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Aim # 14: How Do We Determine the Income from our Investments? CD Rate is 1.2%

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Presentation on theme: "Aim # 14: How Do We Determine the Income from our Investments? CD Rate is 1.2%"— Presentation transcript:

1 Aim # 14: How Do We Determine the Income from our Investments? CD Rate is 1.2%

2 Do Now Julie Fee is a real estate broker who earns 8.5% commission on each house she sells. If she earned $35,700 on a house she sold, what was the selling price of the house? Answer: $420,000

3 Minilesson: Formula for Interest Earned on a Deposit: This is I = prt Where I = simple interest earned p = your original deposit r = interest rate as a decimal t = period of time (in our case, 1 yr)

4 Minilesson (cont’d): For any question, Either follow the wording of the verbal problem, OR Set-up a table (to help organize your thoughts) YOU decide

5 Minilesson (cont’d): Either follow the wording of the verbal problem, Interest Rate for Investment X Amount Invested = Amount Earned

6 Minilesson (cont’d): Either follow the wording of the verbal problem, Amt Earned Investment # 1 + = Total Amount Earned from BOTH Investments Amt Earned Investment # 2

7 Minilesson (cont’d): Set-up a table (to help organize your thoughts) Interest Rate X Amt Earned = Amt Invested

8 Minilesson (cont’d): Set-up a table (to help organize your thoughts) Interest Rate X Amt Earned = Amt Invested Investment # 1 Investment # 2

9 Guided Practice Handout, qq. 318 – 319, qq. 1, 2, 7

10 Independent Practice Handout Aim # 14, qq. 5, 6, 8, 9, 10

11 Independent Practice (cont’d) Question 5 Let m = amt invested at 3.5 % 9000 — m = amt invested at 8 % Interest Rate X Amt Earned = Amt Invested Investment # 1 Investment # m 0.035m —m0.08(9000 —m) Note: First investment income exceeds 2 nd by $ 16.

12 Independent Practice (cont’d) Question 5 Let m = amt invested at 3.5 % 9000 — m = amt invested at 8 % Interest Rate X Amt Earned = Amt Invested Investment # 1 Investment # m 0.035m —m0.08(9000 —m) Note: 1 st minus 2 nd equals 16

13 Independent Practice (cont’d) Question 5 Let m = amt invested at 3.5 % 9000 — m = amt invested at 8 % Interest Rate X Amt Earned = Amt Invested Investment # 1 Investment # m 0.035m —m0.08(9000 —m)

14 Independent Practice (cont’d) Question 5 Let m = amt invested at 3.5 % 9000 — m = amt invested at 8 % Interest Rate X Amt Earned = Amt Invested Investment # 1 Investment # m 0.035m —m0.08(9000 —m) Multiply through by 1000.

15 Independent Practice (cont’d) Question 5 Let m = amt invested at 3.5 % 9000 — m = amt invested at 8 % Interest Rate X Amt Earned = Amt Invested Investment # 1 Investment # m 0.035m —m0.08(9000 —m) Distribute 80 across parentheses.

16 Independent Practice (cont’d) Question 5 Let m = amt invested at 3.5 % 9000 — m = amt invested at 8 % Interest Rate X Amt Earned = Amt Invested Investment # 1 Investment # m 0.035m —m0.08(9000 —m) NOTICE: Minus sign changed to plus.

17 Independent Practice (cont’d) Question 5 Let m = amt invested at 3.5 % 9000 — m = amt invested at 8% Interest Rate X Amt Earned = Amt Invested Investment # 1 Investment # m 0.035m —m0.08(9000 —m) Combine like terms.

18 Independent Practice (cont’d) Question 5 Let m = amt invested at 3.5 % 9000 — m = amt invested at 8 % Interest Rate X Amt Earned = Amt Invested Investment # 1 Investment # m 0.035m —m0.08(9000 —m)

19 Independent Practice (cont’d) Question 5 Let m = amt invested at 3.5 % 9000 — m = amt invested at 8 % Interest Rate X Amt Earned = Amt Invested Investment # 1 Investment # m 0.035m —m0.08(9000 —m) Divide both sides by coefficient 115.

20 Independent Practice (cont’d) Question 5 Let m = amt invested at 3.5 % 9000 — m = amt invested at 8 % ANSWER $6,400 invested at 3.5% $2,600 invested at 8%

21 Independent Practice (cont’d) Question 5 Let m = amt invested at 3.5 % 9000 — m = amt invested at 8 % CHECK $6,400 invested at 3.5% $2,600 invested at 8% 0.035(6400) = (2600) = − 208 = 16 It works!!

22 Independent Practice (cont’d) Question 6 Let m = amt invested at 6 % 2m = amt invested at 4.5 % Interest Rate X Amt Earned = Amt Invested Investment # 1 Investment # — (m+2m) = amt invested at 2 % The remaining is $9000 minus the sum of the first two investments

23 Independent Practice (cont’d) Question 6 Let m = amt invested at 6 % 2m = amt invested at 4.5 % Interest Rate X Amt Earned = Amt Invested Investment # 1 Investment # — 3m = amt invested at 2 % The remaining is $9000 minus the sum of the first two investments

24 Independent Practice (cont’d) Question 6 Let m = amt invested at 6 % 2m = amt invested at 4.5 % Interest Rate X Amt Earned = Amt Invested Investment # 1 Investment # m 0.06m —3m 0.02(9000 —3m) Note: The money earned on the three investments is $ — 3m = amt invested at 2 % The remaining is $9000 minus the sum of the first two investments Investment # m 0.045(2m)

25 Independent Practice (cont’d) Question 6 Let m = amt invested at 6 % 2m = amt invested at 4.5 % Interest Rate X Amt Earned = Amt Invested Investment # 1 Investment # m 0.06m —3m 0.02(9000 —3m) 9000 — 3m = amt invested at 2 % Investment # m 0.045(2m) Note: 1 st plus 2 nd plus 3 rd equals 360

26 Independent Practice (cont’d) Question 6 Let m = amt invested at 6 % 2m = amt invested at 4.5 % Interest Rate X Amt Earned = Amt Invested Investment # 1 Investment # m 0.06m —3m 0.02(9000 —3m) 9000 — 3m = amt invested at 2 % Investment # m 0.045(2m)

27 Independent Practice (cont’d) Question 6 Let m = amt invested at 6 % 2m = amt invested at 4.5 % Interest Rate X Amt Earned = Amt Invested Investment # 1 Investment # m 0.06m —3m 0.02(9000 —3m) 9000 — 3m = amt invested at 2 % Investment # m 0.045(2m)

28 Independent Practice (cont’d) Question 6 Let m = amt invested at 6 % 2m = amt invested at 4.5 % Interest Rate X Amt Earned = Amt Invested Investment # 1 Investment # m 0.06m —3m 0.02(9000 —3m) 9000 — 3m = amt invested at 2 % Investment # m 0.045(2m)

29 Independent Practice (cont’d) Question 6 Let m = amt invested at 6 % 2m = amt invested at 4.5 % Interest Rate X Amt Earned = Amt Invested Investment # 1 Investment # m 0.06m —3m 0.02(9000 —3m) 9000 — 3m = amt invested at 2 % Investment # m 0.045(2m) Combine like terms.

30 Independent Practice (cont’d) Question 6 Let m = amt invested at 6 % 2m = amt invested at 4.5 % Interest Rate X Amt Earned = Amt Invested Investment # 1 Investment # m 0.06m —3m 0.02(9000 —3m) 9000 — 3m = amt invested at 2 % Investment # m 0.045(2m) Combine like terms. The 60m cancels out.

31 Independent Practice (cont’d) Question 6 Let m = amt invested at 6 % 2m = amt invested at 4.5 % Interest Rate X Amt Earned = Amt Invested Investment # 1 Investment # m 0.06m —3m 0.02(9000 —3m) 9000 — 3m = amt invested at 2 % Investment # m 0.045(2m) Subtract from both sides.

32 Independent Practice (cont’d) Question 6 Let m = amt invested at 6 % 2m = amt invested at 4.5 % Interest Rate X Amt Earned = Amt Invested Investment # 1 Investment # m 0.06m —3m 0.02(9000 —3m) 9000 — 3m = amt invested at 2 % Investment # m 0.045(2m) Divide both sides.

33 Independent Practice (cont’d) Question 6 ANSWER $2,000 invested at 6% $4,000 invested at 4.5% $3,000 invested at 2% Let m = amt invested at 6 % 2m = amt invested at 4.5 % 9000 — 3m = amt invested at 2 %

34 Independent Practice (cont’d) Question 6 CHECK! 0.06(2,000) (4000) (3000) Let m = amt invested at 6 % 2m = amt invested at 4.5 % 9000 — 3m = amt invested at 2 % 360

35 Independent Practice (cont’d) Question 8 Let m = amt invested at 3 % 8000 — m = amt invested at 5 % Interest Rate X Amt Earned = Amt Invested Investment # 1 Investment # m 0.03m —m0.05(8000 —m) Note: Man LOST money from 2 nd Investment.

36 Independent Practice (cont’d) Question 8 Let m = amt invested at 3 % 8000 — m = amt invested at 5 % Interest Rate X Amt Earned = Amt Invested Investment # 1 Investment # m 0.03m —m0.05(8000 —m) Note: GAIN of 1 st + LOSS 2 nd = Net Income.

37 Independent Practice (cont’d) Question 8 Let m = amt invested at 3 % 8000 — m = amt invested at 5 % Interest Rate X Amt Earned = Amt Invested Investment # 1 Investment # m 0.03m —m—0.05(8000 —m) Note: GAIN of 1 st + LOSS 2 nd = Net Income.

38 Independent Practice (cont’d) Question 8 Let m = amt invested at 3 % 8000 — m = amt invested at 5 % Interest Rate X Amt Earned = Amt Invested Investment # 1 Investment # m 0.03m —m—0.05(8000 —m)

39 Independent Practice (cont’d) Question 8 Let m = amt invested at 3 % 8000 — m = amt invested at 5 % Interest Rate X Amt Earned = Amt Invested Investment # 1 Investment # m 0.03m —m—0.05(8000 —m)

40 Independent Practice (cont’d) Question 8 Let m = amt invested at 3 % 8000 — m = amt invested at 5 % Interest Rate X Amt Earned = Amt Invested Investment # 1 Investment # m 0.03m —m—0.05(8000 —m) Distributive Property changes signs.

41 Independent Practice (cont’d) Question 8 Let m = amt invested at 3 % 8000 — m = amt invested at 5 % Interest Rate X Amt Earned = Amt Invested Investment # 1 Investment # m 0.03m —m—0.05(8000 —m)

42 Independent Practice (cont’d) Question 8 Let m = amt invested at 3 % 8000 — m = amt invested at 5 % Interest Rate X Amt Earned = Amt Invested Investment # 1 Investment # m 0.03m —m—0.05(8000 —m)

43 Independent Practice (cont’d) Question 8 Let m = amt invested at 3 % 8000 — m = amt invested at 5 % Interest Rate X Amt Earned = Amt Invested Investment # 1 Investment # m 0.03m —m—0.05(8000 —m)

44 Independent Practice (cont’d) Question 8 Let m = amt invested at 3 % 8000 — m = amt invested at 5 % ANSWER $6,000 invested at 3% $2,000 invested at 5%

45 Independent Practice (cont’d) Question 8 Let m = amt invested at 3 % 8000 — m = amt invested at 5 % CHECK 0.03(6,000) = $180 MINUS 0.05(2,000) = $100 Net Gain = $ 80

46 Independent Practice (cont’d) Question 9 Let m = amt invested at 5 % 9600 — m = amt invested at 3.5 % Interest Rate X Amt Earned = Amt Invested Investment # 1 Investment # m 0.05m —m 0.035(9600 —m) Note: 1 st Investment yields twice 2 nd Investment.

47 Independent Practice (cont’d) Question 9 Let m = amt invested at 5 % 9600 — m = amt invested at 3.5 % Interest Rate X Amt Earned = Amt Invested Investment # 1 Investment # m 0.05m —m 0.035(9600 —m) Twice the amt earned from 2 nd investment

48 Independent Practice (cont’d) Question 9 Let m = amt invested at 5 % 9600 — m = amt invested at 3.5 % Interest Rate X Amt Earned = Amt Invested Investment # 1 Investment # m 0.05m —m 0.035(9600 —m) Doubled Doubled 0.35

49 Independent Practice (cont’d) Question 9 Let m = amt invested at 5 % 9600 — m = amt invested at 3.5 % Interest Rate X Amt Earned = Amt Invested Investment # 1 Investment # m 0.05m —m 0.035(9600 —m) Multiply through by 100

50 Independent Practice (cont’d) Question 9 Let m = amt invested at 5 % 9600 — m = amt invested at 3.5 % Interest Rate X Amt Earned = Amt Invested Investment # 1 Investment # m 0.05m —m 0.035(9600 —m) Distribute the 7.

51 Independent Practice (cont’d) Question 9 Let m = amt invested at 5 % 9600 — m = amt invested at 3.5 % Interest Rate X Amt Earned = Amt Invested Investment # 1 Investment # m 0.05m —m 0.035(9600 —m)

52 Independent Practice (cont’d) Question 9 Let m = amt invested at 5 % 9600 — m = amt invested at 3.5 % Interest Rate X Amt Earned = Amt Invested Investment # 1 Investment # m 0.05m —m 0.035(9600 —m)

53 Independent Practice (cont’d) Question 9 Let m = amt invested at 5 % 9600 — m = amt invested at 3.5 % Interest Rate X Amt Earned = Amt Invested Investment # 1 Investment # m 0.05m —m 0.035(9600 —m)

54 Independent Practice (cont’d) Question 9 Let m = amt invested at 5 % 9600 — m = amt invested at 3.5 % ANSWER $5,600 invested at 5% $4,000 invested at 3.5%

55 Independent Practice (cont’d) Question 9 Let m = amt invested at 5 % 9600 — m = amt invested at 3.5 % CHECK 0.05(5600) = (4000) = 140 It works! $280 is twice $140. Yay!

56 Independent Practice (cont’d) Question 10 Let E = amt in entire estate Plan: ¼ of the estate is invested at 5%. This means there is now ¾ remaining. 1/3 of ¾ is 1/4, which is then invested at 2%. ¼ plus ¼ is 1/2, so the rest of the estate is ½ (which is invested at 6%.

57 Independent Practice (cont’d) Question 10 More Explanation ¼ of the estate is invested at 5%. This means there is now ¾ remaining.

58 Independent Practice (cont’d) Question 10 Plan: 1/3 of ¾ is 1/4, which is then invested at 2%. ¼ plus ¼ is 1/2, so the rest of the estate is ½ (which is invested at 6%.

59 Independent Practice (cont’d) Question 10 Plan: 1/3 of ¾ is 1/4, which is then invested at 2%. ¼ plus ¼ is 1/2, so the rest of the estate is ½ (which is invested at 6%.

60 Independent Practice (cont’d) Question 10 Plan: 1/3 of ¾ is 1/4, which is then invested at 2%. ¼ plus ¼ is 1/2, so the rest of the estate is ½ (which is invested at 6%.

61 Independent Practice (cont’d) Question 10 Plan:

62 Independent Practice (cont’d) Question 10 Therefore:

63 Independent Practice (cont’d) Question 10 Therefore: Fractions were converted into decimals.

64 Independent Practice (cont’d) Question 10 Therefore: Multiplied through by 100.

65 Independent Practice (cont’d) Question 10 Therefore: Simplified products.

66 Independent Practice (cont’d) Question 10 Therefore: Combined like terms.

67 Independent Practice (cont’d) Question 10 Therefore: Divided both sides by 4.75

68 Independent Practice (cont’d) Question 10 ANSWER The original estate was $16,000.

69 Independent Practice (cont’d) Question 10 CHECK The estate was $16, /4 = /2 = 8000 TOTAL = Works here, too!

70 Our Textbook, p. 319, qq. 12 –16, EVEN only


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