1. What should be the annual compound interest rate for a certain amount of money to become 1.96 times that amount in 2 years?

2. What should be the annual interest rate (percentage) for a principal amount to become three times its original value in 25 years?

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

4. 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)?

5. 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?

6. 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?

7. If the principal is \(p\) rupees and the annual compound interest rates for the first, second, and third years are \(r_1\%\), \(r_2\%\), and \(r_3\%\) respectively, then what will be the total compound amount after 3 years?

8. If a certain principal becomes 7 times in a fixed period at an annual interest rate of 6%, what should the annual interest rate be for it to become 10 times?

(a) 10% (b) 12% (c) 16% (d) 9%

9. At an annual interest rate of \(6\cfrac{2}{3}\%\), determine the time required for the amount to become \(1.5\) times the principal.

10. My aunt wants to will 56,000 INR between her two sons, aged 13 and 15, in such a way that when they turn 18, the total amount received (principal + interest) for each son will be equal, given a 10% annual simple interest rate. Determine the amount allocated for each son in the will.

11. What should be the annual compound interest rate for ₹625 to grow to ₹784 in 2 years?

12. My aunt wants to will ₹56,000 between her two sons, aged 13 and 15, in such a way that by the time each turns 18, the total amount (principal + interest) received by both sons is equal. The interest is calculated at an annual simple interest rate of 10%. Determine how much should be allotted to each son in the will.

13. Write the calculation to determine the principal amount for which the compound interest for 3 years at an annual compound interest rate of 10% will be ₹2648.

14. A principal amount doubles in 20 years at a certain simple interest rate. At the same rate of simple interest, the time required for the principal to become three times will be:

(a) 30 Years (b) 35 Years (c) 40 Years (d) 45 Years

15. 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

16. 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

17. What should be the annual simple interest rate so that the principal increases by 75% in 6 years?

(a) 8% (b) 20% (c) 12.5% (d) 15%

18. 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%

19. If the annual interest rate is 6%, the time required for the principal to double with interest is —

(a) 16 years (b) 17 years (c) 18 years (d) None of the above

20. What should be the annual compound interest rate for ₹400 to become ₹441 in 2 years?

21. If interest is compounded every 6 months, then at an annual compound interest rate of 10%, what will be the compound amount and compound interest on ₹8000 for 1½ years?

22. 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.

23. A man left ₹28,000 for his 13-year-old son and 15-year-old daughter with the instruction that, at the age of 18, the amount each receives — including simple interest at an annual rate of 10% — should be equal. Determine the amount allocated to each child.

24. 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.

25. 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

26. When Mr. Subir retired from his job, he received a lump sum of ₹6,00,000 from his Provident Fund and Gratuity. He wants to divide this amount between the post office and the bank in such a way that he earns ₹34,000 annually as interest. If the annual simple interest rates of the post office and the bank are 6% and 5% respectively, determine how much money he should deposit in each.

27. 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.

28. 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?

29. 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?

30. 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.