1. If a sum of money doubles in \(n\) years at a fixed annual compound interest rate, then in how many years will it become 4 times?

2. If a certain amount of money doubles in \(n\) years under a fixed annual compound interest rate, in how many years will it become 4 times its original value?

3. If a certain amount of money doubles in 4 years at a fixed annual compound interest rate, in how many years will it become four times?

4. If a certain amount of money doubles in \(n\) years at a fixed annual compound interest rate, then in how many years will it become four times?

5. If a certain amount of money triples in 7 years at an annual compound interest rate, in how many years will it become 9 times?

(a) 10 (b) 12 (c) 14 (d) 13

6. Determine how many years it will take for an amount to become eight times its original value under a fixed annual compound interest rate, given that it doubles in \(n\) years.

7. If a machine’s value depreciates at a fixed annual rate and becomes \(\frac{1}{2}\) of its original value in 5 years, then in how many years will it become \(\frac{1}{4}\) of its original value?

8. 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?

9. If a certain amount of money doubles in \(n\) years at an annual compound interest rate, determine in how many years it will become eight times.

10. If a certain amount of money triples in 11 years at a fixed interest rate, in how many years will it become five times?

(a) 12 years (b) 6 years (c) 20 years (d) 22 years

11. 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

12. If a sum of money doubles in \(n\) years at an annual compound interest rate, then it will become four times in –

(a) \(2n\) years (b) \(\cfrac{n}{2}\) years (c) \(3n\) years (d) \(\cfrac{n}{3}\) years

13. At an annual simple interest rate of 18%, in how many years will a principal amount become 6 times its original value?

(a) 25 years (b) 30 years (c) 31.78 years (d) 27.78 years

14. 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.

15. If the amount becomes ₹\(y\) in \(x\) years at an annual interest rate of 4%, then the principal (original amount) will be –

(a) ₹ \(4xy\) (b) ₹\(\cfrac{4x}{100+y}\) (c) ₹ \(\cfrac{100y}{100+4x}\) (d) ₹\(\cfrac{100x}{4}\)

16. At an annual compound interest rate of 10%, in how many years will ₹4000 amount to ₹5324? Let’s calculate and write it down.

17. If a principal amount doubles in 4 years at a compound interest rate of \(r\%\), then it will become 4 times in ______ years.

18. Some money becomes 5 times its original amount in 5 years at simple interest. At the same rate of interest, the time required for that principal to become 17 times is:

(a) 17 years (b) 20 years (c) 18 years (d) 19 years

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

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 a principal becomes five times through simple interest in 10 years, then in how many years will it become nine times the original amount including interest?

(a) 18 (b) 20 (c) 25 (d) 30

22. At an annual simple interest rate of \(6\frac{1}{4}\%\), in how many years will a sum of money double?

23. If a certain amount of money triples in 20 years with interest and principal, in how many years will it become six times?

(a) 40 years (b) 60 years (c) 50 years (d) 30 years

24. If a certain principal amount becomes 5 times its original value in 20 years due to interest, then the rate of interest is –

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

25. If ₹27,500 doubles in 6 years at compound interest, then in how many years will it become four times?

(a) 16 (b) 15 (c) 12 (d) 10

26. If the compound principal of a certain principal amount after 4 years becomes \(\cfrac{256}{81}\) times the principal, then what is the interest rate?

(a) 15% (b) 30% (c) 33\(\cfrac{1}{3}\)% (d) 25%

27. At an annual compound interest rate of 20%, in how many years will ₹1000 amount to ₹1440?

28. At an annual compound interest rate of 4%, in how many years will a principal amount of ₹40,000 accumulate to ₹46,656?

29. If a machine's value depreciates at a fixed annual rate and becomes \(\cfrac{1}{2}\) of its original value in 5 years, find the number of years required for its value to become \(\cfrac{1}{4}\) of its original value.

30. Let us determine in how many years ₹40000 will amount to ₹46656 at an annual compound interest rate of 8%.