26.Compounding-More-Than-Once-a-Year [Autosaved].pptx

Math

1. Compounding More Than Once a Year

2. Example1: Given a principal of P10, 000 which of the following options will yield greater interest after 5 years. OPTION A: Earn an annual interest rate of 2% at the end of the year. OPTION B: Earn an annual interest rate of 2% in two portions - 1% after 6 months, and 1% after another 6 months?

3. Example1 Solution: OPTION A: Interest is compounded annually Time (t) in years Principal = P10, 000 Annual Interest Rate = 2% compounded annually Amount at the end of the year 1 (10, 000)(1.02) = 10, 200

4. Example1 Solution: OPTION A: Interest is compounded annually Time (t) in years Principal = P10, 000 Annual Interest Rate = 2% compounded annually Amount at the end of the year 1 (10, 000)(1.02) = 10, 200 2 (10, 200)(1.02) = 10, 404

5. Example1 Solution: OPTION A: Interest is compounded annually Time (t) in years Principal = P10, 000 Annual Interest Rate = 2% compounded annually Amount at the end of the year 1 (10, 000)(1.02) = 10, 200 2 (10, 200)(1.02) = 10, 404 3 (10, 404)(1.02) = 10, 612.08

6. Example1 Solution: OPTION A: Interest is compounded annually Time (t) in years Principal = P10, 000 Annual Interest Rate = 2% compounded annually Amount at the end of the year 1 (10, 000)(1.02) = 10, 200 2 (10, 200)(1.02) = 10, 404 3 (10, 404)(1.02) = 10, 612.08 4 (10, 612.08)(1.02) = 10, 824.32

7. Example1 Solution: OPTION A: Interest is compounded annually Time (t) in years Principal = P10, 000 Annual Interest Rate = 2% compounded annually Amount at the end of the year 1 (10, 000)(1.02) = 10, 200 2 (10, 200)(1.02) = 10, 404 3 (10, 404)(1.02) = 10, 612.08 4 (10, 612.08)(1.02) = 10, 824.32 5 (10, 824.32)(1.02) = 11, 040.81

8. Example1 Solution: OPTION B: Interest is compounded semi-annually, or every 6 months. Time (t) in years Principal = P10, 000 Annual Interest rate = 2%, compounded semi-annually Amount at the end of the year 1/2 (10, 000)(1.01) = 10, 100

9. Example1 Solution: OPTION B: Interest is compounded semi-annually, or every 6 months. Time (t) in years Principal = P10, 000 Annual Interest rate = 2%, compounded semi-annually Amount at the end of the year 1/2 (10, 000)(1.01) = 10, 100 1 (10, 100)(1.01) = 10, 201

10. Example1 Solution: OPTION B: Interest is compounded semi-annually, or every 6 months. Time (t) in years Principal = P10, 000 Annual Interest rate = 2%, compounded semi-annually Amount at the end of the year 1/2 (10, 000)(1.01) = 10, 100 1 (10, 100)(1.01) = 10, 201 1 1/2 (10, 201)(1.01) = 10, 303.01

11. Example1 Solution: OPTION B: Interest is compounded semi-annually, or every 6 months. Time (t) in years Principal = P10, 000 Annual Interest rate = 2%, compounded semi-annually Amount at the end of the year 1/2 (10, 000)(1.01) = 10, 100 1 (10, 100)(1.01) = 10, 201 1 1/2 (10, 201)(1.01) = 10, 303.01 2 (10, 303.01)(1.01) = 10, 406.04

12. Example1 Solution: OPTION B: Interest is compounded semi-annually, or every 6 months. Time (t) in years Principal = P10, 000 Annual Interest rate = 2%, compounded semi-annually Amount at the end of the year 1/2 (10, 000)(1.01) = 10, 100 1 (10, 100)(1.01) = 10, 201 1 1/2 (10, 201)(1.01) = 10, 303.01 2 (10, 303.01)(1.01) = 10, 406.04 2 1/2 (10, 406.04)(1.01) = 10, 510.10

13. Example1 Solution: OPTION B: Interest is compounded semi-annually, or every 6 months. Time (t) in years Principal = P10, 000 Annual Interest rate = 2%, compounded semi-annually Amount at the end of the year 1/2 (10, 000)(1.01) = 10, 100 1 (10, 100)(1.01) = 10, 201 1 1/2 (10, 201)(1.01) = 10, 303.01 2 (10, 303.01)(1.01) = 10, 406.04 2 1/2 (10, 406.04)(1.01) = 10, 510.10 3 (10, 510.10)(1.01) = 10, 615.20

14. Example1 Solution: OPTION B: Interest is compounded semi-annually, or every 6 months. Time (t) in years Principal = P10, 000 Annual Interest rate = 2%, compounded semi-annually Amount at the end of the year 1/2 (10, 000)(1.01) = 10, 100 1 (10, 100)(1.01) = 10, 201 1 1/2 (10, 201)(1.01) = 10, 303.01 2 (10, 303.01)(1.01) = 10, 406.04 2 1/2 (10, 406.04)(1.01) = 10, 510.10 3 (10, 510.10)(1.01) = 10, 615.20 3 1/2 (10, 615.20)(1.01) = 10, 721.35

15. Example1 Solution: OPTION B: Interest is compounded semi-annually, or every 6 months. Time (t) in years Principal = P10, 000 Annual Interest rate = 2%, compounded semi-annually Amount at the end of the year 1/2 (10, 000)(1.01) = 10, 100 1 (10, 100)(1.01) = 10, 201 1 1/2 (10, 201)(1.01) = 10, 303.01 2 (10, 303.01)(1.01) = 10, 406.04 2 1/2 (10, 406.04)(1.01) = 10, 510.10 3 (10, 510.10)(1.01) = 10, 615.20 3 1/2 (10, 615.20)(1.01) = 10, 721.35 4 (10, 721.35)(1.01) = 10, 828.56

16. Example1 Solution: OPTION B: Interest is compounded semi-annually, or every 6 months. Time (t) in years Principal = P10, 000 Annual Interest rate = 2%, compounded semi-annually Amount at the end of the year 1/2 (10, 000)(1.01) = 10, 100 1 (10, 100)(1.01) = 10, 201 1 1/2 (10, 201)(1.01) = 10, 303.01 2 (10, 303.01)(1.01) = 10, 406.04 2 1/2 (10, 406.04)(1.01) = 10, 510.10 3 (10, 510.10)(1.01) = 10, 615.20 3 1/2 (10, 615.20)(1.01) = 10, 721.35 4 (10, 721.35)(1.01) = 10, 828.56 4 1/2 (10, 828.56)(1.01) = 10, 936.85

17. Example1 Solution: OPTION B: Interest is compounded semi-annually, or every 6 months. Time (t) in years Principal = P10, 000 Annual Interest rate = 2%, compounded semi-annually Amount at the end of the year 1/2 (10, 000)(1.01) = 10, 100 1 (10, 100)(1.01) = 10, 201 1 1/2 (10, 201)(1.01) = 10, 303.01 2 (10, 303.01)(1.01) = 10, 406.04 2 1/2 (10, 406.04)(1.01) = 10, 510.10 3 (10, 510.10)(1.01) = 10, 615.20 3 1/2 (10, 615.20)(1.01) = 10, 721.35 4 (10, 721.35)(1.01) = 10, 828.56 4 1/2 (10, 828.56)(1.01) = 10, 936.85 5 (10, 936.85)(1.01) = 11, 046.22

18. Definition of Terms: Conversion or interest period - time between successive conversions of interest Frequency of conversion ( m ) - number of conversion periods in one year Nominal rate ( i m ) - annual rate of interest Rate (j) of interest for each conversion period j = i m / m = (annual rate of interest)/(frequency of conversion) Total number of conversion periods ( n ) n = tm = (frequency of conversion) X (time in years)

19. Examples of nominal rate and the corresponding frequencies of conversion and interest rate for each period. i m = Nominal Rate (Annual Interest Rate) m = Frequency of Conversions j = Interest Rate per conversion period One conversion period 2% compounded annually; i 1 = 0.02

20. Examples of nominal rate and the corresponding frequencies of conversion and interest rate for each period. i m = Nominal Rate (Annual Interest Rate) m = Frequency of Conversions j = Interest Rate per conversion period One conversion period 2% compounded annually; i 1 = 0.02 1

21. Examples of nominal rate and the corresponding frequencies of conversion and interest rate for each period. i m = Nominal Rate (Annual Interest Rate) m = Frequency of Conversions j = Interest Rate per conversion period One conversion period 2% compounded annually; i 1 = 0.02 1 0.02/1 = 0.02 = 2%

22. Examples of nominal rate and the corresponding frequencies of conversion and interest rate for each period. i m = Nominal Rate (Annual Interest Rate) m = Frequency of Conversions j = Interest Rate per conversion period One conversion period 2% compounded annually; i 1 = 0.02 1 0.02/1 = 0.02 = 2% 1 year

23. Examples of nominal rate and the corresponding frequencies of conversion and interest rate for each period. i m = Nominal Rate (Annual Interest Rate) m = Frequency of Conversions j = Interest Rate per conversion period One conversion period 2% compounded annually; i 1 = 0.02 1 0.02/1 = 0.02 = 2% 1 year 2% compounded semi-annually; i 2 = 0.02

24. Examples of nominal rate and the corresponding frequencies of conversion and interest rate for each period. i m = Nominal Rate (Annual Interest Rate) m = Frequency of Conversions j = Interest Rate per conversion period One conversion period 2% compounded annually; i 1 = 0.02 1 0.02/1 = 0.02 = 2% 1 year 2% compounded semi-annually; i 2 = 0.02 2

25. Examples of nominal rate and the corresponding frequencies of conversion and interest rate for each period. i m = Nominal Rate (Annual Interest Rate) m = Frequency of Conversions j = Interest Rate per conversion period One conversion period 2% compounded annually; i 1 = 0.02 1 0.02/1 = 0.02 = 2% 1 year 2% compounded semi-annually; i 2 = 0.02 2 0.02/2 = 0.01 = 1%

26. Examples of nominal rate and the corresponding frequencies of conversion and interest rate for each period. i m = Nominal Rate (Annual Interest Rate) m = Frequency of Conversions j = Interest Rate per conversion period One conversion period 2% compounded annually; i 1 = 0.02 1 0.02/1 = 0.02 = 2% 1 year 2% compounded semi-annually; i 2 = 0.02 2 0.02/2 = 0.01 = 1% 6 months

27. Examples of nominal rate and the corresponding frequencies of conversion and interest rate for each period. i m = Nominal Rate (Annual Interest Rate) m = Frequency of Conversions j = Interest Rate per conversion period One conversion period 2% compounded annually; i 1 = 0.02 1 0.02/1 = 0.02 = 2% 1 year 2% compounded semi-annually; i 2 = 0.02 2 0.02/2 = 0.01 = 1% 6 months 2% compounded quarterly; i 4 = 0.02

28. Examples of nominal rate and the corresponding frequencies of conversion and interest rate for each period. i m = Nominal Rate (Annual Interest Rate) m = Frequency of Conversions j = Interest Rate per conversion period One conversion period 2% compounded annually; i 1 = 0.02 1 0.02/1 = 0.02 = 2% 1 year 2% compounded semi-annually; i 2 = 0.02 2 0.02/2 = 0.01 = 1% 6 months 2% compounded quarterly; i 3 = 0.02 4

29. Examples of nominal rate and the corresponding frequencies of conversion and interest rate for each period. i m = Nominal Rate (Annual Interest Rate) m = Frequency of Conversions j = Interest Rate per conversion period One conversion period 2% compounded annually; i 1 = 0.02 1 0.02/1 = 0.02 = 2% 1 year 2% compounded semi-annually; i 2 = 0.02 2 0.02/2 = 0.01 = 1% 6 months 2% compounded quarterly; i 3 = 0.02 4 0.02/4 = 0.005 = 0.5%

30. Examples of nominal rate and the corresponding frequencies of conversion and interest rate for each period. i m = Nominal Rate (Annual Interest Rate) m = Frequency of Conversions j = Interest Rate per conversion period One conversion period 2% compounded annually; i 1 = 0.02 1 0.02/1 = 0.02 = 2% 1 year 2% compounded semi-annually; i 2 = 0.02 2 0.02/2 = 0.01 = 1% 6 months 2% compounded quarterly; i 3 = 0.02 4 0.02/4 = 0.005 = 0.5% 3 months

31. Examples of nominal rate and the corresponding frequencies of conversion and interest rate for each period. i m = Nominal Rate (Annual Interest Rate) m = Frequency of Conversions j = Interest Rate per conversion period One conversion period 2% compounded annually; i 1 = 0.02 1 0.02/1 = 0.02 = 2% 1 year 2% compounded semi-annually; i 2 = 0.02 2 0.02/2 = 0.01 = 1% 6 months 2% compounded quarterly; i 3 = 0.02 4 0.02/4 = 0.005 = 0.5% 3 months 2% compounded monthly; i 12 = 0.02

32. Examples of nominal rate and the corresponding frequencies of conversion and interest rate for each period. i m = Nominal Rate (Annual Interest Rate) m = Frequency of Conversions j = Interest Rate per conversion period One conversion period 2% compounded annually; i 1 = 0.02 1 0.02/1 = 0.02 = 2% 1 year 2% compounded semi-annually; i 2 = 0.02 2 0.02/2 = 0.01 = 1% 6 months 2% compounded quarterly; i 3 = 0.02 4 0.02/4 = 0.005 = 0.5% 3 months 2% compounded monthly; i 12 = 0.02 12

33. Examples of nominal rate and the corresponding frequencies of conversion and interest rate for each period. i m = Nominal Rate (Annual Interest Rate) m = Frequency of Conversions j = Interest Rate per conversion period One conversion period 2% compounded annually; i 1 = 0.02 1 0.02/1 = 0.02 = 2% 1 year 2% compounded semi-annually; i 2 = 0.02 2 0.02/2 = 0.01 = 1% 6 months 2% compounded quarterly; i 3 = 0.02 4 0.02/4 = 0.005 = 0.5% 3 months 2% compounded monthly; i 12 = 0.02 12 0.02/12 = 0.0016 = 0.16%

34. Examples of nominal rate and the corresponding frequencies of conversion and interest rate for each period. i m = Nominal Rate (Annual Interest Rate) m = Frequency of Conversions j = Interest Rate per conversion period One conversion period 2% compounded annually; i 1 = 0.02 1 0.02/1 = 0.02 = 2% 1 year 2% compounded semi-annually; i 2 = 0.02 2 0.02/2 = 0.01 = 1% 6 months 2% compounded quarterly; i 3 = 0.02 4 0.02/4 = 0.005 = 0.5% 3 months 2% compounded monthly; i 12 = 0.02 12 0.02/12 = 0.0016 = 0.16% 1 month

35. Examples of nominal rate and the corresponding frequencies of conversion and interest rate for each period. i m = Nominal Rate (Annual Interest Rate) m = Frequency of Conversions j = Interest Rate per conversion period One conversion period 2% compounded annually; i 1 = 0.02 1 0.02/1 = 0.02 = 2% 1 year 2% compounded semi-annually; i 2 = 0.02 2 0.02/2 = 0.01 = 1% 6 months 2% compounded quarterly; i 3 = 0.02 4 0.02/4 = 0.005 = 0.5% 3 months 2% compounded monthly; i 12 = 0.02 12 0.02/12 = 0.0016 = 0.16% 1 month 2% compounded daily; i 365 = 0.02

36. Examples of nominal rate and the corresponding frequencies of conversion and interest rate for each period. i m = Nominal Rate (Annual Interest Rate) m = Frequency of Conversions j = Interest Rate per conversion period One conversion period 2% compounded annually; i 1 = 0.02 1 0.02/1 = 0.02 = 2% 1 year 2% compounded semi-annually; i 2 = 0.02 2 0.02/2 = 0.01 = 1% 6 months 2% compounded quarterly; i 3 = 0.02 4 0.02/4 = 0.005 = 0.5% 3 months 2% compounded monthly; i 12 = 0.02 12 0.02/12 = 0.0016 = 0.16% 1 month 2% compounded daily; i 365 = 0.02 365

37. Examples of nominal rate and the corresponding frequencies of conversion and interest rate for each period. i m = Nominal Rate (Annual Interest Rate) m = Frequency of Conversions j = Interest Rate per conversion period One conversion period 2% compounded annually; i 1 = 0.02 1 0.02/1 = 0.02 = 2% 1 year 2% compounded semi-annually; i 2 = 0.02 2 0.02/2 = 0.01 = 1% 6 months 2% compounded quarterly; i 3 = 0.02 4 0.02/4 = 0.005 = 0.5% 3 months 2% compounded monthly; i 12 = 0.02 12 0.02/12 = 0.0016 = 0.16% 1 month 2% compounded daily; i 365 = 0.02 365 0.02/365

38. Examples of nominal rate and the corresponding frequencies of conversion and interest rate for each period. i m = Nominal Rate (Annual Interest Rate) m = Frequency of Conversions j = Interest Rate per conversion period One conversion period 2% compounded annually; i 1 = 0.02 1 0.02/1 = 0.02 = 2% 1 year 2% compounded semi-annually; i 2 = 0.02 2 0.02/2 = 0.01 = 1% 6 months 2% compounded quarterly; i 4 = 0.02 4 0.02/4 = 0.005 = 0.5% 3 months 2% compounded monthly; i 12 = 0.02 12 0.02/12 = 0.0016 = 0.16% 1 month 2% compounded daily; i 365 = 0.02 365 0.02/365 1 day

39. Maturity Value, Compounding m times a year F = P(1 + (i m /m)) mt where F = maturity (future) value P = principal i m = nominal rate of interest (annual rate) m = frequency of conversion t = term / time in years

40. F = P(1 + j) n has the same structure as F = P(1 + (i m /m)) mt where j and i m /m refer to the interest rate per conversion period, n and mt refer to the number of times that interest is compounded

41. Example2: Find the maturity value and interest if P10, 000 is deposited in a bank at 2% compounded quarterly for 5 years.

42. Example2: Find the maturity value and interest if P10, 000 is deposited in a bank at 2% compounded quarterly for 5 years. Solution:

43. Example2: Find the maturity value and interest if P10, 000 is deposited in a bank at 2% compounded quarterly for 5 years. Solution: Given:

44. Example2: Find the maturity value and interest if P10, 000 is deposited in a bank at 2% compounded quarterly for 5 years. Solution: Given: P = 10, 000

45. Example2: Find the maturity value and interest if P10, 000 is deposited in a bank at 2% compounded quarterly for 5 years. Solution: Given: P = 10, 000 i 4 = 0.02

46. Example2: Find the maturity value and interest if P10, 000 is deposited in a bank at 2% compounded quarterly for 5 years. Solution: Given: P = 10, 000 i 4 = 0.02 t = 5 years

47. Example2: Find the maturity value and interest if P10, 000 is deposited in a bank at 2% compounded quarterly for 5 years. Solution: Given: P = 10, 000 i 4 = 0.02 t = 5 years m = 4

48. Example2: Find the maturity value and interest if P10, 000 is deposited in a bank at 2% compounded quarterly for 5 years. Solution: Given: P = 10, 000 Find: (a) F i 4 = 0.02 t = 5 years m = 4

49. Example2: Find the maturity value and interest if P10, 000 is deposited in a bank at 2% compounded quarterly for 5 years. Solution: Given: P = 10, 000 Find: (a) F i 4 = 0.02 (b) I c t = 5 years m = 4

50. Continuation_Solution_Example2: Compute for the interest rate in a conversion period by j = i 4 /m = 0.02/4 = 0.005

51. Continuation_Solution_Example2: Compute for the interest rate in a conversion period by j = i 4 /m = 0.02/4 = 0.005 Compute for the total number of conversion periods given by n = mt = (4)(5) = 20 conversion periods

52. Continuation_Solution_Example2: Compute for the interest rate in a conversion period by j = i 4 /m = 0.02/4 = 0.005 Compute for the total number of conversion periods given by n = mt = (4)(5) = 20 conversion periods Compute for the maturity value using F = P(1 + j) n

53. Continuation_Solution_Example2: Compute for the interest rate in a conversion period by j = i 4 /m = 0.02/4 = 0.005 Compute for the total number of conversion periods given by n = mt = (4)(5) = 20 conversion periods Compute for the maturity value using F = P(1 + j) n F = (10, 000)(1 + 0.005) 20

54. Continuation_Solution_Example2: Compute for the interest rate in a conversion period by j = i 4 /m = 0.02/4 = 0.005 Compute for the total number of conversion periods given by n = mt = (4)(5) = 20 conversion periods Compute for the maturity value using F = P(1 + j) n F = (10, 000)(1 + 0.005) 20 F = 11, 048.96

55. Continuation_Solution_Example2: Compute for the interest rate in a conversion period by j = i 4 /m = 0.02/4 = 0.005 Compute for the total number of conversion periods given by n = mt = (4)(5) = 20 conversion periods Compute for the maturity value using F = P(1 + j) n F = (10, 000)(1 + 0.005) 20 F = 11, 048.96 The compound interest is given by I c = F - P

56. Continuation_Solution_Example2: Compute for the interest rate in a conversion period by j = i 4 /m = 0.02/4 = 0.005 Compute for the total number of conversion periods given by n = mt = (4)(5) = 20 conversion periods Compute for the maturity value using F = P(1 + j) n F = (10, 000)(1 + 0.005) 20 F = 11, 048.96 The compound interest is given by I c = F - P = 11, 048.96 - 10, 000

57. Continuation_Solution_Example2: Compute for the interest rate in a conversion period by j = i 4 /m = 0.02/4 = 0.005 Compute for the total number of conversion periods given by n = mt = (4)(5) = 20 conversion periods Compute for the maturity value using F = P(1 + j) n F = (10, 000)(1 + 0.005) 20 F = 11, 048.96 The compound interest is given by I c = F - P = 11, 048.96 - 10, 000 = P1, 048.96

58. Example3: Find the maturity value and interest if P10, 000 is deposited in a bank at 2% compounded monthly for 5 years.

59. Example3: Find the maturity value and interest if P10, 000 is deposited in a bank at 2% compounded monthly for 5 years. Solution:

60. Example3: Find the maturity value and interest if P10, 000 is deposited in a bank at 2% compounded monthly for 5 years. Solution: Given:

61. Example3: Find the maturity value and interest if P10, 000 is deposited in a bank at 2% compounded monthly for 5 years. Solution: Given: P = 10, 000

62. Example3: Find the maturity value and interest if P10, 000 is deposited in a bank at 2% compounded monthly for 5 years. Solution: Given: P = 10, 000 i 12 = 0.02

63. Example3: Find the maturity value and interest if P10, 000 is deposited in a bank at 2% compounded monthly for 5 years. Solution: Given: P = 10, 000 i 12 = 0.02 t = 5 years

64. Example3: Find the maturity value and interest if P10, 000 is deposited in a bank at 2% compounded monthly for 5 years. Solution: Given: P = 10, 000 i 12 = 0.02 t = 5 years m = 12

65. Example3: Find the maturity value and interest if P10, 000 is deposited in a bank at 2% compounded monthly for 5 years. Solution: Find: Given: P = 10, 000 i 12 = 0.02 t = 5 years m = 12

66. Example3: Find the maturity value and interest if P10, 000 is deposited in a bank at 2% compounded monthly for 5 years. Solution: Find: (a) F, Given: P = 10, 000 i 12 = 0.02 t = 5 years m = 12

67. Example3: Find the maturity value and interest if P10, 000 is deposited in a bank at 2% compounded monthly for 5 years. Solution: Find: (a) F, (b) I c Given: P = 10, 000 i 12 = 0.02 t = 5 years m = 12

68. Example3: Find the maturity value and interest if P10, 000 is deposited in a bank at 2% compounded monthly for 5 years. Solution: Find: (a) F, (b) I c Given: P = 10, 000 j = i 12 /m = 0.02/12 = 0.0016 i 12 = 0.02 t = 5 years m = 12

69. Example3: Find the maturity value and interest if P10, 000 is deposited in a bank at 2% compounded monthly for 5 years. Solution: Find: (a) F, (b) I c Given: P = 10, 000 j = i 12 /m = 0.02/12 = 0.0016 i 12 = 0.02 n = mt = (12)(5) = 60 t = 5 years m = 12

70. Example3: Find the maturity value and interest if P10, 000 is deposited in a bank at 2% compounded monthly for 5 years. Solution: Find: (a) F, (b) I c Given: P = 10, 000 j = i 12 /m = 0.02/12 = 0.0016667 i 12 = 0.02 n = mt = (12)(5) = 60 t = 5 years F = P(1 + j) n m = 12

71. Example3: Find the maturity value and interest if P10, 000 is deposited in a bank at 2% compounded monthly for 5 years. Solution: Find: (a) F, (b) I c Given: P = 10, 000 j = i 12 /m = 0.02/12 = 0.0016667 i 12 = 0.02 n = mt = (12)(5) = 60 t = 5 years F = P(1 + j) n m = 12 F = (10, 000)(1 + 0.0016667) 60

72. Example3: Find the maturity value and interest if P10, 000 is deposited in a bank at 2% compounded monthly for 5 years. Solution: Find: (a) F, (b) I c Given: P = 10, 000 j = i 12 /m = 0.02/12 = 0.0016667 i 12 = 0.02 n = mt = (12)(5) = 60 t = 5 years F = P(1 + j) n m = 12 F = (10, 000)(1 + 0.0016667) 60 F = P11, 050.81

73. Example3: Find the maturity value and interest if P10, 000 is deposited in a bank at 2% compounded monthly for 5 years. Solution: Find: (a) F, (b) I c Given: P = 10, 000 j = i 12 /m = 0.02/12 = 0.0016667 i 12 = 0.02 n = mt = (12)(5) = 60 t = 5 years F = P(1 + j) n m = 12 F = (10, 000)(1 + 0.0016667) 60 F = P11, 050.81 I c = F - P

74. Example3: Find the maturity value and interest if P10, 000 is deposited in a bank at 2% compounded monthly for 5 years. Solution: Find: (a) F, (b) I c Given: P = 10, 000 j = i 12 /m = 0.02/12 = 0.0016 i 12 = 0.02 n = mt = (12)(5) = 60 t = 5 years F = P(1 + j) n m = 12 F = (10, 000)(1 + 0.0016) 60 F = P11, 050.79 I c = F - P = 11, 050.81 - 10, 000

75. Example3: Find the maturity value and interest if P10, 000 is deposited in a bank at 2% compounded monthly for 5 years. Solution: Find: (a) F, (b) I c Given: P = 10, 000 j = i 12 /m = 0.02/12 = 0.0016667 i 12 = 0.02 n = mt = (12)(5) = 60 t = 5 years F = P(1 + j) n m = 12 F = (10, 000)(1 + 0.0016667) 60 F = P11, 050.81 I c = F - P = 11, 050.79 - 10, 000 = P1, 050.81

76. Example4: Cris borrows P50, 000 and promises to pay the principal and interest at 12% compounded monthly. How much must he repay after 6 years?

77. Example4: Cris borrows P50, 000 and promises to pay the principal and interest at 12% compounded monthly. How much must he repay after 6 years? Solution:

78. Example4: Cris borrows P50, 000 and promises to pay the principal and interest at 12% compounded monthly. How much must he repay after 6 years? Solution: Given:

79. Example4: Cris borrows P50, 000 and promises to pay the principal and interest at 12% compounded monthly. How much must he repay after 6 years? Solution: Given: P = 50,000

80. Example4: Cris borrows P50, 000 and promises to pay the principal and interest at 12% compounded monthly. How much must he repay after 6 years? Solution: Given: P = 50,000 i 12 = 0.12

81. Example4: Cris borrows P50, 000 and promises to pay the principal and interest at 12% compounded monthly. How much must he repay after 6 years? Solution: Given: P = 50,000 i 12 = 0.12 t = 6

82. Example4: Cris borrows P50, 000 and promises to pay the principal and interest at 12% compounded monthly. How much must he repay after 6 years? Solution: Given: P = 50,000 i 12 = 0.12 t = 6 m = 12

83. Example4: Cris borrows P50, 000 and promises to pay the principal and interest at 12% compounded monthly. How much must he repay after 6 years? Solution: Given: P = 50,000 Find: F i 12 = 0.12 t = 6 m = 12

84. Example4: Cris borrows P50, 000 and promises to pay the principal and interest at 12% compounded monthly. How much must he repay after 6 years? Solution: Given: P = 50,000 Find: F i 12 = 0.12 F = P(1 + (i 12 /m)) tm t = 6 m = 12

85. Example4: Cris borrows P50, 000 and promises to pay the principal and interest at 12% compounded monthly. How much must he repay after 6 years? Solution: Given: P = 50,000 Find: F i 12 = 0.12 F = P(1 + (i 12 /m)) tm t = 6 F = (50, 000)(1 + (0.12/12)) (6)(12) m = 12

86. Example4: Cris borrows P50, 000 and promises to pay the principal and interest at 12% compounded monthly. How much must he repay after 6 years? Solution: Given: P = 50,000 Find: F i 12 = 0.12 F = P(1 + (i 12 /m)) tm t = 6 F = (50, 000)(1 + (0.12/12)) (6)(12) m = 12 F = (50, 000)(1.01) 72

87. Example4: Cris borrows P50, 000 and promises to pay the principal and interest at 12% compounded monthly. How much must he repay after 6 years? Solution: Given: P = 50,000 Find: F i 12 = 0.12 F = P(1 + (i 12 /m)) tm t = 6 F = (50, 000)(1 + (0.12/12)) (6)(12) m = 12 F = (50, 000)(1.01) 72 F = 102, 354.97

88. Present Value P at Compound Interest P = F / (1 + (i m /m)) mt where F = maturity (future) value P = principal i m = nominal rate of interest (annual rate) m = frequency of conversion t = term / time in years

89. Example5: Find the present value of P50, 000 due in 4 years if money is invested at 12% compounded semi-annually.

90. Example5: Find the present value of P50, 000 due in 4 years if money is invested at 12% compounded semi-annually. Solution:

91. Example5: Find the present value of P50, 000 due in 4 years if money is invested at 12% compounded semi-annually. Solution: Given:

92. Example5: Find the present value of P50, 000 due in 4 years if money is invested at 12% compounded semi-annually. Solution: Given: F = 50, 000

93. Example5: Find the present value of P50, 000 due in 4 years if money is invested at 12% compounded semi-annually. Solution: Given: F = 50, 000 t = 4

94. Example5: Find the present value of P50, 000 due in 4 years if money is invested at 12% compounded semi-annually. Solution: Given: F = 50, 000 t = 4 i 2 = 0.12

95. Example5: Find the present value of P50, 000 due in 4 years if money is invested at 12% compounded semi-annually. Solution: Given: F = 50, 000 Find : t = 4 i 2 = 0.12

96. Example5: Find the present value of P50, 000 due in 4 years if money is invested at 12% compounded semi-annually. Solution: Given: F = 50, 000 Find : P t = 4 i 2 = 0.12 m= 2

97. Example5: Find the present value of P50, 000 due in 4 years if money is invested at 12% compounded semi-annually. Solution: Given: F = 50, 000 Find : P t = 4 j = i 2 /m = 0.12/2 = 0.06 i 2 = 0.12

98. Example5: Find the present value of P50, 000 due in 4 years if money is invested at 12% compounded semi-annually. Solution: Given: F = 50, 000 Find : P t = 4 j = i 2 /m = 0.12/2 = 0.06 i 2 = 0.12 n = tm = (4)(2) = 8 m = 2

99. Example5: Find the present value of P50, 000 due in 4 years if money is invested at 12% compounded semi-annually. Solution: Given: F = 50, 000 Find : P t = 4 j = i 2 /m = 0.12/2 = 0.06 i 2 = 0.12 n = tm = (4)(2) = 8 P = F / (1 + j) n

100. Example5: Find the present value of P50, 000 due in 4 years if money is invested at 12% compounded semi-annually. Solution: Given: F = 50, 000 Find : P t = 4 j = i 2 /m = 0.12/2 = 0.06 i 2 = 0.12 n = tm = (4)(2) = 8 P = F / (1 + j) n P = 50, 000/(1 + 0.06) 8

101. Example5: Find the present value of P50, 000 due in 4 years if money is invested at 12% compounded semi-annually. Solution: Given: F = 50, 000 Find : P t = 4 j = i 2 /m = 0.12/2 = 0.06 i 2 = 0.12 n = tm = (4)(2) = 8 P = F / (1 + j) n P = 50, 000/(1 + 0.06) 8 P = 50, 000/(1.06) 8

102. Example5: Find the present value of P50, 000 due in 4 years if money is invested at 12% compounded semi-annually. Solution: Given: F = 50, 000 Find : P t = 4 j = i 2 /m = 0.12/2 = 0.06 i 2 = 0.12 n = tm = (4)(2) = 8 P = F / (1 + j) n P = 50, 000/(1 + 0.06) 8 P = 50, 000/(1.06) 8 = 31, 370.62

103. Example6: What is the present value of P25, 000 due in 2 years and 6 months if money is worth 10% compounded quarterly?

104. Example6: What is the present value of P25, 000 due in 2 years and 6 months if money is worth 10% compounded quarterly? Solution:

105. Example6: What is the present value of P25, 000 due in 2 years and 6 months if money is worth 10% compounded quarterly? Solution: Given:

106. Example6: What is the present value of P25, 000 due in 2 years and 6 months if money is worth 10% compounded quarterly? Solution: Given: F = 25, 000

107. Example6: What is the present value of P25, 000 due in 2 years and 6 months if money is worth 10% compounded quarterly? Solution: Given: F = 25, 000 t = 2 1/2 years

108. Example6: What is the present value of P25, 000 due in 2 years and 6 months if money is worth 10% compounded quarterly? Solution: Given: F = 25, 000 t = 2 1/2 years i 4 = 0.10

109. Example6: What is the present value of P25, 000 due in 2 years and 6 months if money is worth 10% compounded quarterly? Solution: Given: F = 25, 000 Find: t = 2 1/2 years i 4 = 0.10 m = 4

110. Example6: What is the present value of P25, 000 due in 2 years and 6 months if money is worth 10% compounded quarterly? Solution: Given: F = 25, 000 Find: P t = 2 1/2 years i 4 = 0.10

111. Example6: What is the present value of P25, 000 due in 2 years and 6 months if money is worth 10% compounded quarterly? Solution: Given: F = 25, 000 Find: P t = 2 1/2 years j = i 4 /m = 0.10/4 = 0.025 i 4 = 0.10 m = 4

112. Example6: What is the present value of P25, 000 due in 2 years and 6 months if money is worth 10% compounded quarterly? Solution: Given: F = 25, 000 Find: P t = 2 1/2 years j = i 4 /m = 0.10/4 = 0.025 i 4 = 0.10 n = tm = (2 1/2)(4) = 10

113. Example6: What is the present value of P25, 000 due in 2 years and 6 months if money is worth 10% compounded quarterly? Solution: Given: F = 25, 000 Find: P t = 2 1/2 years j = i 4 /m = 0.10/4 = 0.025 i 4 = 0.10 n = tm = (2 1/2)(4) = 10 P = F/(1 + j) n

114. Example6: What is the present value of P25, 000 due in 2 years and 6 months if money is worth 10% compounded quarterly? Solution: Given: F = 25, 000 Find: P t = 2 1/2 years j = i 4 /m = 0.10/4 = 0.025 i 4 = 0.10 n = tm = (2 1/2)(4) = 10 P = F/(1 + j) n P = 25, 000/(1 + 0.025) 10

115. Example6: What is the present value of P25, 000 due in 2 years and 6 months if money is worth 10% compounded quarterly? Solution: Given: F = 25, 000 Find: P t = 2 1/2 years j = i 4 /m = 0.10/4 = 0.025 i 4 = 0.10 n = tm = (2 1/2)(4) = 10 m = 4 P = F/(1 + j) n P = 25, 000/(1 + 0.025) 10 P = 19, 529.96

116. Seatwork1: Complete the table by computing the interest rate per period and total number of conversion periods. Nominal Rate (i m ) Interest Compounded Frequency of conversion (m) Interest Rate per Conversion Period 12% Semi-annualy (1) (2) 16% Quarterly (3) (4) 9% Monthly (5) (6) (7) Daily (8) 0.03%

117. Seatwork1: Complete the table by computing the interest rate per period and total number of conversion periods. Nominal Rate (i m ) Interest Compounded Frequency of conversion (m) Interest Rate per Conversion Period 12% Semi-annualy Ans: 2 (2) 16% Quarterly (3) (4) 9% Monthly (5) (6) (7) Daily (8) 0.03%

118. Seatwork1: Complete the table by computing the interest rate per period and total number of conversion periods. Nominal Rate (i m ) Interest Compounded Frequency of conversion (m) Interest Rate per Conversion Period 12% Semi-annualy Ans: 2 Ans: 6% 16% Quarterly (3) (4) 9% Monthly (5) (6) (7) Daily (8) 0.03%

119. Seatwork1: Complete the table by computing the interest rate per period and total number of conversion periods. Nominal Rate (i m ) Interest Compounded Frequency of conversion (m) Interest Rate per Conversion Period 12% Semi-annualy Ans: 2 Ans: 6% 16% Quarterly Ans: 4 (4) 9% Monthly (5) (6) (7) Daily (8) 0.03%

120. Seatwork1: Complete the table by computing the interest rate per period and total number of conversion periods. Nominal Rate (i m ) Interest Compounded Frequency of conversion (m) Interest Rate per Conversion Period 12% Semi-annualy Ans: 2 Ans: 6% 16% Quarterly Ans: 4 Ans: 4% 9% Monthly (5) (6) (7) Daily (8) 0.03%

121. Seatwork1: Complete the table by computing the interest rate per period and total number of conversion periods. Nominal Rate (i m ) Interest Compounded Frequency of conversion (m) Interest Rate per Conversion Period 12% Semi-annualy Ans: 2 Ans: 6% 16% Quarterly Ans: 4 Ans: 4% 9% Monthly Ans: 12 (6) (7) Daily (8) 0.03%

122. Seatwork1: Complete the table by computing the interest rate per period and total number of conversion periods. Nominal Rate (i m ) Interest Compounded Frequency of conversion (m) Interest Rate per Conversion Period 12% Semi-annualy Ans: 2 Ans: 6% 16% Quarterly Ans: 4 Ans: 4% 9% Monthly Ans: 12 Ans: 0.75% (7) Daily (8) 0.03%

123. Seatwork1: Complete the table by computing the interest rate per period and total number of conversion periods. Nominal Rate (i m ) Interest Compounded Frequency of conversion (m) Interest Rate per Conversion Period 12% Semi-annualy Ans: 2 Ans: 6% 16% Quarterly Ans: 4 Ans: 4% 9% Monthly Ans: 12 Ans: 0.75% Ans: 10.95% Daily (8) 0.03%

124. Seatwork1: Complete the table by computing the interest rate per period and total number of conversion periods. Nominal Rate (i m ) Interest Compounded Frequency of conversion (m) Interest Rate per Conversion Period 12% Semi-annualy Ans: 2 Ans: 6% 16% Quarterly Ans: 4 Ans: 4% 9% Monthly Ans: 12 Ans: 0.75% Ans: 10.95% Daily Ans: 365 0.03%

125. Seatwork2: Complete the table by computing for compound amounts, compound interests and present values. Principal Nominal Rate Interest Compounded Frequency of Conversion (m) Interest rate per period (j) Time in Years Total no. of conversions (n) Compound Interest ( Ic ) Compound Amount (F) 10, 000 8% Semi- annually (1) (2) 15 (3) (4) (5) 3, 000 5% quarterly (6) (7) 6 years and 3 months (8) (9) (10) (11) 12% monthly (12) (13) 10 (14) (15) 50, 000

126. Seatwork2: Complete the table by computing for compound amounts, compound interests and present values. Principal Nominal Rate Interest Compounded Frequency of Conversion Interest rate per period Time in Years Total no. of conversions Compound Interest Compound Amount 10, 000 8% Semi- annually Ans: 2 (2) 15 (3) (4) (5) 3, 000 5% quarterly (6) (7) 6 years and 3 months (8) (9) (10) (11) 12% monthly (12) (13) 10 (14) (15) 50, 000

127. Seatwork2: Complete the table by computing for compound amounts, compound interests and present values. Principal Nominal Rate Interest Compounded Frequency of Conversion Interest rate per period Time in Years Total no. of conversions Compound Interest Compound Amount 10, 000 8% Semi- annually Ans: 2 Ans: 4% 15 (3) (4) (5) 3, 000 5% quarterly (6) (7) 6 years and 3 months (8) (9) (10) (11) 12% monthly (12) (13) 10 (14) (15) 50, 000

128. Seatwork2: Complete the table by computing for compound amounts, compound interests and present values. Principal Nominal Rate Interest Compounded Frequency of Conversion Interest rate per period Time in Years Total no. of conversions Compound Interest Compound Amount 10, 000 8% Semi- annually Ans: 2 Ans: 4% 15 Ans: 30 (4) (5) 3, 000 5% quarterly (6) (7) 6 years and 3 months (8) (9) (10) (11) 12% monthly (12) (13) 10 (14) (15) 50, 000

129. Seatwork2: Complete the table by computing for compound amounts, compound interests and present values. Principal Nominal Rate Interest Compounded Frequency of Conversion Interest rate per period Time in Years Total no. of conversions Compound Interest Compound Amount 10, 000 8% Semi- annually Ans: 2 Ans: 4% 15 Ans: 30 Ans: 22, 433.98 (5) 3, 000 5% quarterly Ans: 4 (7) 6 years and 3 months (8) (9) (10) (11) 12% monthly (12) (13) 10 (14) (15) 50, 000

130. Seatwork2: Complete the table by computing for compound amounts, compound interests and present values. Principal Nominal Rate Interest Compounded Frequency of Conversion Interest rate per period Time in Years Total no. of conversions Compound Interest Compound Amount 10, 000 8% Semi- annually Ans: 2 Ans: 4% 15 Ans: 30 Ans: 22, 433.98 Ans: 32, 433.98 3, 000 5% quarterly (6) (7) 6 years and 3 months (8) (9) (10) (11) 12% monthly (12) (13) 10 (14) (15) 50, 000

131. Seatwork2: Complete the table by computing for compound amounts, compound interests and present values. Principal Nominal Rate Interest Compounded Frequency of Conversion Interest rate per period Time in Years Total no. of conversions Compound Interest Compound Amount 10, 000 8% Semi- annually Ans: 2 Ans: 4% 15 Ans: 30 Ans: 22, 433.98 Ans: 32, 433.98 3, 000 5% quarterly Ans: 4 (7) 6 years and 3 months (8) (9) (10) (11) 12% monthly (12) (13) 10 (14) (15) 50, 000

132. Seatwork2: Complete the table by computing for compound amounts, compound interests and present values. Principal Nominal Rate Interest Compounded Frequency of Conversion Interest rate per period Time in Years Total no. of conversions Compound Interest Compound Amount 10, 000 8% Semi- annually Ans: 2 Ans: 4% 15 Ans: 30 Ans: 22, 433.98 Ans: 32, 433.98 3, 000 5% quarterly Ans: 4 Ans: 1.25% 6 years and 3 months (8) (9) (10) (11) 12% monthly (12) (13) 10 (14) (15) 50, 000

133. Seatwork2: Complete the table by computing for compound amounts, compound interests and present values. Principal Nominal Rate Interest Compounded Frequency of Conversion Interest rate per period Time in Years Total no. of conversions Compound Interest Compound Amount 10, 000 8% Semi- annually Ans: 2 Ans: 4% 15 Ans: 30 Ans: 22, 433.98 Ans: 32, 433.98 3, 000 5% quarterly Ans: 4 Ans: 1.25% 6 years and 3 months Ans: 25 (9) (10) (11) 12% monthly (12) (13) 10 (14) (15) 50, 000

134. Seatwork2: Complete the table by computing for compound amounts, compound interests and present values. Principal Nominal Rate Interest Compounded Frequency of Conversion Interest rate per period Time in Years Total no. of conversions Compound Interest Compound Amount 10, 000 8% Semi- annually Ans: 2 Ans: 4% 15 Ans: 30 Ans: 22, 433.98 Ans: 32, 433.98 3, 000 5% quarterly Ans: 4 Ans: 1.25% 6 years and 3 months Ans: 25 Ans: 1, 092.58 (10) (11) 12% monthly (12) (13) 10 (14) (15) 50, 000

135. Seatwork2: Complete the table by computing for compound amounts, compound interests and present values. Principal Nominal Rate Interest Compounded Frequency of Conversion Interest rate per period Time in Years Total no. of conversions Compound Interest Compound Amount 10, 000 8% Semi- annually Ans: 2 Ans: 4% 15 Ans: 30 Ans: 22, 433.98 Ans: 32, 433.98 3, 000 5% quarterly Ans: 4 Ans: 1.25% 6 years and 3 months Ans: 25 Ans: 1, 092.58 Ans: 4, 092.58 (11) 12% monthly (12) (13) 10 (14) (15) 50, 000

136. Seatwork2: Complete the table by computing for compound amounts, compound interests and present values. Principal Nominal Rate Interest Compounded Frequency of Conversion Interest rate per period Time in Years Total no. of conversions Compound Interest Compound Amount 10, 000 8% Semi- annually Ans: 2 Ans: 4% 15 Ans: 30 Ans: 22, 433.98 Ans: 32, 433.98 3, 000 5% quarterly Ans: 4 Ans: 1.25% 6 years and 3 months Ans: 25 Ans: 1, 092.58 Ans: 4, 092.58 Ans: 15, 149.74 12% monthly (12) (13) 10 (14) (15) 50, 000

137. Seatwork2: Complete the table by computing for compound amounts, compound interests and present values. Principal Nominal Rate Interest Compounded Frequency of Conversion Interest rate per period Time in Years Total no. of conversions Compound Interest Compound Amount 10, 000 8% Semi- annually Ans: 2 Ans: 4% 15 Ans: 30 Ans: 22, 433.98 Ans: 32, 433.98 3, 000 5% quarterly Ans: 4 Ans: 1.25% 6 years and 3 months Ans: 25 Ans: 1, 092.58 Ans: 4, 092.58 Ans: 15, 149.74 12% monthly Ans: 12 (13) 10 (14) (15) 50, 000

138. Seatwork2: Complete the table by computing for compound amounts, compound interests and present values. Principal Nominal Rate Interest Compounded Frequency of Conversion Interest rate per period Time in Years Total no. of conversions Compound Interest Compound Amount 10, 000 8% Semi- annually Ans: 2 Ans: 4% 15 Ans: 30 Ans: 22, 433.98 Ans: 32, 433.98 3, 000 5% quarterly Ans: 4 Ans: 1.25% 6 years and 3 months Ans: 25 Ans: 1, 092.58 Ans: 4, 092.58 Ans: 15, 149.74 12% monthly Ans: 12 Ans: 1% 10 (14) (15) 50, 000

139. Seatwork2: Complete the table by computing for compound amounts, compound interests and present values. Principal Nominal Rate Interest Compounded Frequency of Conversion Interest rate per period Time in Years Total no. of conversions Compound Interest Compound Amount 10, 000 8% Semi- annually Ans: 2 Ans: 4% 15 Ans: 30 Ans: 22, 433.98 Ans: 32, 433.98 3, 000 5% quarterly Ans: 4 Ans: 1.25% 6 years and 3 months Ans: 25 Ans: 1, 092.58 Ans: 4, 092.58 Ans: 15, 149.74 12% monthly Ans: 12 Ans: 1% 10 Ans: 120 (15) 50, 000

140. Seatwork2: Complete the table by computing for compound amounts, compound interests and present values. Principal Nominal Rate Interest Compounded Frequency of Conversion Interest rate per period Time in Years Total no. of conversions Compound Interest Compound Amount 10, 000 8% Semi- annually Ans: 2 Ans: 4% 15 Ans: 30 Ans: 22, 433.98 Ans: 32, 433.98 3, 000 5% quarterly Ans: 4 Ans: 1.25% 6 years and 3 months Ans: 25 Ans: 1, 092.58 Ans: 4, 092.58 Ans: 15, 149.74 12% monthly Ans: 12 Ans: 1% 10 Ans: 120 Ans: 34, 850.26 50, 000

141. Seatwork2: Complete the table by computing for compound amounts, compound interests and present values. Principal Nominal Rate Interest Compounded Frequency of Conversion Interest rate per period Time in Years Total no. of conversions Compound Interest Compound Amount 10, 000 8% Semi- annually Ans: 2 Ans: 4% 15 Ans: 30 Ans: 22, 433.98 Ans: 32, 433.98 3, 000 5% quarterly Ans: 4 Ans: 1.25% 6 years and 3 months Ans: 25 Ans: 1, 092.58 Ans: 4, 092.58 Ans: 15, 149.74 12% monthly Ans: 12 Ans: 1% 10 Ans: 1% Ans: 34, 850.26 50, 000

142. 3rd Performance Task (2nd Quarter) in GenMath September 06, 2019

143. 1. Fill in the blanks with the correct answers. a. When money is compounded monthly, the frequency of conversion is .

144. 1. Fill in the blanks with the correct answers. b. When the annual interest rate is 16% compounded quarterly, the interest rate in a conversion period is .

145. 1. Fill in the blanks with the correct answers. c. If the interest rate per conversion period is 1% and money is compounded monthly, the nominal rate is .

146. 1. Fill in the blanks with the correct answers. d. When the term is 3 years and 6 months and money is compounded semi-annually, the total number of conversion periods is .

147. 1. Fill in the blanks with the correct answers. e. When the total number of conversion period is 12 and the term is 6 years, then money is compounded .

148. 2. How much should Kaye set aside and invest in a fund earning 2% compounded quarterly if she needs P75, 000 in 15 months?

149. 3. Find the compound amount due in 8 years if P200, 000 is invested at 12% compounded monthly.

150. 4. What present value, compounded quarterly at 6%, will amount to P59, 780.91 in 3 years?

151. 5. Alex borrowed P15, 000 payable with interest that is compounded semi-annually at 9%. How much must he pay after 3 years?