1. Under compound interest, a certain principal becomes ₹6,600 in 1 year and ₹7,986 in 3 years. Find the principal and the rate of interest.

2. At the same rate of simple interest, a certain principal amounts to ₹1056 in 4 years and ₹1248 in 7 years. Find the rate of interest and the principal.

3. If a certain principal amount becomes ₹1,00,000 in 3 years and ₹1,72,800 in 6 years at compound interest, then what is the interest rate?

(a) 10% (b) 20% (c) 25% (d) 15%

4. 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: \[ P\left(1 + \cfrac{r_1}{100}\right)\left(1 + \cfrac{r_2}{100}\right)\left(1 + \cfrac{r_3}{100}\right) \]

5. Some money amounts to 944 rupees in 3 years at simple interest. If the annual rate of interest increases by 25%, then the same money amounts to 980 rupees in the same time. Find the rate of interest and the principal.

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

7. 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.

8. A certain sum of money amounts to ₹944 in 3 years at simple interest. If the rate of interest is increased by 25%, the same sum amounts to ₹980 in the same time period. Find the principal amount and the original rate of interest.

9. At an annual interest rate of 10%, compounded semi-annually, the difference between the compound interest and simple interest over 2 years is ₹124.05. Find the principal amount.

10. If a principal amount yields a total of ₹7,100 (principal + simple interest) in 7 years and ₹6,200 in 4 years at the same annual rate of simple interest, find the principal and the annual rate of simple interest.

11. If a certain principal amount amounts to ₹1248 in 7 years and ₹1056 in 4 years at the same annual rate of simple interest, find the principal and the annual rate of simple interest.

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. If a certain principal earns ₹560 in 3 years and ₹600 in 5 years at the same annual simple interest rate, find the amount of the principal and the annual rate of simple interest.

14. If the difference between the compound interest and simple interest on a certain sum at a rate of 20% per annum for 3 years is ₹800, what is the principal amount?

(a) ₹ 5250 (b) ₹ 8650 (c) ₹ 6250 (d) none of the above

15. 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?

16. In compound interest, if an amount becomes \(\cfrac{27}{8}\) times the principal in 3 years, what will be the annual rate of interest? Let me know if you'd like the full solution as well—I'm ready when you are.

17. If the difference between the compound interest and simple interest on a certain amount for 3 years at an annual interest rate of 10% is ₹930, then calculate and write that principal amount.

18. 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?

19. Here’s the English translation of your question: At a certain fixed rate of simple interest, if a principal amount becomes double in \(x\) years and triple in \(y\) years, then what is the ratio \(x:y\)?

(a) 2:3 (b) 1:2 (c) 3:2 (d) 2:1

20. If a principal becomes \(3\frac{3}{8}\) times the original amount in 3 years at compound interest, what is the annual rate of interest?

21. A certain amount of money amounts to ₹700 in 4 years at simple annual interest, and during this time the interest is 40% of the principal. What is the amount of the principal?

(a) ₹ 500 (b) ₹ 400 (c) ₹ 600 (d) ₹ 300

22. If the ratio of a principal amount and its amount after 5 years is 5 : 6, then find the annual simple interest rate.

23. The simple interest and compound interest on a certain principal for 2 years are ₹4,000 and ₹4,100 respectively. Find the principal and the rate of interest.

24. The simple interest for 2 years and the compound interest for 1 year (with annual compounding) on the same principal at the same rate are ₹800 and ₹820 respectively. Find the principal and the rate of interest.

25. The simple interest on ₹400 for 5 years and on ₹600 for 4 years together amounts to ₹132. If the rate of interest is the same in both cases, find the rate of interest.

(a) 3% (b) 5% (c) 7% (d) 9%

26. Under the same rate of interest, the simple interest on ₹800 for 3 years and ₹1000 for 5 years together amounts to ₹592. What is the rate of interest?

(a) 6% (b) 8% (c) 7% (d) 9%

27. For a fixed amount of money, at a fixed annual rate of interest, the compound interest and simple interest will be equal in -- years.

28. 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?

29. 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?

30. 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?