1. 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?

2. A person borrows ₹2,40,000 at an annual simple interest rate of 12% to build a house. One year after taking the loan, they start renting out the house for ₹5,200 per month. After how many years from taking the loan will the rental income be enough to repay the entire loan along with the accrued interest?

3. Rahmat Chacha borrowed ₹240000 from a bank at an annual simple interest rate of 12% to build a house. One year after borrowing, he started renting out the house for ₹5200 per month. Calculate and determine after how many years from borrowing he will be able to repay the bank loan along with interest using the rental income.

4. At an annual interest rate of 5%, for how many years will the interest on 300 rupees amount to 120 rupees?

(a) 4 (b) 8 (c) 12 (d) 12\(\frac{1}{2}\)

5. Write down the calculation to determine in how many years a sum of money will double at an annual simple interest rate of 6%.

6. Write down the calculation to determine in how many years a simple interest of ₹168 will be earned on a principal of ₹600 at an annual rate of 8%.

7. Write how many years it will take for a principal to double at an annual simple interest rate of 6 \(\frac{1}{4}\)%.

8. Determine how many years it will take for ₹105 interest to accumulate on ₹500 at an annual compound interest rate of 10%.

9. 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?

10. 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

11. 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?

12. If a sum of money doubles in \(n\) years at a fixed annual compound interest rate, then in how many years will it become 4 times?

13. 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.

14. 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?

15. 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?

16. Rekha divided her savings of ₹50,000 and deposited them in two banks under the same type of savings scheme. One bank offers a simple interest rate of 5%, while the other offers a simple interest rate of 7%. After 2 years, she received a total interest of ₹6000. Determine how much money she had deposited in each bank.

17. Determine how many years it will take for an amount to become eight times its original value under a fixed annual compound interest rate, given that it doubles in \(n\) years.

18. Mr. Rathin deposits money in the bank for each of his two daughters in such a way that when each daughter turns 18 years old, she will receive ₹120000. The bank offers simple interest at an annual rate of 10%. The current ages of the daughters are 13 years and 8 years respectively. Calculate how much Mr. Rathin deposited in the bank for each daughter.

19. Ramen Babu deposited a total of ₹370,000 across three banks. The annual simple interest rates for these three banks are 40%, 5%, and 6%, respectively. After one year, the amount of interest he earns from each bank is the same. Let us calculate how much money he deposited in each of the three banks.

20. Mr. Gautam borrowed ₹2000 for 2 years at an annual compound interest rate of 6%. Write the calculation to determine how much compound interest he will pay after 2 years.

21. If a certain amount of money doubles in \(n\) years at a fixed annual compound interest rate, then in how many years will it become four times?

22. At an annual interest rate of 4%, for how much money will the difference between the simple interest and the compound interest for 2 years be 80 rupees? Let’s calculate and write it down.

23. 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

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. If a certain amount of money doubles in 4 years at a fixed annual compound interest rate, in how many years will it become four times?

26. If a principal amount doubles in 8 years at an annual compound interest rate of \(r\%\), then in how many years will it become four times?

27. 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?

28. 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.

29. A man takes a loan of ₹500 at 6% simple interest per annum. Exactly two years after taking the first loan, he takes a second loan of ₹900 at 4% simple interest per annum. After how many years from the time of the first loan will the interest amounts on both loans be equal? Also, what will be the total interest on both loans at that time?

30. 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?