this amount in a bank at an annual compound interest rate of 8.5%. Write the calculation to determine the total amount (principal + interest) I will receive after 2 years.

15. Rahmat Chacha deposited a certain amount of money in a cooperative bank at an annual compound interest rate of 9%. After 2 years, he received ₹29,702.50 as the total amount (principal + interest). Let us determine how much money Rahmat Chacha originally deposited in the cooperative bank.

16. 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

17. At an annual simple interest rate of \(x\%\), if the interest on a principal in \(x\) years is \(x\) rupees, then the amount of the principal is –

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

18. 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

19. 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

20. 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

21. What will be the total amount of 450 rupees after 3 years at an annual simple interest rate of 4%?

(a) ₹ 135 (b) ₹ 180 (c) ₹ 504 (d) ₹ 600

22. ₹1200 is lent at an annual interest rate of 6\(\frac{1}{4}\)% and ₹1000 is lent at an annual interest rate of 4\(\frac{1}{3}\)% on the same day. After how much time will the amounts (principal + interest) of both loans become equal?

(a) 20 years (b) 24 years (c) 15 years (d) 30 years

23. What annual rate of simple interest will make the interest on a sum over 10 years equal to \(\cfrac{2}{5}\) of the total amount?

(a) \(6\frac{1}{3}\%\) (b) \(6\%\) (c) \(6\frac{2}{3}\%\) (d) \(2\frac{1}{6}\%\)

24. If the simple interest on ₹850 for 3 years and on ₹1250 for 4 years at the same rate amounts to ₹302 in total, then what will be the annual rate of interest?

(a) 3% (b) 5% (c) 7% (d) None of the above

25. At an annual simple interest rate of 6%, in how many years will the interest on ₹\(x\) amount become ₹\(\frac{9x}{25}\)? Find the value of the time.

(a) 6 years (b) 8 years (c) 10 years (d) 12 years

26. If a sum of money becomes 4 times its original amount in *n* years at a fixed annual compound interest rate, then in how many years will it become 4 times?

27. 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?

28. 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?

29. 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?

30. 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.