1. 11-2 Terms to be familiar with…

2. Interest

3. Money charged for the use of money

4. Principal

5. The amount of money initially invested

6. Account Balance

7. Amount of money in the account at a given time

8. Interest Rate

9. Percent charged annually a.k.a. APR

10. Compound Interest

11. Interest charged on interest

12. Number of times interest is usually compounded AnnuallySemi- annually QuarterlyMonthlyWeeklyDailyContinu- ously

13. Number of times interest is usually compounded AnnuallySemi- annually QuarterlyMonthlyWeeklyDailyContinu- ously 1

14. Number of times interest is usually compounded AnnuallySemi- annually QuarterlyMonthlyWeeklyDailyContinu- ously 12

15. Number of times interest is usually compounded AnnuallySemi- annually QuarterlyMonthlyWeeklyDailyContinu- ously 124

16. Number of times interest is usually compounded AnnuallySemi- annually QuarterlyMonthlyWeeklyDailyContinu- ously 12412

17. Number of times interest is usually compounded AnnuallySemi- annually QuarterlyMonthlyWeeklyDailyContinu- ously 1241252

18. Number of times interest is usually compounded AnnuallySemi- annually QuarterlyMonthlyWeeklyDailyContinu- ously 1241252365

19. Number of times interest is usually compounded AnnuallySemi- annually QuarterlyMonthlyWeeklyDailyContinu- ously 1241252365 ∞

20. Compounded Interest Formula A = P = n = t = r =

21. Compounded Interest Formula A = Account Balance P = n = t = r =

22. Compounded Interest Formula A = Account Balance P = Principal n = t = r =

23. Compounded Interest Formula A = Account Balance P = Principal n = number of times in year interest is compounded t = r =

24. Compounded Interest Formula A = Account Balance P = Principal n = number of times in year interest is compounded t = time in years r =

25. Compounded Interest Formula A = Account Balance P = Principal n = number of times in year interest is compounded t = time in years r = annual percentage rate (as a decimal)

26. Compounded Interest Formula A = P(1 + r/n ) (nt)

27. Example1 $1200 is invested at an APR of 9%. Find the balance in five years if the interest is compounded a)quarterlyb) monthly

28. $1200 is invested at an APR of 9%. Find the balance in five years if the interest is compounded a)quarterly A = P = r = n = t =

29. $1200 is invested at an APR of 9%. Find the balance in five years if the interest is compounded a)quarterly A = ??? P = 1200 r =.09 n = 4 t = 5

30. A = 1200(1 +.09/4) (4∙5)

31. A = $1872.61

32. $1200 is invested at an APR of 9%. Find the balance in five years if the interest is compounded b)monthly A = P = r = n = t =

33. $1200 is invested at an APR of 9%. Find the balance in five years if the interest is compounded b)monthly A = ???? P = 1200 r =.09 n = 12 t = 5

34. A = 1200(1 +.09/12) (12∙5)

35. A = $1878.81

36. Example2 I would like to create a trust fund for my daughter that she can have in 18 years for college. I have $10,000 to invest. Which account would have a greater balance, one earning an APR of 6% compounded semiannually or one that earns an APR of 5.5% compounded daily?

37. 6% compounded semiannually A = P = n = t = r =

38. 6% compounded semiannually A = ??? P = 10,000 n = 2 t = 18 r =.06

39. A = 10000(1 +.06/2) (2∙18)

40. A = $28,982.78

41. 5.5% compounded daily A = P = n = t = r =

42. 5.5% compounded daily A = ??? P = 10,000 n = 365 t = 18 r =.055

43. A = 10000(1 +.055/365) (365∙18)

44. A = $26,910.33

45. Example 3 I would like to retire with a balance of $100,000 in an annuity. Find the amount of money to invest initially (principal) if I want to retire in 30 years and I can invest at an APR of 7% compounded weekly.

46. 7% compounded weekly A = 100,000 P = ??? n = 52 t = 30 r =.07

47. 100000 = P(1 +.07/52) (52∙30)

48. 100000 = P (1 +.07/52) (52∙30)

49. $12,262.95 = P

50. Example 4 At what interest rate do I need to invest $10,000 to double its value in 10 years if interest is compounded quarterly?

51. A = 20,000 P = 10,000 n = 4 t = 10 r = ????

52. 20000 = 10,000(1 + r/4) (4∙10)

53. 2 = (1 + r/4) (4∙10)

54. (2) 1/40 = ((1 + r/4) (40) ) 1/40

55. (2) 1/40 - 1 = r/4

56. 4((2) 1/40 – 1) = (r/4)∙4

57. 4((2) 1/40 – 1) = r

58. r = 0.0699 = 6.99%