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11-2 Terms to be familiar with…. Interest Money charged for the use of money.

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Presentation on theme: "11-2 Terms to be familiar with…. Interest Money charged for the use of money."— Presentation transcript:

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

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

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

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 = $

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 = $

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( /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 = P(1 +.07/52) (52∙30)

48 = P (1 +.07/52) (52∙30)

49 $12, = 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/ = r/4

56 4((2) 1/40 – 1) = (r/4)∙4

57 4((2) 1/40 – 1) = r

58 r = = 6.99%


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