1. 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.

2. 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

3. 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

4. Mr. Amal bequeaths ₹56,000 in his will for his two sons aged 13 and 15 in such a way that, when they each turn 18, the simple interest earned at an annual rate of 10% will be equal to the principal for each. What will be the allocated amount for each son in the will?

5. 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?

6. 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

7. 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

8. 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%

9. 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?

10. 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?

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

12. Bimalkaku deposited ₹187,500 in a bank at an annual 5% simple interest for his 12-year-old son and 14-year-old daughter, in such a way that when both of them turn 18, they will each receive the same amount of money (principal + interest). How much money did he deposit for his son and daughter respectively?

13. 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.

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

15. 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?

16. 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?

17. 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 \(\cfrac{a^3}{60}\)?

18. 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?

19. 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

20. If the annual interest rate is 16% and interest is compounded quarterly, then the compound principal of ₹7,500 after 6 months will be—

(a) ₹ 8500 (b) ₹ 9112 (c) ₹ 8112 (d) ₹ 7812

21. If the simple interest on a certain amount at an annual interest rate of 8% for 2 years is ₹850, then what will be the compound interest for the same period?

(a) ₹ 1684 (b) ₹984 (c) ₹ 884 (d) none of the above

22. If the simple interest on a certain principal at an annual interest rate of 18% for 2 years is ₹800, what will be the compound interest?

(a) ₹ 672 (b) ₹ 872 (c) ₹ 560 (d) ₹ 730

23. At an annual simple interest rate of \(x\%\), the interest on 120 rupees for 10 months will be _____ rupees.

24. 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.

25. 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.

26. Anil Babu wants to allocate ₹56,000 between his two sons, aged 13 and 15, such that when they turn 18, the simple interest earned at an annual rate of 10% is equal to their respective principal amounts. Determine the amount allocated to each son in the will.

27. 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%

28. If the simple interest on \(a\) INR for \(b\) months is \(c\) INR, then the annual percentage interest rate will be? (Question)

(a) \(\cfrac{1200a}{bc}\%\) (b) \(\cfrac{1200c}{ab}\%\) (c) \(\cfrac{100b}{ac}\%\) (d) \(\cfrac{100ac}{ab}\%\)

29. A bank provides an annual simple interest rate of 5%. At the beginning of the year, Mr. Dip deposited 15,000 rupees. Three months later, he withdrew 3,000 rupees, and three months after withdrawing the amount, he deposited 4,000 rupees again. At the end of the year, how much money will Mr. Dip receive from the bank, including interest?

30. Determine the principal amount for which the monthly interest will be 10 rupees at an annual simple interest rate of 5%.