1. 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

2. 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

3. 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.

4. 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) \(4p\)

5. 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?

6. If the total simple interest for \(n\) years at an annual rate of \(x\%\) is \(\frac{pnr}{25}\), > then what is the principal amount?

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

7. 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

8. 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.

9. 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?

10. 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

11. 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.

12. 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.

13. 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) \(\cfrac{z}{4}\)

14. 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.

15. 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) ₹ \(\cfrac{p}{4}\)

16. 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.

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. At an annual simple interest rate of 6%, the interest for 5 months is \(\cfrac{x}{10}\) rupees. What will the principal be?

(a) ₹ 2x (b) ₹ 4x (c) ₹ 10x (d) ₹ 20x

19. 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

20. 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%

21. 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

22. 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

23. If the annual simple interest on a principal is \(\cfrac{1}{9}\) of it, then what will be the accumulated amount in 4 years if the total sum becomes 1326 rupees?

(a) ₹ 1080 (b) ₹ 1120 (c) ₹ 918 (d) ₹ 750

24. 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

25. If a certain principal amount triples in 15 years at simple interest, then the annual rate of simple interest will be —

(a) \(13\frac{1}{3}\%\) (b) \(12\frac{1}{3}\%\) (c) \(11\frac{1}{3}\%\) (d) \(10\frac{1}{3}\%\)

26. If a principal amount doubles in 8 years at an annual compound interest rate of \(r\%\), then in how many years will it become four times?

27. 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?

28. 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?

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

30. 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?