1. If the rate of simple interest and compound interest is 10% per annum, find the ratio of simple interest to compound interest for the second year on any principal. (a) 20:21 (b) 10:11 (c) 5:6 (d) 1:1

2. What is the difference between the simple interest and compound interest on ₹1250 for 2 years at a rate of 4%? (a) ₹ 8 (b) ₹ 4 (c) ₹ 3 (d) ₹ 2

3. If the simple interest on a certain amount for 2 years at a rate of 4% is ₹80, then what is the compound interest? (a) ₹ 91.60 (b) ₹ 81.60 (c) ₹ 71.60 (d) ₹80

4. If Dibas lends ₹5000 at 5% interest for 2 years, then how much total amount will he receive at the end of 2 years with compound interest? (a) ₹ 5511.50 (b) ₹ 5312.50 (c) ₹ 5542.50 (d) ₹ 5512.50

5. In a village, the current population is \(P\), and it increases by 8% every year. What will the population be after two years? (a) \((100P+2R)\) (b) \(\frac{(100P+R)(100+R)}{10000}\) (c) \(\frac{(100P+PR)(100+2R)}{10000}\) (d) None of the above

6. What should be the principal amount so that the compound amount becomes ₹169 in 2 years at a 4% interest rate? (a) ₹ 156.25 (b) ₹160 (c) ₹150.50 (d) ₹ 154.75

7. If the population of a village is \(P\) and the annual population growth rate is \(2r\%\), then the population after \(n\) years will be: (a) \(P\left(1+\cfrac{r}{100}\right)^n\) (b) \(P\left(1+\cfrac{r}{50}\right)^n\) (c) \(P\left(1+\cfrac{r}{100}\right)^{2n}\) (d) \(P\left(1-\cfrac{r}{100}\right)^n\)

8. At the same annual interest rate, the compound interest and simple interest on a principal amount will be equal. (a) 1 years (b) 2 years (c) 3 years (d) 4 years

9. In a village, the population increases annually by \(r\%\). If the population after \(n\) years is \(p\), then the population \(n\) years ago was – (a) \(p\left(1+\cfrac{r}{100}\right)^{-n}\) (b) \(p\left(1-\cfrac{r}{100}\right)^{-n}\) (c) \(p\left(1-\cfrac{r}{100}\right)^n\) (d) None of these

10. When simple interest is calculated at a fixed rate on a given principal, the simple interest for 2 years is greater than the compound interest. True / False

11. For a fixed principal amount at the same rate of interest, the compound interest for 1 year is greater than the simple interest for 1 year. True / False

12. At an annual rate of 10%, the difference between the simple interest and compound interest on ₹100 for 1 year is ₹1. True / False

13. 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: \[ P\left(1 + \cfrac{r_1}{100}\right)\left(1 + \cfrac{r_2}{100}\right)\left(1 + \cfrac{r_3}{100}\right) \] True / False

14. At an annual simple interest rate of \(\cfrac{r}{2}\%\), the amount after \(t\) years on ₹\(2p\) becomes \(\left(2p + \cfrac{prt}{100}\right)\). True / False

15. The sum of the principal amount and the compound interest over a specific period is called amount.

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

17. Calculate the compound interest on ₹10,000 for 9 months at a rate of 4% per quarter.

18. Determine how many years it will take for ₹105 interest to accumulate on ₹500 at an annual compound interest rate of 10%.

19. 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?

20. 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?

21. At an annual interest rate of 4%, what principal amount will yield at least ₹80 difference between simple interest and compound interest over 2 years?

22. If the compound interest on ₹5,000 for 2 years is ₹408, what is the annual rate of interest?

23. At the same annual percentage interest rate, the simple interest and compound interest on a principal amount become equal in _____ years (interest period: 1 year).

24. Divide ₹21,866 into two parts such that the compound amount of the first part for 3 years is equal to the compound amount of the second part for 5 years, at an annual compound interest rate of 5%.

25. Aminur borrowed ₹64,000 from a bank. If the bank's interest rate is 2.5 paise per rupee per year, then what will be the compound interest on that amount for 2 years?

26. At an equal annual interest rate, determine the number of years required for the simple interest and compound interest on a given principal to become equal.

27. What should be the annual compound interest rate for ₹400 to become ₹441 in 2 years?

28. The current value of a printing machine is ₹1,80,000. If the annual depreciation rate is 10%, what will be the value of the machine after 3 years?

29. 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.

30. A person deposited ₹100 in a bank and received ₹121 as compound amount after 2 years. The annual interest rate was ____ %.

31. If the annual compound interest rate is \(r\%\) and the principal amount in the first year is \(P\) rupees, then the principal amount in the second year is _____.

32. At an annual interest rate of 5%, what will be the difference between compound interest and simple interest for ₹20,000 over 2 years?

33. 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.

34. The population of a place was 13,310. At what rate of growth will it become 17,280 in 3 years?

35. 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?

36. If the interest period is 6 months and the annual compound interest rate is 10%, determine the compound interest and the total amount for ₹16,000 in \(1\frac{1}{2}\) years.

37. If the principal amount of **₹400** becomes **₹441** in 2 years under compound interest, determine the annual percentage rate of compound interest.

38. Due to an anti-smoking campaign, the number of smokers decreases at a rate of \(6 \cfrac{1}{4}\%\) per year. If there are currently 22,500 smokers in a city, what was the number of smokers in that city 2 years ago?

39. 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.

40. A tree's height increases at a rate of 20% per year. If the current height of the tree is 20 meters, what will its height be after 2 years?

41. If a sum of money becomes 4 times its original amount in *n* years at a fixed annual compound interest rate, then in how many years will it become 4 times?

42. 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?

43. 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?

44. In your uncle's factory, the value of a machine depreciates at a rate of 10% per year. If the current value of the machine is ₹6000, what will its value be after 3 years?

45. At the same annual interest rate, simple interest and compound interest will be equal in _____ years.

46. If 5000 rupees becomes 5408 rupees in 2 years at a certain compound interest rate, determine the compound interest rate.

47. 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.

48. The value of a machine used in a factory depreciates at a rate of 10% per year. If the value of the machine after 3 years is ₹43,740, what is its present value?

49. 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?

50. A person weighs 80 kg. To lose weight, he started going for regular morning walks. He decided that at the beginning of each year, he would reduce his weight by 5% of whatever it was at that time. What will his weight be after 3 years?

51. A person deposited ₹100 in a bank, and after 2 years received ₹121 as the total amount under compound interest. What is the annual percentage rate of compound interest?