1. 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?

2. Sudip Babu deposited ₹7,800 in the bank at compound interest. If the compound interest rates for the first, second, third, and fourth years are 5%, 4%, 10%, and 12% respectively, then what will be the compound principal after 4 years?

(a) ₹ 10,493.68 (b) ₹ 10,000 (c) ₹ 14,936 (d) none of the above

3. In compound interest, if the interest rates for the first, second, and third years are \(r_1\%\), \(r_2\%\), and \(2r_3\%\) respectively, then the amount after 3 years on a principal of ₹\(P\) will be: \[ P\left(1 + \cfrac{r_1}{100}\right)\left(1 + \cfrac{r_2}{100}\right)\left(1 + \cfrac{r_3}{100}\right) \]

4. If the compound interest rates for the first, second, and third years are 6%, 4%, and 10% respectively, then how much total amount (principal + interest) will a person receive after investing ₹50,000 for 3 years?

5. If the interest is compounded semi-annually, what will be the compound amount on ₹10,000 for \(1\cfrac{1}{2}\) years, where the annual compound interest rates are 10% for the first period, 20% for the second period, and 40% for the third period?

6. If the interest rates for the first, second, and third years are 5%, 8%, and 10%, respectively, then the compound principal at the end of 3 years on ₹16,000 would be—

(a) ₹ 16,958 (b) ₹ 19,958.40 (c) ₹ 17,958 (d) ₹ 18,958.40

7. If the interest rates for the first, second, and third years are 5%, 10%, and 15% respectively, what will be the compound interest on ₹5000 at the end of 3 years?

(a) ₹ 2000 (b) ₹1900 (c) ₹ 1700 (d) ₹ 1641.25

8. Aman borrowed ₹25,000 for 3 years, with annual compound interest rates of 4% for the first year, 5% for the second year, and 6% for the third year. What amount will Aman repay (including principal and interest) at the end of 3 years?

9. 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?

10. If the compound interest rate is 6% for the first year and 4% for the second year, what will be the amount after 2 years on ₹22,000?

11. 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

12. 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.

13. My uncle borrowed ₹40,000 for 3 years in such a way that the annual compound interest rates for the first, second, and third years were 2%, 3%, and 4% respectively. How much money will he repay (principal + interest) at the end of 3 years?

14. At an annual interest rate of 9%, if the difference between the compound interest and simple interest on a certain amount for 2 years is ₹129.60, then calculate and write that principal amount.

15. If the simple interest and compound interest on a certain principal for 2 years are ₹8400 and ₹8652 respectively, then calculate and write the amount of the principal and the annual rate of interest.

16. If the simple interest and compound interest on a certain principal for 2 years are 840 rupees and 869.40 rupees respectively, then let’s calculate and write down the principal amount and the annual rate of interest.

17. 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.

18. 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.

19. Bimal Babu lent a certain amount of money to one person at an annual simple interest rate of 8% for 4 years, and twice that amount to another person at an annual simple interest rate of 10% for the same duration. Bimal Babu received ₹960 more interest from the second person than from the first. Find the total amount of money Bimal Babu lent.

20. If the annual rate of interest and the time in years are equal, then in how many years will the interest on ₹324 amount to ₹16?

(a) \(2\cfrac{2}{9}\) (b) \(2\cfrac{1}{9}\) (c) \(2\cfrac{4}{9}\) (d) \(2\cfrac{5}{9}\)

21. If the simple interest and compound interest on a certain principal for 2 years are ₹8400 and ₹8652 respectively, then determine the principal and the annual rate of interest.

22. If the difference between the compound interest and simple interest on a certain sum of money for 3 years at an annual rate of 10% is ₹930, then what is the amount of that sum?

23. 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?

24. If the interest is compounded every 6 months at an annual rate of 10%, then calculate the compound interest and the total amount on ₹1600 for \(1\cfrac{1}{2}\) years.

25. If the simple interest and compound interest for 2 years on a certain principal are ₹840 and ₹869.40 respectively, determine the principal amount and annual interest rate.

26. At the same time, Amal Roy deposits ₹2000 in a bank, and Pashupati Ghosh deposits ₹2000 in a post office. After 3 years, they receive ₹2360 and ₹2480 respectively, including interest. Determine the ratio of the annual percentage interest rates of the bank and the post office.

27. Rambabu divided his total money between two banks in such a way that he received equal interest from both banks after one year. The annual interest rates of the two banks are 4% and 5%, respectively. The amount of money deposited in the second bank is — of the amount deposited in the first bank.

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

28. 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.

29. If the simple interest and compound interest for 2 years on a principal amount are ₹8,400 and ₹8,652 respectively, find the principal amount and the annual simple interest rate.

30. If the difference between the compound interest and simple interest on a certain sum for 3 years at an annual rate of 10% is 930 rupees, then what is the principal amount?