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. 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?

3. 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

4. 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.

5. 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.

6. 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?

7. If the simple interest for 1 year on a certain principal amount is 500 rupees and the compound interest for 2 years is 1020 rupees, determine the principal amount and the annual simple interest rate.

8. 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.

9. 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.

10. If the simple interest on a certain principal for 1 year is ₹50 and the compound interest for 2 years is ₹102, then calculate and write the amount of the principal and the annual rate of interest.

11. 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

12. At an annual simple interest rate of \(x\%\), if the interest on a principal in \(x\) years is \(x\) rupees, then the amount of the principal is –

(a) \(x\) rupees (b) \(100x\) rupees (c) \(\cfrac{100}{x}\) rupees (d) \(\cfrac{100}{x^2}\) rupees

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

14. 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.

15. 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

16. 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?

17. 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%

18. 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.

19. 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.

20. If the ratio of the principal and the annual compound amount is 10:11, then the annual interest rate is _____.

21. At an annual simple interest rate of \(x\%\), if the total interest on a principal amount for \(y\) years is \(\cfrac{xyz}{25}\) rupees, then the principal amount is –

(a) ₹ 2z (b) ₹ 4z (c) \(\cfrac{z}{2}\) (d) \(\cfrac{z}{4}\)

22. If the annual compound interest rate is \(r\%\), and the interest earned is _____, then the compound amount of \(p\) rupees in \(n\) years will be \(p\left(1+\cfrac{r}{400}\right)^{4n}\) rupees.

23. At an annual interest rate of 4%, the difference between the simple interest and compound interest on a principal amount for 2 years is 40 rupees. Determine the principal amount.

24. If the ratio of the principal amount and the amount with interest after 1 year is 8:9, then the annual simple interest rate is 12.5%.

25. At an annual simple interest rate of x%, if the interest earned in x years is x rupees, then the principal amount is —

(a) ₹ \(x\) (b) ₹ \(100x\) (c) ₹\(\cfrac{100}{x}\) (d) ₹ \(\cfrac{100}{x^2}\)

26. At an annual simple interest rate of \(r\%\), if the total interest in \(n\) years is ₹\(\cfrac{pnr}{25}\), then the principal amount is —

(a) ₹ \(2p\) (b) ₹ \(4p\) (c) ₹ \(\cfrac{p}{2}\) (d) ₹ \(\cfrac{p}{4}\)

27. Translate: If the simple interest on a certain principal for \(n\) years at a rate of \(r\%\) is \(\frac{pnr}{25}\) rupees, then the amount of the principal is –

(a) \(\cfrac{p}{4}\) (b) \(\cfrac{p}{2}\) (c) \(2p\) (d) \(4p\)

28. 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?

29. At an annual interest rate of \( a\% \), if the interest for \( a \) years on a principal is \( b \) rupees, then the amount of the principal is—

(a) \(\cfrac{100a}{b}\)rupees (b) \(\cfrac{100a}{b^2}\) rupees (c) \(\cfrac{100b}{a}\)rupees (d) \(\cfrac{100b}{a^2}\)rupees

30. At an annual simple interest rate of \(x\%\), if the interest on a principal amount for \(x\) years is \(x\) rupees, what is the principal amount?

(a) \(x\) rupees (b) \(100x\) rupees (c) \(\cfrac{100}{x}\) rupees (d) \(\cfrac{100}{x^2}\) rupees