SI & C.I.pptx

Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on principal plus interest. It is the result of reinvesting interest, or adding it to the loaned capital rather than paying it out, or requiring payment from borrower, so that interest in the next period is then earned on the principal sum plus previously accumulated interest. Compound interest is standard in finance and economics.

Compound interest is contrasted with simple interest, where previously accumulated interest is not added to the principal amount of the current period, so there is no compounding. The simple annual interest rate is the interest amount per period, multiplied by the number of periods per year. The simple annual interest rate is also known as the nominal interest rate (not to be confused with the interest rate not adjusted for inflation, which goes by the same name).Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on principal plus interest. It is the result of reinvesting interest, or adding it to the loaned capital rather than paying it out, or requiring payment from borrower, so that interest in the next period is then earned on the principal sum plus previously accumulated interest. Compound interest is standard in finance and economics.

Compound interest is contrasted with simple interest, where previously accumulated interest is not added to the principal amount of the current period, so there is no compounding. The simple annual interest rate is the interest amount per period, multiplied by the number of periods per year. The simple annual interest rate is also known as the nominal interest rate (not to be confused with the interest rate not adjusted for inflation, which goes by the same name).Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on principal plus interest. It is the result of reinvesting interest, or adding it to the loaned capital rather than paying it out, or requiring payment from borrower, so that interest in the next period is then earned on the principal sum plus previously accumulated interest. Compound interest is standard in finance and economics.

Compound interest is contrasted with simple interest, where previously accumulated interest is not added to the principal amount of the current period, so there is no compounding. The simple annual interest rate is the interest amount per period, multiplied by the number of periods per year. The simple annual interest rate is also known as the nominal interest rate (not to be confused with the interest rate not adjusted for inflation, which goes by the same name).

1. S.I & C.I S.S.HARICHANDAN

2. INTRODUCTION OF S.I: In Simple Interest the Principal is constant through out each and every year. As the interest is calculated only on the Principal in case of Simple Interest, it is constant through out each and every year. Suppose the interest in 5 years is Rs5000, in each year it is Rs1000.

3. METHOD TO SOLVE The question on Simple Interest, it must be based on percentage. Take the sum as Rs100, so that at any rate of interest for any number of years we can find out the interest. Then by taking the comparison the given sum with Rs100, we can find out the interest on it. Similarly If sum is given by taking the comparison we can find out amount from the sum or sum from the amount.

4. EXAMPLE: Find the S.I. on Rs4800 @ 2.5%p.a. for 10 years. (a)Rs1000 (b)Rs1200 (c)Rs1250 (d)Rs1280

5. COMPOUND INTEREST Introduction: In case of compound Interest, the interest is calculated on the Principal as well as interest. So the interest is not constant throughout each and every year. In each year, the interest is more than the previous interest by that rate percentage.

6. METHOD TO FIND COMPOUND INTREST: If it is compounded annually: Find out the interest in the first year at the given rate of interest. Then in each year, the interest is more than the previous interest by that rate percentage. Then add all the interest for the mentioned time to get the Compound interest.

7. EXAMPLE What is the compound interest on Rs24000 @ 5% p.a. for 3 years? (a)Rs3000 (b)Rs3200 (c)Rs3600 (d)Rs3783

8. If it is compounded half yearly: If the rater of interest is r% p .a, then half yearly it is 1/2 of r%. Find out the interest in the first six months at the half of the given rate of interest. Then in each six months, the interest is more than the previous six months interest by half of that rate percentage. Then add all the interest for the mentioned time to get the Compound interest.

9. EXAMPLE: What is the compound interest on Rs20000 @ 8% p.a. for 1.5years, if it is compounded half yearly? (a)Rs2400 (b)Rs2497.28 (c)Rs2500 (d)Rs2650

10. If it is compounded quarterly: If the rater of interest is r%p.a, then quarterly it is 1/4th of r%. Find out the interest in the first quarter at the one-fourth of the given rate. Then in each quarter, the interest is more than the previous quarter interest by one-fourth of that rate percentage. Then add all the interest for the mentioned time to get the Compound interest.

11. EXAMPLE What is the compound interest on Rs30000 @ 12%p.a.for 9months, if it is compounded quarterly? (a)Rs2700 (b)Rs2781.81 (c)Rs2800 (d)Rs3000

12. If the sum, amount and the time is given and we have to find rate of interest p.a. Method: Take the ratio of sum and amount for the given years. After 1 year, ratio of sum and amount is Year root of the previous ratio.

13. Example: If Rs16000 amounts to Rs18522 after 3 years in Compound interest, find the rate of interest per annum.

14. If the sum, amount and the rate of interest is given and we have to find time period. Method: Take the ratio of sum and amount for the given years. Take the ratio of the sum and the amount by taking the sum as Rs100 find out the amount after 1 year. Then mark the ratio of the sum and amount is which power of the ratio after 1year as the time period.

15. Example: If Rs20000 amounts to Rs24200 @ 10%p.a. in Compound interest, find the time period.

16. If the Simple interest on a certain sum in a certain period at a certain rate of interest is given and we have to find the compound interest on the same sum at the same rate for the same period: Method: Find out the simple interest in 1 year. Then the simple interest in 1 year is equal to the compound interest in the first year. Then find out the compound interest from second year onwards by increasing each interest by that rate percent in each year over the previous year interest. Then add the total compound interest for the given time.

17. Example: If the S.I on a certain sum of money in 2 years @ 6%p.a. is Rs3600, then what will be the C.I. on the same sum at the same rate for the same period?

18. If the Compound interest on a certain sum in a certain period at a certain rate of interest is given and we have to find the Simple interest on the same sum at the same rate for the same period: Method: Take the sum as Rs100 and find out the compound interest and simple interest for the given time at the given rate of interest. Then by taking the comparison find out the simple interest with respect to the compound interest.

19. Example: If the C.I on a certain sum of money in 2 years @ 5%p.a. is Rs2050, then what will be the S.I. on the same sum at the same rate for the same period?

20. If the difference between the S.I & C.I on a certain sum at a certain rate for a certain period is given and we have to find the sum: Method: Take the sum as Rs100 and find out the S.I. & C.I at the given rate for the given period. Then by taking the difference between S.I & C.I by taking the comparison with it with Rs100 find out the sum.

21. Example: If the difference between the C.I & S.I on a certain sum of money @ 8%p.a. in 2 years is Rs128, find the sum.

22. SOME IMPORTANT QUESTIONS Question:1 What is the Simple Interest on Rs 64 00 @ 2.5%p.a.in 10 years? (a)Rs1000 (b)Rs1200 (c)Rs1250 (d)Rs1600

23. Question:2 If a certain sum amounts to Rs7800 in 5 years @ 6% p.a. at S.I, find the sum. (a)Rs5000 (b)Rs6000 (c)Rs7200 (d)Rs7500

24. Question:3 What will be the amount on Rs8000 @ 5% p.a. in 6 years at S.I? (a)Rs10000 (b)Rs10400 (c)Rs12000 (d)Rs12500

25. Question:4 If a certain sum doubles it self in 9 years at S.I, then it will be four times in how many years? (a)18years (b)24years (c)27years (d)36years

26. Question:5 If a certain sum triples it self in 25 years at S.I, find the rate percent p.a. (a)6%p.a. (b)7.5%p.a. (c)8%p.a. (d)10%p.a.

27. Question:6 If a certain sum doubles it self @ 12.5 p.a. at S.I. find the time period. (a)6years (b)7years (c)8years (d)9years

28. Question:7 A sum was put at a certain rate of interest for 6 years at S.I. Had it been put at 3% higher rate it would have fetched Rs540 more interest. Find the sum. (a)Rs2000 (b)Rs2500 (c)Rs3000 (d)Rs4000

29. Question:8 If the S.I on a certain sum in 7 years @ 5% p.a. is Rs780 less than the sum find the sum. (a)Rs800 (b)Rs1000 (c)Rs1200 (d)Rs1500

30. Question:9 The S.I. on a certain sum for the first 2 years is 3%p.a. for the next 3 years 4%p.a. and for the period beyond 5 years 6%p.a. respectively. If the total interest in 8 years is Rs1080, find the sum. (a)Rs2000 (b)Rs3000 (c)Rs4000 (d)Rs5000

31. Question:10 What annual payment will discharge a debt of Rs 8480 due in 4 years hence @ 4% p.a. at S.I.? (a)Rs2000 (b)Rs3000 (c)Rs4000 (d)Rs5000

32. Question:11 In simple interest what sum amounts to Rs1120 in 4 years and Rs1200 in 5 years? (a)Rs750 (b)Rs800 (c)Rs850 (d)Rs900

33. Question:12 Rs5000 invested at S.I. @ 6% p.a. and Rs900 is obtained as interest in a certain number of years. In order to earn Rs540 as interest on Rs6000 in the same number of years, what should be the rate of interest? (a)2%p.a. (b)3%p.a. (c)4%p.a. (d)5%p.a.

34. Question:13 Two equal sums are deposited at the same time at 5% and 4% simple interest respectively. The former is received 2 years earlier than the later, and the amount in each case is Rs2800. Find the sum. (a)Rs2000 (b)Rs2500 (c)Rs3000 (d)Rs3200

35. Question:13 What annual payment will discharge a debt of Rs18000 due in 5 years @ 10% p.a. at S.I.? (a)Rs2000 (b)Rs2500 (c)Rs3000 (d)Rs3500

36. Question:14 If the simple interest on Rs2000, increases by Rs480, when the time increases by 4 years. Find the rate percent per annum. (a)4% (b)5% (c)6% (d)7.5%

37. Question:15 The simple interest on a sum of money is 1/9th of the principal, and the number of years is equal to the rate percent per annum. Find the rate percent. (a)2.5% (b)3% (c)3.5% (d)3 .33%

38. Question:16 If the simple interest on Rs1500 is more than the interest on Rs1000 by Rs60 in 3 years, find the rate percent per annum. (a)2% (b)3% (c)4% (d)5%

39. I Question:17 f simple interest on Rs6000, increases by Rs480, when the rate % increases by 2% per annum. Find the time period. (a)2years (b)3years (c)4years (d)5years

40. Question:18 Rakish deposited two parts of a sum of Rs20000 in two different banks @15%p.a. and 18% p.a. respectively. In 2 years he got Rs8100 as the total interest. What was the amount deposited at the rate of 18% p.a.? (a)Rs8000 (b)Rs10000 (c)Rs12000 (d)Rs1 4 000

41. Question:19 A man invests an amount of Rs15, 860 in the names of his three sons A, B and C in such a way that they receive the same amount after 2, 3 and 4 years respectively. If the rate of simple interest is 5% then find the ratio in which the amount was invested for A, B and C? (a)276:264:2 5 3 (b)243:264:276 (c)276:265:242 (d)279:265:243

42. Question:20 The S.I on Rs1250 will be less than the interest on Rs1400 at3% S.I by Rs90.Find the time. (a)12years (b)15years (c)18years (d)20years

43. Question:21 Two equal sums are deposited in two banks each at 15% for 3.5 years and 5 years respectively. If the difference between their interests is Rs144, find each sum (a)Rs600 (b)Rs625 (c)Rs640 (d)Rs650

44. The difference between the interests received from two different banks on Rs600 for 6 years is Rs216. Find the difference between their rates. (a)3% (b)4% (c)5% (d)6%

45. Question:22 Out of a certain sum, 1/3rd is invested at 3%, 1/6th at 6% and the rest at 8%. If the S.I for 2 years from all these investments amounts to Rs672, find the original sum. (a)Rs500 (b)Rs600 (c)Rs625 (d)Rs650

46. Question:23 A certain sum of money is borrowed by a person at 6% S.I for 8 years. If he has to pay Rs144 as interest, find the total amount he has to pay. (a)Rs296 (b) Rs444 (c)RsRs576 (d) None of these

47. Question:24 If the simple interest on Rs3000, increases by Rs450, when the time increases by 5 years. Find the rate percent per annum. (a) 3%p.a (b) 4%p.a (c) 5%p.a (d) None of these

48. Question:25 A lent Rs1200 to B for 2 years, and Rs750 to C for 4 years and received altogether from both Rs162 as interest. Find the rate of S.I. (a) 2%p.a (b) 3%p.a (c) 4%p.a (d) None of these

49. Question:26 If the rate of interest rises from 6 ½ to 8%, a man’s income increases by Rs405. Find the sum. (a)Rs24000 (b) Rs27000 (c)Rs30000 (d) None of these

50. Question:27 A sum of money invested for a certain number of years at 8% p.a. simple interest grows to Rs.180. The same sum of money invested for the same number of years at 4% p.a. simple interest grows to Rs.120 only. For how many years was the sum invested? (a) 15yrs (b) 20yrs (c) 25yrs (d) None of these

51. Question:28 A father left a will of Rs.35lakhs between his two daughters aged 8.5 and 16 such that they may get equal amounts when each of them reaches the age of 21 years. The original amount of Rs.35lakhs has been instructed to be invested at 10% p.a. simple interest. How much did the elder daughter get at the time of the will? (a)Rs7lakhs (b) Rs14lakhs (c)Rs21lakhs (d) None of these

52. Question:29 If the S.I on a certain sum of money in 2 years @ 6%p.a. is Rs2400, then what will be the C.I. on the same sum at the same rate for the same period? (a)Rs2448 (b)Rs2472 (c)Rs2484 (d)Rs2500

53. Question:30 If the S.I on a certain sum of money in 3 years @ 5%p.a. is Rs4800, then what will be the C.I. on the same sum at the same rate for the same period? (a)Rs5000 (b)Rs5200 (c)Rs5044 (d)Rs5600

54. Question:31 What is the compound interest on Rs2 000 @ 5% p.a. for 3 years? (a)Rs3 000 (b)Rs3 152.50 (c)Rs3 600 (d)Rs3750

55. Question:32 Amir invested an amount of Rs8000 in a fixed deposit scheme for 2 years at compound interest rate 5% p.a. How much amount will Amir get on maturity of the fixed deposit? (a)Rs8600 (b) Rs8620 (c) Rs8820 (d) None of these

56. Question:33 A bank offers 5% compound interest calculated on half-yearly basis. A customer deposits Rs2400 each on 1st January and 1st July of a year. At the end of the year, the amount he would have gained by way of interest is: (a)Rs180 (b) Rs181 .50 (c) Rs182 (d) Rs183

57. Question:34 What is the difference between the compound interests on Rs5000 for 1 years at 4% per annum compounded yearly and half-yearly? (a)Rs2.04 (b) Rs3.06 (c) Rs4.80 (d) Rs8.30

58. Question:35 The difference between S.I in one year and compound interest on Rs1500 for one year at 10% per annum reckoned half-yearly is: (a)Rs2.50 (b) Rs3 (c) Rs3.75 (d) Rs4

59. Question:36 The compound interest on Rs30, 000 at 7% per annum is Rs4347. The period (in years) is: (a) 2 (b) 2 ½ (c) 3 (d) 4

60. Question:37 Simple interest on a certain sum of money for 3 years at 8% per annum is half the compound interest on Rs4000 for 2 years at 10% per annum. The sum placed on simple interest is: (a)Rs1550 (b) Rs1650 (c) Rs1750 (d) Rs2000

61. Question:38 The difference between compound interest and simple interest on a sum of Rs15, 000 for 2 years is Rs96. What is the rate of interest per annum? (a) 8 (b)10 (c) 12 (d) None of these

62. Question:39 There is 60% increase in an amount in 6 years at simple interest. What will be the compound interest of Rs12, 000 after 3 years at the same rate? (a)Rs2160 (b) Rs3120 (c) Rs3972 (d) Rs6240

63. Question:40 The effective annual rate of interest corresponding to a nominal rate of 6% per annum payable half-yearly is: (a) 6.06% (b) 6.07% (c) 6.08% (d) 6.09%

64. Question:41 The least number of complete years in which a sum of money put out at 20% compound interest will be more than doubled is: (a) 3 (b) 4 (c) 5 (d) 6

65. Question:42 A person invested one half of his savings in a bond that paid simple interest for 2 years and received Rs480 as interest. He invested the remaining in a bond that paid compound interest, interest being compounded annually, for the same 2 years at the same rate of interest and received Rs492 as interest. What was the value of his total savings before investing in these two bonds? (a)Rs9000 (b) Rs9200 (c) Rs9600 (d) Rs9750

66. Question:43 A man invests Rs.5000 for 3 years at 5% p.a. compound interest reckoned yearly. Income tax at the rate of 20% on the interest earned is deducted at the end of each year. Find the amount at the end of the third year. (a)Rs5600 (b) Rs5624 (c) Rs5624.32 (d) None of these

67. Question:44 The difference between the compound interest and the simple interest on a certain sum at 12% p.a. for two years is Rs.90. What will be the value of the amount at the end of 3 years? (a) Rs8780.80 (b) Rs8778.80 (c) Rs8080.80 (d) None of these

68. Question:45 Rs. 5887 is divided between Amir and Samar, such that Amir’s share at the end of 9 years is equal to Samar's share at the end of 11 years, compounded annually at the rate of 5%. Find the share of Samar. (a) Rs3087 (b) Rs2800 (c) Rs2687 (d) None of these

69. Question:46 The population of a town was 4800 three years back. It is 6000 right now. What will be the population three years down the line, if the rate of growth of population has been constant over the years and has been compounding annually? (a)3000 (b)3200 (c)3600 (d) 3840

70. Question:47 What will be the amount if sum of Rs.10,00,000 is invested at compound interest for 3 years with rate of interest 11%, 12% and 13% respectively? (a) Rs.14,04,816 (b)Rs 12,14,816 (c)Rs. 11, 13,816 (d)Rs.16,00,816

71. Question:48 A sum of money is invested at 10% per annum compounding annually for 2 years. If the interest received is Rs. 210, find the principal. (a) 2100 (b)2500 (c)1900 (d)1000

72. Question:49 If the C.I on a certain sum of money in 2 years @ 7%p.a. is Rs2898, then what will be the S.I. on the same sum at the same rate for the same period? (a)Rs2000 (b) Rs2400 (c)Rs2800 (d)Rs2840

73. Question:50 If the C.I on a certain sum of money in 3 years @ 10%p.a. is Rs6620, then what will be the S.I. on the same sum at the same rate for the same period? (a)Rs5600 (b)Rs6000 (c)Rs6400 (d)Rs6600

74. Question:51 If the difference between the C.I & S.I on a certain sum of money @ 7%p.a. in 2 years is Rs196, find the sum. (a)Rs30000 (b)Rs36000 (c)Rs40000 (d)Rs44000

75. Question:52 Simple interest on a certain sum of money for 3 years at 8% per annum is half the compound interest on Rs4000 for 2 years at 10% per annum. The sum placed on simple interest is: (a) Rs1550 (b) Rs1650 (c) Rs1750 (d) Rs2000

76. Question:53 There is 60% increase in an amount in 6 years at simple interest. What will be the compound interest on Rs12, 000 after 3 years at the same rate? (a)Rs2160 (b)Rs3120 (c)Rs3972 (d)Rs6240

77. Question:54 The difference between compound interest and simple interest on an amount of Rs15, 000 for 2 years is Rs96. What is the rate of interest per annum? (a) 8 (b) 10 (c) 12 (d) None of these

78. Question:55 The difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 4% per annum is Re. 1. The sum (in Rs.) is: (a) 625 (b) 630 (c) 640 (d) 650

79. Question:56 Shawn invested one half of his savings in a bond that paid simple interest for 2 years and received Rs440 as interest. He invested the remaining in a bond that paid compound interest, interest being compounded annually, for the same 2 years at the same rate of interest and received Rs451 as interest. What was the value of his total savings before investing in these two bonds? Rs8000 (b) Rs8800 (c) Rs9200 (d) None of these

80. If a sum of money grows to 144/121 times when invested for two years in a scheme where interest is compounded annually, how long will the same sum of money take to treble if invested at the same rate of interest in a scheme where interest is computed using simple interest method? (a)11 yrs (b) 20 yrs (c) 22yrs (d) None of these

81. Question:57 The difference between S.I in one year and compound interest on Rs1500 for one year at 10% per annum reckoned half-yearly is: (a) Rs2.50 (b) Rs3 (c) Rs3.75 (d) Rs4

82. Question:58 Two equal sums are deposited in two banks each at 12% for 4.5 years and 6 years respectively. If the difference between their interests is Rs162, find each sum (a)Rs800 (b)Rs900 (c)Rs1000 (d)Rs1200

83. Question:59 The difference between the compound interest and the simple interest on a certain sum at 12% p.a. for two years is Rs.90. What will be the value of the amount at the end of 3 years in simple interest? (a)Rs8000 (b) Rs8250 (c)Rs8500 (c) Rs8750